Data-Based Service Networks - Technionie.technion.ac.il/serveng/References/0_SAMSI_Workshop.pdf · Data-Based Service Networks: A Research Framework for Asymptotic Inference, Analysis

Data-Based Service Networks:A Research Framework for

Asymptotic Inference, Analysis & Controlof Service Systems

Avi Mandelbaum

Technion, Haifa, Israel

http://ie.technion.ac.il/serveng

SAMSI Workshop, August 2012

I Overheads available at SAMSI and my Technion websites

1

Research PartnersI Students:

Aldor∗, Baron∗, Carmeli∗, Cohen∗, Feldman∗, Garnett∗, Gurvich∗,Khudiakov∗, Maman∗, Marmor∗, Reich∗, Rosenshmidt∗, Shaikhet∗,Senderovic, Tseytlin∗, Yom-Tov∗, Yuviler, Zaied∗, Zeltyn∗,Zychlinski∗, Zohar∗, Zviran∗, . . .

I Theory:Armony, Atar, Cohen, Gurvich, Huang, Jelenkovic, Kaspi, Massey,Momcilovic, Reiman, Shimkin, Stolyar, Trofimov, Wasserkrug,Whitt, Zeltyn, . . .

I Empirical/Statistical Analysis:Brown, Gans, Shen, Zhao; Zeltyn; Ritov, Goldberg; Gurvich, Huang,Liberman; Armony, Marmor, Tseytlin, Yom-Tov; Nardi, Plonsky;Gorfine, Ghebali; Pang, . . .

I Industry:Mizrahi Bank (A. Cohen, U. Yonissi), Rambam Hospital (R. Beyar, S.Israelit, S. Tzafrir), IBM Research (OCR Project), Hapoalim Bank (G.Maklef, T. Shlasky), Pelephone Cellular, . . .

I Technion SEE Center / Laboratory:Feigin; Trofimov, Nadjharov, Gavako, Kutsy; Liberman, Koren,Plonsky, Senderovic; Research Assistants, . . .

2

ContentsI Service Networks: Call Centers, Hospitals, Websites, · · ·I Redefine the paradigm of modeling/asymptotics via DataI ServNets: QNets, SimNets; FNets, DNets

I Ultimate Goal: Data-based creation and validationof ServNets, automatically in real-time

I Why be Optimistic? Pilot at the Technion SEELabI Lacking but Feasible: Dynamics, Durations, ProtocolsI Simple Models at the Service of Complex Realities

I State-Space Collapse (Queues, Waiting Times)I Congestion Laws (LN, Little, ImPatience, Staffing)I Universal Approximations: Simplifying the Asymptotic LandscapeI Stabilizing Time-Varying Performance (Offered-Load)

I Successes: Palm/Erlang-R (ED Feedback = FNet),Palm/Erlang-A (CC Abandonment = DNet)

I Elsewhere : Process Mining (Petri Nets, BPM), Networks (Social,Biological, Complex, . . .), Simulation-based, . . .

I Scenic Route : Open Problems, New Directions, Uncharted Territories

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I Scenic Route : Open Problems, New Directions, Uncharted Territories

3







I Scenic Route : Open Problems, New Directions, Uncharted Territories3

On Asymptotic Research of Queueing Systems

Queueing asymptotics has grown to become a central researchtheme in Operations Research and Applied Probability, beyond justqueueing theory. Its claim to fame has been the deep insights that itprovides into the dynamics of Queueing Networks (QNets), andrightly so:

I Kingman’s invariance principle in conventional heavy-trafficI Whitt’s sample-path (functional) frameworkI Reiman’s network analysis via oblique reflectionI Bramson-Williams’ framework for state-space collapseI Laws’ resource poolingI Harrison’s paradigm for asymptotic control (Wein; van Mieghem’s Gcµ)I Dai’s fluid-based stabilityI Halfin-Whitt’s (QED regime) (√-staffing for many-server queues)I P = NP : Atar’s equivalence of Preemptive and Non-Preemptive SBR;

Stolyar, GurvichI Massey-Whitt’s research of time-varying queues

4

Applying Queueing Asymptotics

There are by now numerous insightful asymptotic queueingmodels at our disposal, and many arise from, and create, deepbeautiful theory:

Has it helped one approximate or simulate a service systemmore efficiently, estimate its parameter more accurately, teach itto our students more effectively, perhaps even manage thesystem better?

I am of the opinion that the answers to such questions havebeen too often negative, that positive answers must have theoryand applications nurture each other, which is good, and myapproach to make this good happen is by marrying theory with

data .

5

Models Approximations

QNets SimNets

Accuracy

Phenomenology

Prevalent Asymptotic Approximations

System (Data)

6

2


QNets SimNets FNet DNet Models

Accuracy

Phenomenology

X

Data–Based Prevalent Asymptotic Approximations Models

System (Data)

X X

7

3



Accuracy

Phenomenology Value

X X


System (Data)

X X

8

aviman

Highlight

4

System = Coin Tossing, Model = Binomial ; de Moivre 1738

Approx. / Models: SLLN (FNets), CLT (DNets) ; Laplace 1810

Value: Exceeds Value of originating stylized model

Normal, Brownian Motion ; Bachalier 1900

Poisson ; Poisson 1838



Accuracy

Phenomenology Value

X X


System (Data)

X X

9

Models

Q F

Value

Data–Based Framework: (Almost) All Models Born Equal

SimNets

D

Data

2

Models

Q F

Value

Data–Based (Asymptotic) Framework: Simulation Mining

SimNets

D

Data

Data-Based Real-Time

- Creation - Application

- “Implies” other ServNets - Virtual Realities - Validation: Parsimony - Theory: Reproducibility - Application: Trust

2

Models

Q F

Value

Data–Based Asymptotic Framework: Added Value

SimNets

D

Data

SubstitutionPrinciple

Congestion Laws

Inference: Patience, Predictors Performance: G/G/N, QED Control: Gc , SBR, FJ Design: - Staffing, Pooling Predictions

aviman

Rectangle

3

Models

Q F

Value

Ultimately: Automatic “Discovery, Conformance, Enhancement”

SimNets

D

Data

State-Space Collapse Multiple Scales (Regimes, UA) Snapshots Pathwise Little, ASTA, …

SubstitutionPrinciple

Congestion Laws

Service Science

Inference: Patience, Predictors Performance: G/G/N, QED Control: Gc , SBR, FJ Design: - Staffing, Pooling Predictions

aviman

Rectangle

Scope of the Service Industry

Guangzhou Railway Station, Southern China

14

Call Centers, Then Hospitals, Now Internet

Call Centers - U.S. Stat.

I $200 – $300 billion annual expendituresI 100,000 – 200,000 call centersI “Window" into the company, for better or worseI Over 3 million agents = 2% – 4% workforce

Healthcare - similar, plus unique challenges:

I Cost-figures far more staggeringI Risks much higherI ED (initial focus) = hospital-windowI Over 3 million nurses

Internet - . . .

15

Call Centers, Then Hospitals, Now Internet

Call Centers - U.S. Stat.

I $200 – $300 billion annual expendituresI 100,000 – 200,000 call centersI “Window" into the company, for better or worseI Over 3 million agents = 2% – 4% workforce

Healthcare - similar, plus unique challenges:

I Cost-figures far more staggeringI Risks much higherI ED (initial focus) = hospital-windowI Over 3 million nurses

Internet - . . .

15

Call-Center Environment: Service Network

16

Operational Focus

Operational Measures:I Surrogates for overall performance: Financial, Psychological; Clinical

I Easiest to quantify, measure, track online, react upon / Research

17

Call-Center Network: Gallery of Models

Agents(CSRs)

Back-Office

Experts)(Consultants

VIP)Training (

Arrivals(Business Frontier

of the21th Century)

Redial(Retrial)

Busy)Rare(

Goodor

Bad

Positive: Repeat BusinessNegative: New Complaint

Lost Calls

Abandonment

Agents

ServiceCompletion

Service Engineering: Multi-Disciplinary Process View

ForecastingStatistics

New Services Design (R&D)Operations,Marketing

Organization Design:Parallel (Flat)Sequential (Hierarchical)Sociology/Psychology,Operations Research

Human Resource Management

Service Process Design

To Avoid Delay

To Avoid Starvation Skill Based Routing

(SBR) DesignMarketing,Human Resources,Operations Research,MIS

Customers Interface Design

Computer-Telephony Integration - CTIMIS/CS

Marketing

Operations/BusinessProcessArchiveDatabaseDesignData Mining:MIS, Statistics, Operations Research, Marketing

InternetChatEmailFax

Lost Calls

Service Completion)75% in Banks (

( Waiting TimeReturn Time)

Logistics

Customers Segmentation -CRM

Psychology, Operations Research,Marketing

Expect 3 minWilling 8 minPerceive 15 min

PsychologicalProcessArchive

Psychology,Statistics

Training, IncentivesJob Enrichment

Marketing,Operations Research

Human Factors Engineering

VRU/IVR

Queue)Invisible (

VIP Queue

(If Required 15 min,then Waited 8 min)(If Required 6 min, then Waited 8 min)

Information DesignFunctionScientific DisciplineMulti-Disciplinary

IndexCall Center Design

(Turnover up to 200% per Year)(Sweat Shops

of the21th Century)

Tele-StressPsychology

18

Call-Center Network: Gallery of ModelsCall-Center Network: Gallery of Models

Agents(CSRs)

Back-Office

Experts)(Consultants

VIP)Training (

Arrivals(Business Frontier

of the21th Century)

Redial(Retrial)

Busy)Rare(

Goodor

Bad

Positive: Repeat BusinessNegative: New Complaint

Lost Calls

Abandonment

Agents

ServiceCompletion

Service Engineering: Multi-Disciplinary Process View

ForecastingStatistics

New Services Design (R&D)Operations,Marketing

Organization Design:Parallel (Flat)Sequential (Hierarchical)Sociology/Psychology,Operations Research

Human Resource Management


To Avoid Delay

To Avoid Starvation Skill Based Routing

(SBR) DesignMarketing,Human Resources,Operations Research,MIS

CustomersInterface Design

Computer-TelephonyIntegration - CTIMIS/CS

Marketing

Operations/BusinessProcessArchiveDatabaseDesignData Mining:MIS, Statistics, OperationsResearch,Marketing

InternetChatEmailFax

Lost Calls

Service Completion)75% in Banks (

( Waiting TimeReturn Time)

Logistics

CustomersSegmentation -CRM

Psychology, OperationsResearch,Marketing

Expect 3 minWilling 8 minPerceive 15 min



Training, IncentivesJob Enrichment

Marketing,Operations Research

Human Factors Engineering

VRU/IVR

Queue)Invisible (

VIP Queue

(If Required 15 min,then Waited 8 min)(If Required 6 min,then Waited 8 min)

Information DesignFunctionScientific DisciplineMulti-Disciplinary

IndexCall Center Design

(Turnover up to 200% per Year)(Sweat Shops

of the21th Century)

Tele-StressPsychology

1619

Skills-Based Routing in Call CentersEDA and OR, with I. Gurvich and P. Liberman

Mktg. ⇒

OR ⇒

HRM ⇒

MIS ⇒

20

ER / ED Environment: Service Network

Acute (Internal, Trauma) Walking

Multi-Trauma

21

ED-Environment in Israel

22

Queueing in a “Good" HospitalTong-ren Hospital at 6am, Beijing

23

Emergency-Department Network: Gallery of Models

ImagingLaboratory

Experts

Interns

Returns (Old or New Problem)

“Lost” Patients

LWBS

Nurses

Statistics,HumanResourceManagement(HRM)

New Services Design (R&D)Operations,Marketing,MIS

Organization Design:Parallel (Flat) = ERvs. a true ED Sociology, Psychology,Operations Research


Quality

Efficiency


Medicine

(High turnoversMedical-Staff shortage)


StretcherWalking

Service Completion(sent to other department)

( Waiting TimeActive Dashboard )

PatientsSegmentation

Medicine,Psychology, Marketing


Human FactorsEngineering(HFE)

InternalQueue

OrthopedicQueue

Arrivals

FunctionScientific DisciplineMulti-Disciplinary

Index

ED-StressPsychology

OperationsResearch, Medicine


Returns

TriageReception

Skill Based Routing (SBR) DesignOperations Research,HRM, MIS, Medicine

IncentivesGame Theory,Economics

Job EnrichmentTrainingHRM

HospitalPhysiciansSurgical

Queue

Acute,Walking

Blocked(Ambulance Diversion)

Forecasting

Information DesignMIS, HFE,Operations Research


Home

I Forecasting, Abandonment = LWBS, SBR ≈ Flow Control24

ED Patient Flow: The Physicians Viewwith J. Huang, B. Carmeli

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λ01 λ0

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· · ·

P 0(j,k)

P (k, l)

d1 d2 dJ

m01 m0

2 m0J

Triage-Patients

IP-Patients

ExitsS

Arrivals

C1(·) C2(·) C3(·) CK(·)

m1 m2 m3 mK

· · ·

1

I Goal: Adhere to Triage-Constraints, then release In-Process PatientsI Model = Multi-class Q with Feedback: Min. convex congestion costs of

IP-Patients, s.t. deadline constraints on Triage-Patients.

I Solution: In conventional heavy-traffic, asymptotic least-cost s.t. asymptoticcompliance (as in Plambeck, Harrison, Kumar, who applied admission control):

I Triage or IP? former, if some deadline is “too" closeI Triage Priorities: Chose the closest deadlineI IP-Priorities: Gcµ, modified (simply) to account for feedback

25

ED Patient Flow: The Physicians Viewwith J. Huang, B. Carmeli

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λ01 λ0

2 λ0J

· · ·

P 0(j,k)

P (k, l)

d1 d2 dJ

m01 m0

2 m0J

Triage-Patients

IP-Patients

ExitsS

Arrivals

C1(·) C2(·) C3(·) CK(·)

m1 m2 m3 mK

· · ·

1

I Goal: Adhere to Triage-Constraints, then release In-Process PatientsI Model = Multi-class Q with Feedback: Min. convex congestion costs of

IP-Patients, s.t. deadline constraints on Triage-Patients.I Solution: In conventional heavy-traffic, asymptotic least-cost s.t. asymptotic

compliance (as in Plambeck, Harrison, Kumar, who applied admission control):I Triage or IP? former, if some deadline is “too" closeI Triage Priorities: Chose the closest deadlineI IP-Priorities: Gcµ, modified (simply) to account for feedback

25

Emergency-Department Network: Flow Control

ImagingLaboratory

Experts

Interns


“Lost” Patients

LWBS

Nurses





Quality

Efficiency


Medicine



StretcherWalking







InternalQueue

OrthopedicQueue

Arrivals


Index

ED-StressPsychology



Returns

TriageReception





Queue

Acute,Walking


Forecasting



Home

I ∗Queueing-Science, w/ Armony, Marmor, Tseytlin, Yom-TovI ∗Fair ED-to-IW Routing (Patients vs. Staff), w/ Momcilovic, TseytlinI ∗Triage vs. InProcess/Release (Plambeck et al, van Mieghem) in EDs, w/

Carmeli, Huang; ShimkinI ∗Staffing Time-Varying Q’s with Re-Entrant Customers (de Vericourt &

Jennings), w/ Yom-TovI The Offered-Load in Fork-Join Nets (Adlakha & Kulkarni), w/ Kaspi, ZaeidI Synchronization Control of Fork-Join Nets, w/ Atar, Zviran

26

Prerequisite I: Data

Averages Prevalent (and could be useful / interesting).But I need data at the level of the Individual Transaction:For each service transaction (during a phone-service in a call center,or a patient’s visit in a hospital, or browsing in a website, or . . .), itsoperational history = time-stamps of events (events-log files).

27

Interesting Averages: The Human Factor, orEven “Doctors" Can Manage

Afternoon, by Case

Morning, by Hour

Operations Time In a Hospital

Operations Time Histogram: Operations Time - Morning (by Hour) vs. Afternoon (by Case): Ethical?

Even Doctors Can Manage!

0%2%4%6%8%

10%12%14%16%18%20%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14

Hours

Freq

uenc

y

AVG: 2.08 HoursSTD: 4.12 HoursSample Size: 4347

CV >> 1

0

1

2

3

4

5

6

EEG Orthopedics Surgery Blood Surgery Plastic Surgery Heart/ChestSurgery

Neuro-Surgery Eyes E.I. Surgery

Department

Hou

rs

AM

PM

20

28

Beyond Averages: The Human Factor

Histogram of Service-Time in an Israeli Call Center, 1999

January-OctoberJanuary-October

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 185STD: 238

November-December

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 201STD: 263

5.59%

?6.83%

Log-Normal

November-DecemberJanuary-October

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 185STD: 238

November-December

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 201STD: 263

5.59%

?6.83%

Log-Normal

I 6.8% Short-Services:

Agents’ “Abandon" (improve bonus, rest),(mis)lead by incentives

I Distributions must be measured (in seconds = natural scale)I LogNormal service-durations (???, common, more later)

29

Beyond Averages: The Human Factor

Histogram of Service-Time in an Israeli Call Center, 1999

January-OctoberJanuary-October

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 185STD: 238

November-December

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 201STD: 263

5.59%

?6.83%

Log-Normal

November-DecemberJanuary-October

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 185STD: 238

November-December

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 201STD: 263

5.59%

?6.83%

Log-Normal

I 6.8% Short-Services: Agents’ “Abandon" (improve bonus, rest),(mis)lead by incentives

I Distributions must be measured (in seconds = natural scale)I LogNormal service-durations (???, common, more later)

29

Pause for a Commercial:

The Technion SEE Center

30

Pause for a Commercial: The Technion SEE Center

30

Technion SEE = Service Enterprise Engineering

SEELab: Data-repositories for research and teachingI For example:

I Bank Anonymous: 1 year, 350K calls by 15 agents - in 2000.Brown, Gans, Sakov, Shen, Zeltyn, Zhao (JASA),paved the way to:

I U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agentsI Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agentsI Israeli Bank: from January 2010, daily-deposit at a SEESafeI Home (Rambam) Hospital: 4 years, 1000 beds, ward-level flowI 5 EDs: gathered by the late David Sinreich, ED arrivals & LOS

SEEStat: Environment for graphical EDA in real-timeI Universal Design, Internet Access, Real-Time Response.

SEEServer: Free for academic useI RegisterI Access U.S. Bank, Bank Anonymous, Home Hospital

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31







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eg. RFID-Based Data: Mass Casualty Event (MCE)Drill: Chemical MCE, Rambam Hospital, May 2010

מאייר -קלים ודחק'מרתף פנימית ו-משפחותקרדיולוגיהעורנוירולוגיהבינוניים

נספח לנוהלקרדיולוגיה,עור,נוירולוגיה-בינונייםחדר אוכל-קשים

ד"מלר-משולבים

Focus on severely wounded casualties (≈ 40 in drill)Note: 20 observers support real-time control (helps validation)

32

Data Cleaning: MCE with RFID Support

Data-base Company report comment Asset id order Entry date Exit date Entry date Exit date

4 1 1:14:07 PM 1:14:00 PM 6 1 12:02:02 PM 12:33:10 PM 12:02:00 PM 12:33:00 PM 8 1 11:37:15 AM 12:40:17 PM 11:37:00 AM exit is missing

10 1 12:23:32 PM 12:38:23 PM 12:23:00 PM 12 1 12:12:47 PM 12:35:33 PM 12:35:00 PM entry is missing 15 1 1:07:15 PM 1:07:00 PM 16 1 11:18:19 AM 11:31:04 AM 11:18:00 AM 11:31:00 AM 17 1 1:03:31 PM 1:03:00 PM 18 1 1:07:54 PM 1:07:00 PM 19 1 12:01:58 PM 12:01:00 PM 20 1 11:37:21 AM 12:57:02 PM 11:37:00 AM 12:57:00 PM 21 1 12:01:16 PM 12:37:16 PM 12:01:00 PM

22 1 12:04:31 PM 12:20:40 PM first customer is missing

22 2 12:27:37 PM 12:27:00 PM 25 1 12:27:35 PM 1:07:28 PM 12:27:00 PM 1:07:00 PM 27 1 12:06:53 PM 12:06:00 PM

28 1 11:21:34 AM 11:41:06 AM 11:41:00 AM 11:53:00 AMexit time instead of entry time

29 1 12:21:06 PM 12:54:29 PM 12:21:00 PM 12:54:00 PM 31 1 11:40:54 AM 12:30:16 PM 11:40:00 AM 12:30:00 PM 31 2 12:37:57 PM 12:54:51 PM 12:37:00 PM 12:54:00 PM 32 1 11:27:11 AM 12:15:17 PM 11:27:00 AM 12:15:00 PM 33 1 12:05:50 PM 12:13:12 PM 12:05:00 PM 12:15:00 PM wrong exit time 35 1 11:31:48 AM 11:40:50 AM 11:31:00 AM 11:40:00 AM 36 1 12:06:23 PM 12:29:30 PM 12:06:00 PM 12:29:00 PM 37 1 11:31:50 AM 11:48:18 AM 11:31:00 AM 11:48:00 AM 37 2 12:59:21 PM 12:59:00 PM 40 1 12:09:33 PM 12:35:23 PM 12:09:00 PM 12:35:00 PM 43 1 12:58:21 PM 12:58:00 PM 44 1 11:21:25 AM 11:52:30 AM 11:52:00 AM entry is missing 46 1 12:03:56 PM 12:03:00 PM 48 1 11:19:47 AM 11:19:00 AM 49 1 12:20:36 PM 12:20:00 PM 52 1 11:21:29 AM 11:50:49 AM 11:21:00 AM 11:50:00 AM 52 2 12:10:07 PM 1:07:28 PM 12:10:00 PM 1:07:00 PM recorded as exit 53 1 12:24:26 PM 12:24:00 PM 57 1 11:32:02 AM 11:58:31 AM 11:58:00 AM entry is missing 57 2 12:59:41 PM 1:14:00 PM 12:59:00 PM 1:14:00 PM 60 1 12:27:12 PM 12:48:41 PM 12:27:00 PM 12:48:00 PM 63 1 12:10:04 PM 12:10:00 PM 64 1 11:30:29 AM 12:43:38 PM 11:30:00 AM 12:43:00 PM

- Imagine “Cleaning" 60,000+ customers per day (call centers) !

- “Psychology" of Data Trust and Transfer (e.g. 2 years till transfer)33

Event-Logs in a Call Center (Bank Anonymous)

5

A Data Sample (Excel worksheet)

vru+line call_id customer_id priority type date vru_entry vru_exit vru_time q_start q_exit q_time outcome ser_start ser_exit ser_time server

AA0101 44749 27644400 2 PS 990901 11:45:33 11:45:39 6 11:45:39 11:46:58 79 AGENT 11:46:57 11:51:00 243 DORIT

AA0101 44750 12887816 1 PS 990905 14:49:00 14:49:06 6 14:49:06 14:53:00 234 AGENT 14:52:59 14:54:29 90 ROTH

AA0101 44967 58660291 2 PS 990905 14:58:42 14:58:48 6 14:58:48 15:02:31 223 AGENT 15:02:31 15:04:10 99 ROTH

AA0101 44968 0 0 NW 990905 15:10:17 15:10:26 9 15:10:26 15:13:19 173 HANG 00:00:00 00:00:00 0 NO_SERVER

AA0101 44969 63193346 2 PS 990905 15:22:07 15:22:13 6 15:22:13 15:23:21 68 AGENT 15:23:20 15:25:25 125 STEREN

AA0101 44970 0 0 NW 990905 15:31:33 15:31:47 14 00:00:00 00:00:00 0 AGENT 15:31:45 15:34:16 151 STEREN

AA0101 44971 41630443 2 PS 990905 15:37:29 15:37:34 5 15:37:34 15:38:20 46 AGENT 15:38:18 15:40:56 158 TOVA

AA0101 44972 64185333 2 PS 990905 15:44:32 15:44:37 5 15:44:37 15:47:57 200 AGENT 15:47:56 15:49:02 66 TOVA

AA0101 44973 3.06E+08 1 PS 990905 15:53:05 15:53:11 6 15:53:11 15:56:39 208 AGENT 15:56:38 15:56:47 9 MORIAH

AA0101 44974 74780917 2 NE 990905 15:59:34 15:59:40 6 15:59:40 16:02:33 173 AGENT 16:02:33 16:26:04 1411 ELI

AA0101 44975 55920755 2 PS 990905 16:07:46 16:07:51 5 16:07:51 16:08:01 10 HANG 00:00:00 00:00:00 0 NO_SERVER

AA0101 44976 0 0 NW 990905 16:11:38 16:11:48 10 16:11:48 16:11:50 2 HANG 00:00:00 00:00:00 0 NO_SERVER


AA0101 44978 23817067 2 PS 990905 16:19:11 16:19:17 6 16:19:17 16:19:39 22 AGENT 16:19:38 16:21:57 139 TOVA

AA0101 44764 0 0 PS 990901 15:03:26 15:03:36 10 00:00:00 00:00:00 0 AGENT 15:03:35 15:06:36 181 ZOHARI

AA0101 44765 25219700 2 PS 990901 15:14:46 15:14:51 5 15:14:51 15:15:10 19 AGENT 15:15:09 15:17:00 111 SHARON

AA0101 44766 0 0 PS 990901 15:25:48 15:26:00 12 00:00:00 00:00:00 0 AGENT 15:25:59 15:28:15 136 ANAT

AA0101 44767 58859752 2 PS 990901 15:34:57 15:35:03 6 15:35:03 15:35:14 11 AGENT 15:35:13 15:35:15 2 MORIAH

AA0101 44768 0 0 PS 990901 15:46:30 15:46:39 9 00:00:00 00:00:00 0 AGENT 15:46:38 15:51:51 313 ANAT

AA0101 44769 78191137 2 PS 990901 15:56:03 15:56:09 6 15:56:09 15:56:28 19 AGENT 15:56:28 15:59:02 154 MORIAH

AA0101 44770 0 0 PS 990901 16:14:31 16:14:46 15 00:00:00 00:00:00 0 AGENT 16:14:44 16:16:02 78 BENSION

AA0101 44771 0 0 PS 990901 16:38:59 16:39:12 13 00:00:00 00:00:00 0 AGENT 16:39:11 16:43:35 264 VICKY

AA0101 44772 0 0 PS 990901 16:51:40 16:51:50 10 00:00:00 00:00:00 0 AGENT 16:51:49 16:53:52 123 ANAT

AA0101 44773 0 0 PS 990901 17:02:19 17:02:28 9 00:00:00 00:00:00 0 AGENT 17:02:28 17:07:42 314 VICKY

AA0101 44774 32387482 1 PS 990901 17:18:18 17:18:24 6 17:18:24 17:19:01 37 AGENT 17:19:00 17:19:35 35 VICKY

AA0101 44775 0 0 PS 990901 17:38:53 17:39:05 12 00:00:00 00:00:00 0 AGENT 17:39:04 17:40:43 99 TOVA

AA0101 44776 0 0 PS 990901 17:52:59 17:53:09 10 00:00:00 00:00:00 0 AGENT 17:53:08 17:53:09 1 NO_SERVER

AA0101 44777 37635950 2 PS 990901 18:15:47 18:15:52 5 18:15:52 18:16:57 65 AGENT 18:16:56 18:18:48 112 ANAT

AA0101 44778 0 0 NE 990901 18:30:43 18:30:52 9 00:00:00 00:00:00 0 AGENT 18:30:51 18:30:54 3 MORIAH

AA0101 44779 0 0 PS 990901 18:51:47 18:52:02 15 00:00:00 00:00:00 0 AGENT 18:52:02 18:55:30 208 TOVA

AA0101 44780 0 0 PS 990901 19:19:04 19:19:17 13 00:00:00 00:00:00 0 AGENT 19:19:15 19:20:20 65 MEIR


AA0101 44782 0 0 NW 990901 20:08:13 20:08:25 12 00:00:00 00:00:00 0 AGENT 20:08:28 20:08:41 13 NO_SERVER


AA0101 44784 0 0 NW 990901 20:36:54 20:37:14 20 00:00:00 00:00:00 0 AGENT 20:37:13 20:38:07 54 BENSION


AA0101 44786 0 0 PS 990901 21:04:41 21:04:51 10 00:00:00 00:00:00 0 AGENT 21:04:50 21:05:59 69 TOVA

AA0101 44787 0 0 PS 990901 21:25:00 21:25:13 13 00:00:00 00:00:00 0 AGENT 21:25:13 21:28:03 170 AVI

AA0101 44788 0 0 PS 990901 21:50:40 21:50:54 14 00:00:00 00:00:00 0 AGENT 21:50:54 21:51:55 61 AVI

AA0101 44789 9103060 2 NE 990901 22:05:40 22:05:46 6 22:05:46 22:09:52 246 AGENT 22:09:51 22:13:41 230 AVI

AA0101 44790 14558621 2 PS 990901 22:24:11 22:24:17 6 22:24:17 22:26:16 119 AGENT 22:26:15 22:27:28 73 VICKY

AA0101 44791 0 0 PS 990901 22:46:27 22:46:37 10 00:00:00 00:00:00 0 AGENT 22:46:36 22:47:03 27 AVI

AA0101 44792 67158097 2 PS 990901 23:05:07 23:05:13 6 23:05:13 23:05:30 17 AGENT 23:05:29 23:06:49 80 VICKY

AA0101 44793 15317126 2 PS 990901 23:28:52 23:28:58 6 23:28:58 23:30:08 70 AGENT 23:30:07 23:35:03 296 DARMON


AA0101 44795 0 0 PS 990902 07:16:52 07:17:01 9 00:00:00 00:00:00 0 AGENT 07:17:01 07:17:44 43 ANAT

AA0101 44796 0 0 PS 990902 07:50:05 07:50:16 11 00:00:00 00:00:00 0 AGENT 07:50:16 07:53:03 167 STEREN

- Unsynchronized transition times, consistently34

aviman

Highlight

aviman

Highlight

aviman

Highlight

aviman

Highlight

aviman

Highlight

aviman

Highlight

33975

4221

2006

2886

2741

361

354697

1111

43

1049

994

319

162

2281

3908

160

504

266

193

122

158

118

7

1

32246

35916

1259

2006

2823

3798

876 352

370

107 491

545

566

127

48

48

2052

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19

17

390

547

14

3

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221

20

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282

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1

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516

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266

11

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8 132

132

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5

11

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22

8

135

150

24

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1 11

11

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7

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2

18

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9

33

2 7

2

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6

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6

1

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1

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22

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4

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327

14

1

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1058

26

18932

15

28

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31 94

2

58

15

49

39

9

94 36

52

5916

70

5

1

8

27

8

4

4

2

10

9

6

1

71

3

5

86

7

5

4

1

1

1

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21

1

1

1

1

3

1

2

3

1

1

Entry

VRURetail

VRUPremier

VRUBusiness

VRUConsumer Loans

VRUSubanco

VRUSummit

Business LineRetail

Business LinePremier

Business LineBusiness

Business LinePlatinum

Business LineConsumer Loans

Business LineOnline Banking

Business LineEBO

Business LineTelesales

Business LineSubanco

Business LineSummit

AnnouncementRetail

AnnouncementPremier

AnnouncementPlatinum

AnnouncementConsumer Loans

AnnouncementOnline Banking

AnnouncementTelesales

AnnouncementSubanco

MessageRetail

MessagePremier

MessageBusiness

MessagePlatinum

MessageConsumer Loans

MessageTelesales

NonBusiness LineBusiness

NonBusiness LineSubanco

NonBusiness LinePriority Service

NonBusiness Line NonCC ServiceCCO

NonCC ServiceQuick&Reilly

Overnight ClosedRetail

Overnight ClosedConsumer Loans

Overnight ClosedEBO

TrunkRetail

TrunkPremier

TrunkBusiness

TrunkConsumer Loans

TrunkOnline Banking

TrunkEBO

TrunkTelesales

TrunkPriority Service

Trunk

Trunk

Trunk

Trunk

Trunk

InternalTotal

OutgoingTotal

NormalTermination

NormalTermination

UndeterminedTermination

AbandonedShort

Abandoned

OtherUnhandled

Transfer

Transfer

1 Day in a Call Center - Customers

USBank April 2, 2001

33975

4221

2006

2886

2741

361

354697

1111

43

1049

994

319

162

2281

3908

160

504

266

193

122

158

118

7

1

32246

35916

1259

2006

2823

3798

876 352

370

107 491

545

566

127

48

48

2052

47

59

33

307

19

17

390

547

14

3

192

221

20

12

60

282

174

355

1405

169 91

23 1

1022

73

35

112

27

3

119

4

34

243

2935

3908

7

23

17

1

44

71

2

516

267229

266

11

78

8 132

132

172

5

11

41

67

7

17

8

8

118

45

27

13

22

8

135

150

24

1

8

3

3

37

24

16

19

26

67

32

10

3

4

2516

1 11

11

11

8

35

6

7

11

6

4

13

6

3

1

6

13

1

11

2

18

1

7

1

9

33

2 7

2

4

2

6

6

4

3

4

1

1

11

6

1

3

8

1

2

1

4

2

2

1

1

1

1

1

1

1

1

1

2

2

3

1

1

1

1

1

1

1

34

3

1

1

26102

735

4489

1704

2232

2240

53

782 95

10

604

393

24134

105

32

2194

82

1369

1362

33

71

501

22

57

205

757

545

3

208

4

1497

2561

34

254

176

25

82

115

153

2843

3071 560

327

14

1

17

1058

26

18932

15

28

1215

34

46

31 94

2

58

15

49

39

9

94 36

52

5916

70

5

1

8

27

8

4

4

2

10

9

6

1

71

3

5

86

7

5

4

1

1

1

4

21

1

1

1

1

3

1

2

3

1

1

Entry

VRURetail

VRUPremier

VRUBusiness

VRUConsumer Loans

VRUSubanco

VRUSummit

Business LineRetail

Business LinePremier

Business LineBusiness

Business LinePlatinum

Business LineConsumer Loans

Business LineOnline Banking

Business LineEBO

Business LineTelesales

Business LineSubanco

Business LineSummit

AnnouncementRetail

AnnouncementPremier

AnnouncementPlatinum

AnnouncementConsumer Loans

AnnouncementOnline Banking

AnnouncementTelesales

AnnouncementSubanco

MessageRetail

MessagePremier

MessageBusiness

MessagePlatinum

MessageConsumer Loans

MessageTelesales

NonBusiness LineBusiness

NonBusiness LineSubanco

NonBusiness LinePriority Service

NonBusiness Line NonCC ServiceCCO

NonCC ServiceQuick&Reilly

Overnight ClosedRetail

Overnight ClosedConsumer Loans

Overnight ClosedEBO

TrunkRetail

TrunkPremier

TrunkBusiness

TrunkConsumer Loans

TrunkOnline Banking

TrunkEBO

TrunkTelesales

TrunkPriority Service

Trunk

Trunk

Trunk

Trunk

Trunk

InternalTotal

OutgoingTotal

NormalTermination

NormalTermination

UndeterminedTermination

AbandonedShort

Abandoned

OtherUnhandled

Transfer

Transfer

1 Day in a Call Center - Customers


ILDUBank January 24, 2010 from 06:00 to 23:59:59

Call-Backs Outgoing

Inbound

Available

IdleBreak

ILDUBank January 24, 2010 from 06:00 to 23:59:59

Call-Backs Outgoing

Inbound

Available

IdleBreak

ED

Pediatric

Neurology Nephrology Derrmatology

Internal

IntensiveCare

Cardiology

Rheumatology

UrologyOtorhinolaryngology Orthopedics

Surgery

Maternity

Gynecology

Psychiatry Ophthalmology

R

L

D

Out

R

R

R

R

R R

R

RR RR

R

R

R

R

R

L

LL

L

L

L

L

L

L

D

D

D

D

D DD

D

DD

D

D

Out

Out

Out

Out Out

Out

OutOut Out OutOut

Out

Out

1 Day in a Hospital - Patients

Rambam August, 2004

Released (Home)

Left with Medical File

Deceased

Transfer

115

17

5

43

2

1

1

1

8

6

2

1

1

2

23

3

15

1

7

1

11

1

2

1

6

1

1

1 13

1

1

1

1

1

1

1 3

1

1

1

1

1

1 1

1 1

1

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1 1

1 11

1

11 11 1

1

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1

1

1

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1

3

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2

1

1

1

1

1

1

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1

1

1

1

1

1

1

1

2

1

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

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1 1

1

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1

11

1

1

1

1

1

1 11

1 1

2 2

1

2

1

1 1 1 11

2

1

1

serveng

lectures

references

predictionmay1809.pdf

homeworks

hw1_amusement_park_mgt.pdf

recitations

hazard_phase_type.pdf

course2011winter

icpr_service_engineering.pdfon_cc_data_frommsom.pdf pivot_table.pdf

thesis_polyna.pdf

proposal_polina.pdf

moss.pdf

files

nurse_proj_psu_tech.pdf

national_cranberry_1.pdf

hw9par_sol_2012w.pdf

syllabus8.pdfexams

statanalysis.pdf

agent-heterogeneity-brown-book-final.pdf

1_1_qed_lecture_introduction_2011w.pdf

course2004

retail.pdf hall_6.pdf

jasa_callcenter.pdf dantzig.pdf

bacceli.pdf

avishai-class-april-2003.ppt

hw7_2011w_par_sol_part2.pdf

ibmrambam technion srii presentation final.ppt

dimensioning.pdf

palmannoyance.pdf

yair_sergurywaitingtimeanalysis.pdf

nejmsb1002320.pdf

qed_qs_scientific_generic_caschina.pdf

web_summary13_2011s.pdf

4callcenters_coverpage.pdf

documentation.pdf rec9part2.pdf

web_summary9_2010w.pdf

qed_qs_scientific_wharton_stat_seminar.pdf

l2_measurements_class_2009s.pdf

ccreview.pdfvdesign_ecompanion.pdf

wharton_lecture_avi_printout.pdflarson_atoa.pdf

proposal_michael.pdf

stanford_seminar_avi_printout.pdf

solver_guide.pdf

fitz.pdf

rec10_part2.pdf rec5.pdf

paxson.pdf

connect_to_see_terminal.pdf

project_ug_simulationinterface.pdf revenue_manage.pdf

hw7_2009s_forecast.xls

syllabus2.pdf

infocom04.pdf

hall_transportation.pdf

whitt_handout_chapter1.pdf

fromprojecttoprocess.pdf

nytimes.2007-06-23.pdf ds_pert_lec1.pdf syllabus6.pdf hw9_2011w.pdf hw7_2011w.pdf

mmng_constraint_supp_or.pdf

awam-april_2011.pdfwhitt_scaling_slides.pdfmmng_seminar.pdf

syllabus4.pdf

syllabus12_2012w.pdf

syllabus5.pdf

mm1_strong_apprximations.pdf seestat_tutorial.ppt

kaplan_porter_2011-9_how-to-solve-the-cost-crisis-in-health-care_hbr.pdf

rec9_part2.pdf

callcenterdata

bocaraton.ps

gccreport 20-04-07 uk version.pdf hall_manpower_planning.pdf

bi18.pdf

syllabus12.pdf fluidview_2010w_short_version.pdf hw7_2009s_par_sol_part2.pdf

moed_b_2007w_solution.pdf

newell.pdf

rec11.pdf

moedb_2009w.pdf

rec3.pdf

hw10_par_sol_2011s.pdf

thirdlevel support ijtm1_cs.pdf

hw4_full.pdf

moedb_2010s_sol.pdf

chandra.pdf

gurvich_seminar.pdf

ed_sinreich_marmor.ppt regimes_supplement.pdf

web_summary10_2011s.pdf hw6par_sol_2009s.xls

exam_2005s_sol.pdf

servicefull.pdf

witor09_empirical_adventures_sep2009.pdf

web_summary12_2011s.pdf

heb_summary_yulia.pdf

hw9par_sol_2011s.pdf

seminar_yulia_9_2.pdf

bpr_2003.pdf staffing_italian_us_2011w.xlsdesignofqueues.pdf thepsychologyofwaitinglines.pdf

erlangabc.pdf

studentsevaluations.pdf hw8_2011s.pdf

hw9_2012w.pdf

edie.pdf

syllabus9.pdf

ds_pert_lec2.pdf

zohar_seminar.ppt

hist-normal.pdf

vandergraft.pdf

rec13.pdf

desighn_ivr.pdf

cohen_aircraft_failures.pdf

sbr.pdf

nano.pdf

hw2_2011w.pdf seminar_presentation_boaz_estimatinger load.ppt

project_ug_meirav.pdf see_report_output_june_2011.pdf

see_report_2010.pdf

1 Day in a Website - Spiders (e.g. Googlebot)

ServEng May 19, 2012

470

228

5

101

8 4 3

30

53

44 35

6 33

7334 3

4

4

321

3

314 93

3

4 43

19

4

3 3

5

48 34

64

3 3 4

14

7 3

5 4

3

6

7

335 3 33 3

58 4 3

53

44 35 7334 3

4

3

3

5

14 93

3

4 43

4

3

5

48 34

64

3 3 45 4

3

6 335 3 33 3

serveng

lectures

hall_flows_hospitals_chapter1text.pdf

references

4callcenterscourse2004 homeworks

icpr_service_engineering.pdf keycorp.pdf

files

revenue_manage.pdfhw1_amusement_park_mgt.pdf

recitations

setup.exe

garnett.pdf abandon02.pdf erlang_a.pdf ccbib.pdf

us7_cc_avi.pdf

jasa_callcenter.pdfsbr.pdf


mazeget_noa_yul.pptexams technion-call-center-report-sept-2004.pdfbrandt.pdf statanalysis.pdfmjp_into_erlang_a.pdf loch.pdf sbr_stolyar.pdf

callcenterdata

larson_atoa.pdf sivanthesisfinal.pdf columbia05.pdf crmis.pptfluid_systems.rar

januarytxt.zip

sbr_wharton_ccforum_short_may03.pdf predictingwaitingtime.pdf avishaicourse_munichor.ppt vdesign_pub.pdf hierarchical_modelling_chen_mandelbaum_part1.pdf

solver_guide.pdf

datamocca_february_2008_cc_forum_lecture.ppt seminar_presentation_galit.pptntro_to_serveng_teaching_note.pdf

pivot_table.pdf

project_ug_simulationinterface.pdf

course2010winter

ed_simulation_modeling_supp.pdf avim_cv.pdfdantzig.pdf yariv_phd.pdf

rec10_part2.pdf

fr6.pdfnejmsb1002320.pdf

hebrew_syllabus_2011s.pdf

patientflow main.pdf

hw9_2012w.pdf

avim_cv_18_12_2011.pdf

1 Day in a Website - Clickstream Structure - Menus, Files

ServEng January 5, 2012

470

228

5

101

8 4 3

30

53

44 35

6 33

7334 3

4

4

321

3

314 93

3

4 43

19

4

3 3

5

48 34

64

3 3 4

14

7 3

5 4

3

6

7

335 3 33 3

58 4 3

53

44 35 7334 3

4

3

3

5

14 93

3

4 43

4

3

5

48 34

64

3 3 45 4

3

6 335 3 33 3

serveng

lectures

hall_flows_hospitals_chapter1text.pdf

references

4callcenterscourse2004 homeworks

icpr_service_engineering.pdf keycorp.pdf

files

revenue_manage.pdfhw1_amusement_park_mgt.pdf

recitations

setup.exe

garnett.pdf abandon02.pdf erlang_a.pdf ccbib.pdf

us7_cc_avi.pdf

jasa_callcenter.pdfsbr.pdf


mazeget_noa_yul.pptexams technion-call-center-report-sept-2004.pdfbrandt.pdf statanalysis.pdfmjp_into_erlang_a.pdf loch.pdf sbr_stolyar.pdf

callcenterdata

larson_atoa.pdf sivanthesisfinal.pdf columbia05.pdf crmis.pptfluid_systems.rar

januarytxt.zip

sbr_wharton_ccforum_short_may03.pdf predictingwaitingtime.pdf avishaicourse_munichor.ppt vdesign_pub.pdf hierarchical_modelling_chen_mandelbaum_part1.pdf

solver_guide.pdf

datamocca_february_2008_cc_forum_lecture.ppt seminar_presentation_galit.pptntro_to_serveng_teaching_note.pdf

pivot_table.pdf

project_ug_simulationinterface.pdf

course2010winter

ed_simulation_modeling_supp.pdf avim_cv.pdfdantzig.pdf yariv_phd.pdf

rec10_part2.pdf

fr6.pdfnejmsb1002320.pdf

hebrew_syllabus_2011s.pdf

patientflow main.pdf

hw9_2012w.pdf

avim_cv_18_12_2011.pdf

1 Day in a Website - Clickstream Structure - Menus, Files

ServEng January 5, 2012

Menus:

Files:

8 AM - 9 AM

55888

1113 43320 160505194 7

36512 23633845 3792

845 103

120

314

3314

155

43

13

4

34

594 140

547

191

16

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6

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432

242

3052 3908

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472131 202

19

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14 46 10

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20863633 3536

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260

294

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666

198 35148

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213

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3671

11

19 356

126

10

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4

12

3

Entry

Entry Entry Entry Entry EntryEntry Entry

VRU

Retail Premier Business PlatinumConsumer Loans EBOTelesales Subanco Summit

VRU

Retail PremierBusiness PlatinumConsumer LoansEBO Telesales SummitOut

VRU

Retail

C

A

C

CC C

C

C

C

C

C

C

C

C C

C

C

C

C

C

C

AA

A

A AA A A

A

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OutOut Out Out OutOut OutOut Out

Out OutOut

1 Hour in a Call Center - Customers - Hierarchical


Abandoned Continued (Branch, Another ID)

Completed

Zoom Out: Call Center Network Inter-Queues


Philadelphia NYC

Boston

C C

AA

C

A


Zoom Out: Call Center Network Inter-Queues

Daily(Deposit)

OrderCheckbooks

Identification

ChangePassword

Agent

Fax

Query Transfer

Securities

StockMarket

PerformOperation

Credit

Error

43123

234

270

1352

35315

3900

7895

830

68

65

273

1063

231

768

133

1032

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40

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107

6

5

21

8

26091

4115

12317

962

1039

147

42

18

28

114

14

72

20

Zoom In: Interactive Voice Response (IVR)

ILBank May 2, 2008

ILDUBank January 24, 2010 Agent #043 Shift: 16:00 - 23:45

Inbound Call-Backs

Outgoing

Available Idle

Private Call

Break

Private Prepaid

PrivatePrivate VIP Private Customer RetentionBusiness Business VIP Business Customer Retention

Language 2 Prepaid Language 2 Prepaid Low PriorityLanguage 2 PrivateLanguage 3 Internet Surfing Internet

Overseas

1 24 5 810 11 12 1315161718 20 21 24 25

2104

2208 26264592 445 3411432049 1484 8734785 4658 411 444480 43 847 181 974

1253823 843343 1390109630 4454 1240792 3793 49 735

1433 193

Zoom In: Skills - Based Routing (SBR) Network Structure (Protocol)

Israeli Telecom February 10, 2008

N -Design

L -Design

Agent Pool

Customer Class

Connected Component

1 24 5 810 11 12 1315161718 20 21 24 25

2104

2208 26264592 445 3411432049 1484 8734785 4658 411 444480 43 847 181 974

1253823 843343 1390109630 4454 1240792 3793 49 735

1433 193

Goal: Data-Based Real-Time Simulation (SimNet)

Private Prepaid Language 3 Language 2 Private Language 2 Prepaid Language 2 Prepaid Low Priority Internet Surfing Internet

Private VIP Private Business Business VIP Business Customer Retention Private Customer Retention Overseas

What is lacking?

1. Dynamics

2. Durations

3. Protocols

Israeli Telecom February 10, 2008

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8 AM - 9 AM


8 AM - 9 AM

9 AM - 10 AM

10 AM - 11 AM

11 AM - 12 PM

Dynamics: Time-Varying Arrival-Rates2 Daily Peaks

CC: Dec. 1995, (USA, 700 Helpdesks) CC: May 1959 (England)

Q-Science

May 1959!

Dec 1995!

(Help Desk Institute)

Arrival Rate

Time 24 hrs

Time 24 hrs

% Arrivals

(Lee A.M., Applied Q-Th)

28

Q-Science

May 1959!

Dec 1995!

(Help Desk Institute)

Arrival Rate

Time 24 hrs

Time 24 hrs

% Arrivals

(Lee A.M., Applied Q-Th)

28

CC: Nov. 1999 (Israel) ED: Jan.–July 2007 (Israel)

Arrival Process, in 1999

Yearly Monthly

Daily Hourly

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

22.50

25.00

27.50

30.00

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00

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Time (Resolution 60 min.)

HomeHospital Patients Arrivals to Emergency Department Total for January2007 February2007 March2007 April2007 May2007 June2007 July2007,Sundays

55

Dynamics: Parsimonious Models (Congestion Laws)3 Queue-Lengths at 30 sec. resolution (ILBank, 10/6/2007)

ILBank Customers in queue (average), Private10.06.2007

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00

Time (Resolution 30 sec.)

Perc

enta

geMedium priority Low priority Unidentified

ILBank Customers in queue (average)10.06.2007

0.00

25.00

50.00

75.00

100.00

125.00

150.00

175.00

200.00

225.00

06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00


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Medium priority Low priority Unidentified

Queue “Shape"


0.0050.00

100.00150.00200.00250.00300.00350.00400.00450.00500.00550.00600.00

06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00


Perc

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ean



0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00


Perc

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I Area normalized to 100%I State-Space Collapse

56

Durations: Phone Calls (2 Surprises)

Israeli Call Center, Nov–Dec, 1999

Log(Service Times)

0 2 4 6 8

0.0

0.1

0.2

0.3

0.4

Log(Service Time)

Pro

port

ion

LogNormal QQPlot

Log-normalS

ervi

ce ti

me

0 1000 2000 3000

010

0020

0030

00

I Practically Important: (mean, std)(log) characterizationI Theoretically Intriguing: Why LogNormal ? Naturally multiplicative

but, in fact, also Infinitely-Divisible (Generalized Gamma-Convolutions)

57

Durations: Answering MachineIsraeli Bank: IVR/VRU Only, May 2008

IVR_onlyMay 2008, Week days

0.000.100.200.300.400.500.600.700.800.901.001.101.201.301.40

00:00 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30

Time(mm:ss) (Resolution 1 sec.)

Rel

ativ

e fr

eque

ncie

s %

mean=99st.dev.=101

Tree-Network Tomography:Reconstruct topologyfrom root and leaves

Mixture: 7 LogNormals

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

00:00 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30

Rel

ativ

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s %

Time(mm:ss) (Resolution 1 sec.)

Fitting Mixtures of Distributions for VRU only timeMay 2008, Week days

Empirical Total Lognormal Lognormal Lognormal

58

Durations: Waiting Times in a Call Center⇒ Protocols

Exponential in Heavy-Traffic (min.)Small Israeli Bank

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

22.50

25.00

27.50

30.00

0.00 100.00 200.00 300.00 400.00 500.00 600.00

Rel

ativ

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cies

%

Time(seconds)( resolution 30)

AnonymousBank Handled Wait Time, TOTAL Total for January1999 February1999 March1999 April1999 May1999 June1999 July1999 August1999 September1999 October1999

November1999 December1999,Weekdays

Empirical Exponential (scale=106.67)

Mean = 106 SD = 109

Routing via Thresholds (sec.)Large U.S. Bank

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

2.00 7.00 12.00 17.00 22.00 27.00 32.00 37.00

Rel

ativ

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%


USBank Wait time(waiting), Retail May 2002, Weekdays

Scheduling Priorities (sec.) [compare Hospital LOS (hours)]Medium Israeli Bank

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

20.00 70.00 120.00 170.00 220.00 270.00 320.00 370.00

Rel

ativ

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cies

%


ILBank Wait time (all) August 2007, Weekdays

59

LogNormal & Beyond: Length-of-Stay in a Hospital

Israeli Hospital, in Days: LN

0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Israeli Hospital, in Hours: Mixture

0 .2.4 .6 .8 11.21.51.82.12.42.7 33.23.53.84.14.44.7 55.25.55.86.16.46.7 7 7.37.67.98.28.58.89.19.49.7 10

Explanation: Patients releasedaround 3pm (1pm in Singapore)

Why Bother ?I Hourly Scale: Staffing,. . .I Daily: Flow / Bed Control,. . .

Workload at the Internal Ward (In Progress): Arrivals, Departures, # Patients in Ward A, by Hour

60



0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49


0 .2.4 .6 .8 11.21.51.82.12.42.7 33.23.53.84.14.44.7 55.25.55.86.16.46.7 7 7.37.67.98.28.58.89.19.49.7 10




60



0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49


0 .2.4 .6 .8 11.21.51.82.12.42.7 33.23.53.84.14.44.7 55.25.55.86.16.46.7 7 7.37.67.98.28.58.89.19.49.7 10




60

Durations: (Im)Patience while Waiting (Psychology)Palm: (1943–53): Irritation ∝ Hazard Rate

Regular over VIP Customers – Israeli Bank

14

16

I Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data

I Here: VIP Customers are more Patient (Needy)I Peaks of abandonment at times of Announcements

61



14

16I Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data


61



14

16I Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data


61

Protocols + PsychologyPatient Customers, Announcements, Priority Upgrades

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900

Ha

zard

Fu

nct

ion

Time (seconds)

USBank December 2002, Week days, Quick&Reilly

time willing to wait (hazard rate)

time willing to wait (Pspline)

virtual wait (hazard rate)

virtual wait (Pspline)

62

Little’s Law: Call Center & Emergency Department

Time-Gap: # in System lags behind Piecewise-Little (L = λ×W )

Little’s Law and the Offered-Load: Empirical Adventures in Call Centers and Hospitals

The Black-Box View of a Call Center: Number in Q vs. Little shows a time-gap.

USBank Customers in queue(average), Telesales10.10.2001

0.0020.0040.0060.0080.00

100.00120.00140.00160.00180.00200.00

07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


Num

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Customers in queue(average) Little's law

HomeHospital Average patients in EDFebruary 2004, Wednesdays

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00


Ave

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Average patients in ED Lambda*E(S) smoothed

בהסתכלות ממוצעת על יום באמצע השבוע לאורך מספר חודשים

HomeHospital Average patients in EDTotal for February2004 March2004 April2004 May2004 June2004 July2004 August2004 September2004 October2004,Week days

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00


Ave

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Average patients in ED Lambda*E(S)

⇒ Time-Varying Little’s LawI Berstemas & Mourtzinou;I Fralix, Riano, Serfozo; . . .

63

Little’s Law: Call Center & Emergency Department

Time-Gap: # in System lags behind Piecewise-Little (L = λ×W )

Little’s Law and the Offered-Load: Empirical Adventures in Call Centers and Hospitals

The Black-Box View of a Call Center: Number in Q vs. Little shows a time-gap.

USBank Customers in queue(average), Telesales10.10.2001

0.0020.0040.0060.0080.00

100.00120.00140.00160.00180.00200.00

07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


Num

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f cas

es

Customers in queue(average) Little's law

HomeHospital Average patients in EDFebruary 2004, Wednesdays

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00


Ave

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Average patients in ED Lambda*E(S) smoothed

בהסתכלות ממוצעת על יום באמצע השבוע לאורך מספר חודשים

HomeHospital Average patients in EDTotal for February2004 March2004 April2004 May2004 June2004 July2004 August2004 September2004 October2004,Week days

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00


Ave

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num

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Average patients in ED Lambda*E(S)

⇒ Time-Varying Little’s LawI Berstemas & Mourtzinou;I Fralix, Riano, Serfozo; . . .

63

Protocols: Staffing (N) vs. Offered-Load (R = λ× E(S))IL Telecom; June-September, 2004; w/ Nardi, Plonski, Zeltyn

Empirical Analysis of a QED Call Center

• 2205 half-hour intervals of an Israeli call center • Almost all intervals are within R R− and 2R R+ (i.e. 1 2β− ≤ ≤ ),

implying: o Very decent forecasts made by the call center o A very reasonable level of service (or does it?)

• QED? o Recall: ( )GMR x is the asymptotic probability of P(Wait>0) as a

function of β , where x θµ=

o In this data-set, 0.35x θµ= =

o Theoretical analysis suggests that under this condition, for 1 2β− ≤ ≤ , we get 0 ( 0) 1P Wait≤ > ≤ …

2205 half-hour intervals (13 summer weeks, week-days)64

Technion - Israel Institute of Technology

The William Davidson Faculty of Industrial Engineering and Management Center for Service Enterprise Engineering (SEE)

http://ie.technion.ac.il/Labs/Serveng/

SEEStat 3.0 Tutorial

August 23, 2012

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HomeHospital Data Background: The data we rely on was collected at a large Israeli hospital. This hospital consists of about 1000 beds and 45 medical units. The data includes detailed information on patient flow throughout the hospital, over a period of several years (January 2004–October 2007). In particular, the data allows one to follow the paths of individual patients throughout their stay at the hospital, including admission, discharge, and transfers between hospital units. The data does not acknowledge resolutions within the ED or within wards.

Nd - average number of patients that arrived per weekday, for period January 1, 2004 - October, 31, 2007

Ny - average number of patients that arrived per year, for years 2004, 2005, 2006, all days (for year 2007 data not fully completed; missing two months - November and December).

N - average number of patients in ED/ED-to-Ward transfer/Wards, recorded at 12:00 per weekday, for period January 1, 2004 - October, 31, 2007

NX-Ray - average number of patients in X-Ray at 10:00 per weekday, for period January 1, 2004 - October, 31, 2007

LOS - length of stay in ED/ED-to-Ward transfer/Wards/X-Ray per weekday, for period January 1, 2004 - October, 31, 2007

Arrivals at the ED

Arrivals directly to Wards

Arrivals at the X-Ray

Ward

WardWard

Hospitalization

X-Ray Exits

Discharges

Discharges

Emergency Department

Hospital

X-Ray

ED-to-Ward transfer

Nd = 341 patients

Ny= 115997 patients

Nd = 228 patients

(67% from all arrivals at the ED)

N = 60 patientsLOS = 3 hours

N = 11 patientsLOS = 3 hours Nd = 113 patients

Ny = 37973 patients

(33% from all arrivals at the ED)

NX-Ray = 15 patients

LOS = 52 minutes

Nd = 225 patients

N = 905 patients

LOS = 3.7 days

Nd = 106 patients

Ny= 30416 patients (24% from all arrivals at hospital)

Nd = 127 patients

Ny= 32713 patients

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00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00Time (Resolution 60 min.)

HomeHospital Number of Patients in Emergency Department (average), Emergency Internal Medicine Unit03.01.200510.01.200517.01.200524.01.200531.01.200507.02.200514.02.200521.02.200528.02.200507.03.200514.03.200521.03.200528.03.200504.04.200511.04.200518.04.200525.04.200502.05.200509.05.200516.05.200523.05.200530.05.200506.06.200520.06.200527.06.200504.07.200511.07.200518.07.200525.07.200501.08.200508.08.200515.08.200522.08.200529.08.200505.09.200512.09.200519.09.200526.09.200507.11.200514.11.200521.11.200528.11.200505.12.200512.12.200519.12.200526.12.2005Mondays

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Number of patients in ED

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Number of patients (resolution 1)

HomeHospital Time by ED Internal and Surgery state (sec.)January 2004-October 2007, all days

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[00:00:00 - 01:00:00) [01:00:00 - 02:00:00) [02:00:00 - 03:00:00) [03:00:00 - 04:00:00) [04:00:00 - 05:00:00) [05:00:00 - 06:00:00) [06:00:00 - 07:00:00) [07:00:00 - 08:00:00) [08:00:00 - 09:00:00) [09:00:00 - 10:00:00) [10:00:00 - 11:00:00) [11:00:00 - 12:00:00) [12:00:00 - 13:00:00) [13:00:00 - 14:00:00) [14:00:00 - 15:00:00) [15:00:00 - 16:00:00) [16:00:00 - 17:00:00) [17:00:00 - 18:00:00) [18:00:00 - 19:00:00) [19:00:00 - 20:00:00) [20:00:00 - 21:00:00) [21:00:00 - 22:00:00) [22:00:00 - 23:00:00) [23:00:00 - 24:00:00)

15

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HomeHospital Number of Patients in Emergency Department Internal and Surgery,January 2004-October 2007, all days

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Normal (21.45%): location = 17.59 scale = 5.39Gamma (40.19%): scale = 7 shape = 4.55Weibull (38.36%): scale = 49.28 shape = 3.61

MorningNormal

EveningWeibull

Intermediate hoursGamma

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Time by ED Internal and Surgery state (sec.) Statistics N 120960000 N(average per day) 86400 Mean 34.1 Standard Deviation 16.34 Variance 266.87 Median 32 Minimum 0 Maximum 99 Skewness 0.524 Kurtosis -0.44452 Standard Error Mean 0.00149 Interquartile Range 25 Mean Absolute Deviation 13.7 Median Absolute Deviation(MAD) 12 Coefficient of Variation (CV) (%) 47.9 L-moment 2 (half of Gini's Mean Difference) 9.25 L-Skewness 0.121 L-Kurtosis 0.0561 Coefficient of L-variation (L-CV)(%) (Gini's Coefficient) 27.12

Parameter Estimates

Components Mixing Proportions (%) Location Scale Shape Mean Standard Deviation 1. Normal 21.45 17.59 5.39 17.59 5.39 2. Gamma 40.19 7.00 4.55 31.83 14.99 3. Weibull 38.36 49.28 3.61 44.42 13.679

Goodness-of-Fit Tests

Tests Statistic DF p Value Residuals Std 0.011 Kolmogorov-Smirnov 0.028 <.0001 Cramer-von Mises 14953.04 <.0001 Andersen-Darling 96156.09 <.0001 Chi-Square 460741.3 94 <.0001

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HomeHospital Time by ED Internal state (sec.)January 2004-October 2007, all days

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020406080

100120140160180200220240260280300320340

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[00:00:00 - 01:00:00) [01:00:00 - 02:00:00) [02:00:00 - 03:00:00) [03:00:00 - 04:00:00) [04:00:00 - 05:00:00) [05:00:00 - 06:00:00) [06:00:00 - 07:00:00) [07:00:00 - 08:00:00) [08:00:00 - 09:00:00) [09:00:00 - 10:00:00) [10:00:00 - 11:00:00) [11:00:00 - 12:00:00) [12:00:00 - 13:00:00) [13:00:00 - 14:00:00) [14:00:00 - 15:00:00) [15:00:00 - 16:00:00) [16:00:00 - 17:00:00) [17:00:00 - 18:00:00) [18:00:00 - 19:00:00) [19:00:00 - 20:00:00) [20:00:00 - 21:00:00) [21:00:00 - 22:00:00) [22:00:00 - 23:00:00) [23:00:00 - 24:00:00)

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January 2004-October 2007, all days

7

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Normal (26.47%): location = 13 scale = 4.15Normal (24.17%): location = 20 scale = 6.09Normal (49.36%): location = 30 scale = 9.84Morning

Normal Intermediate hoursNormal Evening

Normal

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Time by ED Internal state (sec.) Statistics N 120960000 N(average per day) 86400 Mean 23.63 Standard Deviation 10.7 Variance 114.4 Median 22 Minimum 0 Maximum 70 Skewness 0.557 Kurtosis -0.23178 Standard Error Mean 0.00097 Interquartile Range 16 Mean Absolute Deviation 8.808 Median Absolute Deviation(MAD) 8 Coefficient of Variation (CV) (%) 45.27 L-moment 2 (half of Gini's Mean Difference) 6.031 L-Skewness 0.121 L-Kurtosis 0.0813 Coefficient of L-variation (L-CV)(%) (Gini's Coefficient) 25.53

Parameter Estimates

Components Mixing Proportions (%) Location Scale Shape Mean Standard Deviation 1. Normal 26.47 13.01 4.15 13.01 4.15 2. Normal 24.17 20.00 6.09 20.00 6.09 3. Normal 49.36 30.04 9.84 30.04 9.84

Goodness-of-Fit Tests

Tests Statistic DF p Value Residuals Std 0.017 Kolmogorov-Smirnov 0.04 <.0001 Cramer-von Mises 34138.3 <.0001 Andersen-Darling 200657.9 <.0001 Chi-Square 584234.3 65 <.0001

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Example 5.3: Number of patients in Internal ED Average per 10minute intervals, only on Mondays during 2005

Return to the "Statistical Models (Summaries)" window. Press the "New Model" button. Select "Time Series", then "Intraday". In the “Variable” tab, select "Number of Patients in Emergency Department (average)". In the "Select Categories" tab, select "Emergency Internal Medicine Unit". Click the "Dates->" button. Mark "Individual days for aggregated day. Select months from June 2005 to December 2005.

Open tab "Days" and select "Mondays". Click "OK".

03.10.2005

17.10.2005

0.005.00

10.0015.0020.0025.0030.0035.0040.0045.0050.0055.00

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00

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HomeHospital Number of Patients in Emergency Department (average), Emergency Internal Medicine Unit

June2005 July2005 August2005 September2005 October2005 November2005 December2005,Mondays

06.06.2005 20.06.2005 27.06.2005 04.07.2005 11.07.2005 18.07.2005 25.07.2005 01.08.2005 08.08.2005 15.08.2005 22.08.2005 29.08.2005 05.09.2005 12.09.2005 19.09.2005 26.09.2005 03.10.2005 10.10.2005 17.10.2005 24.10.2005 31.10.2005 07.11.2005 14.11.2005 21.11.2005 28.11.2005 05.12.2005 12.12.2005 19.12.2005 26.12.2005 Mondays

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HomeHospital Time by ED Internal state (sec.), [13:00-23:00)Total for January2005 February2005 March2005 April2005 May2005 June2005 July2005 August2005 September2005

November2005 December2005,Mondays

Empirical Normal (mu=33.22 sigma=5.76)

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13

Time by ED Internal state (sec.), [13:00-23:00) Statistics N 1656000 N(average per day) 36000 Mean 33.22 Standard Deviation 5.756 Variance 33.13 Median 33 Minimum 16 Maximum 54 Skewness 0.282 Kurtosis -0.31791 Standard Error Mean 0.00447 Interquartile Range 8 Mean Absolute Deviation 4.712 Median Absolute Deviation(MAD) 4 Coefficient of Variation(CV) (%) 17.33 L-moment 2 (half of Gini's Mean Difference) 3.263 L-Skewness 0.0601 L-Kurtosis 0.0924 Coefficient of L-variation(L-CV)(%) (Gini's Coefficient) 9.82

Parameters for Normal Distribution

Parameter Estimate mu 33.22 sigma 5.76 mean 33.22 std 5.756

Goodness-of-Fit Tests for Normal Distribution Test Statistic DF p Value Residuals Std 0.025 Kolmogorov-Smirnov 0.069 <.0001 Cramer-von Mises 1068.72 <.0001 Anderson-Darling 6193.27 <.0001 Chi-Square >1000 34 <.0001

aviman

Highlight

aviman

Highlight

Internal ED, non-holiday Mondays, 13:00-23:00

“Recall":I Arrivals processes to EDs “are" inhomogeneous Poisson

(≈ piecewise Poisson)I M/M/∞ (ample-server queue) has Poisson steady-stateI Birth-Death processes are time-reversible hence steady-state

invariant under state-conditioning

Our EDA “implies" (w/ Armony, Marmor, Tseytlin, Yom-Tov):I Israeli ED census d

= M/M/∞I ED d

= Reversible Birth-Death process, hence conditioning onfinite capacity, say B, gives rise to M/M/B/B (Erlang-B)

I U.S. ED census d= M/M/B/B, which can be (has been) used to

analyze Ambulance Diversion (ED Blocking)I Puzzle (getting ahead): Is the ED an Erlang-A system withµ = θ? then the “effective number of servers" can be, perhaps,deduced via those LWBS = Left Without Being Seen (or LAMA)

Simple models at the service of complex realities

79






= M/M/∞

I ED d= Reversible Birth-Death process, hence conditioning on

finite capacity, say B, gives rise to M/M/B/B (Erlang-B)I U.S. ED census d

= M/M/B/B, which can be (has been) used toanalyze Ambulance Diversion (ED Blocking)

I Puzzle (getting ahead): Is the ED an Erlang-A system withµ = θ? then the “effective number of servers" can be, perhaps,deduced via those LWBS = Left Without Being Seen (or LAMA)


79






= M/M/∞I ED d



analyze Ambulance Diversion (ED Blocking)

I Puzzle (getting ahead): Is the ED an Erlang-A system withµ = θ? then the “effective number of servers" can be, perhaps,deduced via those LWBS = Left Without Being Seen (or LAMA)


79






= M/M/∞I ED d



analyze Ambulance Diversion (ED Blocking)I Puzzle (getting ahead): Is the ED an Erlang-A system withµ = θ? then the “effective number of servers" can be, perhaps,deduced via those LWBS = Left Without Being Seen (or LAMA)

Simple models at the service of complex realities79

Emergency-Department Network

ImagingLaboratory

Experts

Interns


“Lost” Patients

LWBS

Nurses





Quality

Efficiency


Medicine



StretcherWalking







InternalQueue

OrthopedicQueue

Arrivals


Index

ED-StressPsychology



Returns

TriageReception





Queue

Acute,Walking


Forecasting



Home

80

Prerequisite II: Models (FNets)“Laws of Large Numbers" capture Predictable Variability

Deterministic Models: Scale Averages-out Stochastic Individualism

# Severely-Wounded Patients, 11:00-13:00 (Censored LOS)

Cleaning Data – An Example: RFID data in an MCE Drill

0

10

20

30

40

50

60

11:09 11:16 11:24 11:31 11:38 11:45 11:52 12:00 12:07 12:14 12:21 12:28 12:36 12:43 12:50 12:57 13:04 13:12 13:19 13:26

entriesexitsentries (original)exits (original)

0

5

10

15

20

25

30

11:09 11:16 11:24 11:31 11:38 11:45 11:52 12:00 12:07 12:14 12:21 12:28 12:36 12:43 12:50 12:57 13:04 13:12 13:19 13:26

number of patientsnumber of patients (original)

I Transient Q’s:I Control of Mass Casualty Events (w/ I. Cohen, N. Zychlinski)I Staffing Chemical MCE (w/ G. Yom-Tov)

81

Prerequisite II: Models (FNets)“Laws of Large Numbers" capture Predictable Variability

Deterministic Models: Scale Averages-out Stochastic Individualism

# Severely-Wounded Patients, 11:00-13:00 (Censored LOS)

Cleaning Data – An Example: RFID data in an MCE Drill

0

10

20

30

40

50

60

11:09 11:16 11:24 11:31 11:38 11:45 11:52 12:00 12:07 12:14 12:21 12:28 12:36 12:43 12:50 12:57 13:04 13:12 13:19 13:26

entriesexitsentries (original)exits (original)

0

5

10

15

20

25

30

11:09 11:16 11:24 11:31 11:38 11:45 11:52 12:00 12:07 12:14 12:21 12:28 12:36 12:43 12:50 12:57 13:04 13:12 13:19 13:26

number of patientsnumber of patients (original)

I Transient Q’s:I Control of Mass Casualty Events (w/ I. Cohen, N. Zychlinski)I Staffing Chemical MCE (w/ G. Yom-Tov)

81

The Basic Service-Network Model: Erlang-R

w/ G. Yom-Tov

Erlang-R:

Needy (s-servers)

Content (Delay)

1-p

p

1

2

Arrivals Patient discharge

Needy (st-servers)

rate- μ

Content (Delay) rate - δ

1-p

p

1

2

Arrivals Poiss(λt) Patient discharge

Erlang-R (IE: Repairman Problem 50’s; CS: Central-Server 60’s) =2-station “Jackson" Network = (M/M/S, M/M/∞) :

I λt – Time-Varying Arrival rateI St – Number of Servers (Nurses / Physicians)I µ – Service rate (E [Service] = 1

µ)

I p – ReEntrant (Feedback) fractionI δ – Content-to-Needy rate (E [Content] = 1

δ)

82

Fluid Model↔ (Time-Varying) Erlang-R System

Erlang-R:

Needy (s-servers)

Content (Delay)

1-p

p

1

2


Needy (st-servers)

rate- μ


1-p

p

1

2


FNet of a 2-station “Jackson" Network:

ddt

q1t = λt − µ ·

(q1

t ∧ st)

+ δ · q2t ,

ddt

q2t = p · µ ·

(q1

t ∧ st)− δ · q2

t .

(1)

83

Fluid Model↔ (Time-Varying) Erlang-R System

Erlang-R:

Needy (s-servers)

Content (Delay)

1-p

p

1

2


Needy (st-servers)

rate- μ


1-p

p

1

2


FNet of a 2-station “Jackson" Network:

ddt

q1t = λt − µ ·

(q1

t ∧ st)

+ δ · q2t ,

ddt

q2t = p · µ ·

(q1

t ∧ st)− δ · q2

t .

(1)

83

Erlang-R: Fitting a Simple Model to a Complex Reality

Chemical MCE Drill (Israel, May 2010)

Arrivals & Departures (RFID) Erlang-R (Fluid, Diffusion)

0

10

20

30

40

50

60

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Tota

l N

um

be

r o

f P

ati

en

ts

Time

Cumulative Arrivals

Cumulative Departures

15

20

25

30

er of M

CE Patients in ED

Actual Q(t)

Fluid Q(t)

Lower Envelope Q(t) (Theoretical)

Upper Envelope Q(t) (Theoretical)

Fluid Q1

0

5

10

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Num

be

Time

I Recurrent/Repeated services in MCE Events: eg. Injection every 15 minutes

I Fluid (Sample-path) Modeling, via Functional Strong Laws of Large NumbersI Stochastic Modeling, via Functional Central Limit Theorems

I ED in MCE: Confidence-interval, usefully narrow for ControlI ED in normal (time-varying) conditions: Personnel Staffing

84

Erlang-R: Fitting a Simple Model to a Complex Reality

Chemical MCE Drill (Israel, May 2010)

Arrivals & Departures (RFID) Erlang-R (Fluid, Diffusion)

0

10

20

30

40

50

60

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Tota

l N

um

be

r o

f P

ati

en

ts

Time

Cumulative Arrivals

Cumulative Departures

15

20

25

30

er of M

CE Patients in ED

Actual Q(t)

Fluid Q(t)

Lower Envelope Q(t) (Theoretical)

Upper Envelope Q(t) (Theoretical)

Fluid Q1

0

5

10

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Num

be

Time

I Recurrent/Repeated services in MCE Events: eg. Injection every 15 minutesI Fluid (Sample-path) Modeling, via Functional Strong Laws of Large NumbersI Stochastic Modeling, via Functional Central Limit Theorems

I ED in MCE: Confidence-interval, usefully narrow for ControlI ED in normal (time-varying) conditions: Personnel Staffing84

An Asymptotic Framework: Erlang-R in the ED

System = Emergency Department (eg. Rambam Hospital)I SimNet = Customized ED-Simulator (Marmor & Sinreich)I QNet = Erlang-R (time-varying 2-station Jackson; w/ Yom-Tov)I FNets = 2-dim dynamical system (Massey & Whitt)I DNets = 2-dim Markovian Service Net (w/ Massey and Reiman)

Asymptotic FrameworkI Data and MeasurementsI Fit a simple model (time-varying Erlang-R) to a complex reality

(ED Physicians)I Develop FNets (Offered-Load of Physicians) and (relevant) DNet

(if needed)I Use FNet / DNet for Design (√-Staffing), Analysis, . . .I Simulate reality (ED with √-staffing of Physicians)I Validation: stable performance, confidence intervals, . . .

85

An Asymptotic Framework: Erlang-R in the ED

System = Emergency Department (eg. Rambam Hospital)I SimNet = Customized ED-Simulator (Marmor & Sinreich)I QNet = Erlang-R (time-varying 2-station Jackson; w/ Yom-Tov)I FNets = 2-dim dynamical system (Massey & Whitt)I DNets = 2-dim Markovian Service Net (w/ Massey and Reiman)

Asymptotic FrameworkI Data and MeasurementsI Fit a simple model (time-varying Erlang-R) to a complex reality

(ED Physicians)I Develop FNets (Offered-Load of Physicians) and (relevant) DNet

(if needed)I Use FNet / DNet for Design (√-Staffing), Analysis, . . .I Simulate reality (ED with √-staffing of Physicians)I Validation: stable performance, confidence intervals, . . .

85

Case Study: Emergency Ward Staffing

Many-Server (↑ ∞) Approximations for Small Systems (1-7)

I Staffing resolution: 1 hourI Lower bound: 1 doctor per typeI Flexible (time-varying square-root) staffing: Yunan’s LectureI Rounding effects⇒ Not all performance levels achievable

90 Servers 1-7 Doctors

Challenges in Applications

Many server approximations; Are they good for smallsystems?

P(wait) in ED using time-varying staffing and MOLapproximation

Large systems (90 servers) Small Systems (1-7 servers)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(W

>0)

0

0.1

0.2

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115

Time [Hour]beta=0.1 beta=0.3 beta=0.5 beta=0.7 beta=1 beta=1.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

P(W

>0)

0

0.1

0.2

0 1000 2000 3000 4000 5000 6000 7000

TimeBeta=0.1 Beta=0.5 Beta=1 Beta=1.5

Average of 100 replications.

Galit Yom-Tov INFORMS 2010

Challenges in Applications

Many server approximations; Are they good for smallsystems?

P(wait) in ED using time-varying staffing and MOLapproximation

Large systems (90 servers) Small Systems (1-7 servers)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(W

>0)

0

0.1

0.2

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115

Time [Hour]beta=0.1 beta=0.3 beta=0.5 beta=0.7 beta=1 beta=1.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

P(W

>0)

0

0.1

0.2

0 1000 2000 3000 4000 5000 6000 7000

TimeBeta=0.1 Beta=0.5 Beta=1 Beta=1.5

Average of 100 replications.

Galit Yom-Tov INFORMS 2010

86

ED Patient Flow: The Physicians Viewwith J. Huang, B. Carmeli; N. Shimkin

&%'$

? ? ?

@@@@@@R

CCCCCCW

��

��

��

��

AAAAK

HHHH

HHHH

HHY�

?

66 66

-

λ01 λ0

2 λ0J

· · ·

P 0(j,k)

P (k, l)

d1 d2 dJ

m01 m0

2 m0J

Triage-Patients

IP-Patients

ExitsS

Arrivals

C1(·) C2(·) C3(·) CK(·)

m1 m2 m3 mK

· · ·

1

Goal: Adhere to Triage-Constraints, then release In-Process PatientsModels: Time-Varying (FNet) - in process; Stationary (DNet) - v. soon

87

Prerequisite II: Models (DNets, QED Q’s)

Traditional Queueing Theory predicts that Service-Quality andServers’ Efficiency must be traded off against each other.

For example, M/M/1 (single-server queue): 91% server’s utilizationgoes with

Congestion Index =E [Wait ]

E [Service]= 10,

and only 9% of the customers are served immediately upon arrival.

Yet, heavily-loaded queueing systems with Congestion Index = 0.1(Waiting one order of magnitude less than Service) are prevalent:

I Call Centers: Wait “seconds" for minutes service;I Transportation: Search “minutes" for hours parking;I Hospitals: Wait “hours" in ED for days hospitalization in IW’s.

Moreover, a significant fraction not delayed in queue: e.g. in well-runI CCs: 50% served “immediately" & 90% utilization⇒ QEDI EDs + IWs: ? Multiple scales! IW-“Beds" (10’s) are QED while

IW-Doctors (1‘s) are in conventional heavy-traffic (hours wait forminutes service), hence the bottlenecks

88





E [Service]= 10,





IW-Doctors (1‘s) are in conventional heavy-traffic (hours wait forminutes service), hence the bottlenecks

88





E [Service]= 10,




Moreover, a significant fraction not delayed in queue: e.g. in well-runI CCs: 50% served “immediately" & 90% utilization⇒ QEDI EDs + IWs: ?

Multiple scales! IW-“Beds" (10’s) are QED whileIW-Doctors (1‘s) are in conventional heavy-traffic (hours wait forminutes service), hence the bottlenecks

88





E [Service]= 10,





IW-Doctors (1‘s) are in conventional heavy-traffic (hours wait forminutes service), hence the bottlenecks88

The Basic Staffing Model: Erlang-A (M/M/N + M)agents

arrivals

abandonment

λ

µ

1

2

n

…

queue

θ

Erlang-A (Palm 1940’s) = Birth & Death Q, with parameters:

I λ – Arrival rate (Poisson)I µ – Service rate (Exponential; E [S] = 1

µ )

I θ – Patience rate (Exponential, E [Patience] = 1θ )

I N – Number of Servers (Agents).89

Erlang-A: Practical Relevance?

Experience:I Arrival process not pure Poisson (time-varying, σ2 too large)I Service times not Exponential (typically close to LogNormal)I Patience times not Exponential (various patterns observed).

I Building Blocks need not be independent (eg. long waitassociated with long service; w/ M. Reich and Y. Ritov)

I Customers and Servers not homogeneous (classes, skills)I Customers return for service (after busy, abandonment;

dependently; P. Khudiakov, M. Gorfine, P. Feigin)I · · · , and more.

Question: Is Erlang-A Relevant?

YES ! Fitting a Simple Model to a Complex Reality, bothTheoretically and Practically

90








90








90

Erlang-A: Fitting a Simple Model to a Complex Reality

Hourly Performance vs. Erlang-A Predictions (1 year)

% Abandon E[Wait] %{Wait > 0}

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Probability to abandon (Erlang−A)

Pro

babi

lity

to a

band

on (

data

)

0 50 100 150 200 2500

50

100

150

200

250

Waiting time (Erlang−A), sec

Wai

ting

time

(dat

a), s

ec

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of wait (Erlang−A)

Pro

babi

lity

of w

ait (

data

)

I Empirically-Based & Theoretically-Supported Estimation of(Im)Patience: θ = P{Ab}/E[Wq])

I Small Israeli Bank (more examples in progress)I Hourly performance vs. Erlang-A predictions, 1 year: aggregated

groups of 40 similar hours91

QED Theory (Erlang ’13; Halfin & Whitt ’81; w/Garnett & Reiman ’02)

Consider a sequence of steady-state M/M/N + M queues, N = 1, 2, 3, . . .Then the following points of view are equivalent, as N ↑ ∞:

• QED %{Cust Wait > 0} ≈ α, 0 < α < 1;

or %{Serv Idle > 0} ≈ 1− α

• Customers {Abandon} ≈ γ√N, 0 < γ;

• Agents OCC ≈ 1− β+γ√N

−∞ < β <∞ ;

• Managers N ≈ R + β√

R , R = λ× E(S) not small;

Here R = Offered Loadeg. R = 25 call/min. × 4 min./call = 100

92

Erlang-A: QED Approximations (Examples)

Assume Offered Load R not small (λ→∞).

Let β = β

√µ

θ, h(·) =

φ(·)1− Φ(·) = hazard rate of N (0,1).

I Delay Probability:

P{Wq > 0} ≈[

1 +

√θ

µ· h(β)

h(−β)

]−1

.

I Probability to Abandon:

P{Ab|Wq > 0} ≈ 1√N·√θ

µ·[h(β)− β

].

I P{Ab} ∝ E[Wq] , both order 1√N

:

P{Ab}E[Wq]

= θ (≈ g(0) > 0).

93

QED Theory vs. Data: P(Wq > 0)

IL Telecom; June-September, 2004

Empirical data: 2204 intervals of Technical category from Telecom call center

(13 summer weeks; week-days only; 30 min. resolution; excluding 6 outliers). Theoretical plot: based on approximations of Erlang-A for the proper rate.

I 2205 half-hour intervals (13 summer weeks, week-days)I Erlang-A approximations for the appropriate µ/θ ≈ 3

94

Process Limits (Queueing, Waiting)• QN = {QN(t), t ≥ 0} : stochastic process obtained by

centering and rescaling:

QN =QN −N√

N

• QN(∞) : stationary distribution of QN

• Q = {Q(t), t ≥ 0} : process defined by: QN(t)d→ Q(t).

��

�

�

� �

QN(t) QN(∞)

Q(t) Q(∞)

t → ∞

t → ∞

N → ∞ N → ∞

Approximating (Virtual) Waiting Time

VN =√N VN ⇒ V =

[1

μQ

]+(Puhalskii, 1994)

stochastic process

Waiting Time

95

QED Intuition: Why P{Wq > 0} ∈ (0, 1) ?

1. Why subtle: Consider a large service system (e.g. call center).I Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.

I Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.I ⇒ Must have both λ and N increase simultaneously:I ⇒ (CLT) Square-root staffing: N ≈ R + β

√R(

λ ≈ Nµ− β√

Nµ)

2. Erlang-A (M/M/N+M), with parameters λ, µ, θ; N, in which µ = θ:(Im)Patience and Service-times are equally distributed.

I Steady-state: L(M/M/N + M)d= L(M/M/∞)

d= Poisson(R), with

R = λ/µ (Offered-Load)I Poisson(R)

d≈ R + Z

√R, with Z d

= N(0, 1).

I P{Wq(M/M/N + M) > 0} PASTA= P{L(M/M/N + M) ≥ N} µ=θ

=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√

R}√· staffing≈ P{Z ≥ β} = 1− Φ(β).

3. QED Excursions

96


1. Why subtle: Consider a large service system (e.g. call center).I Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.I Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.

I ⇒ Must have both λ and N increase simultaneously:I ⇒ (CLT) Square-root staffing: N ≈ R + β

√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with


d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions

96


1. Why subtle: Consider a large service system (e.g. call center).I Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.I Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.I ⇒ Must have both λ and N increase simultaneously:I ⇒ (CLT) Square-root staffing: N ≈ R + β

√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with


d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions

96



√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with


d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions

96



√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with

R = λ/µ (Offered-Load)

I Poisson(R)d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions

96



√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with


d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions

96



√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with


d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions

96



√R(

λ ≈ Nµ− β√

Nµ)



d= Poisson(R), with


d≈ R + Z

√R, with Z d

= N(0, 1).


=

P{L(M/M/∞) ≥ N} ≈ P{R + Z√

R ≥ N} =

P{Z ≥ (N − R)/√


3. QED Excursions96

QED Intuition via Excursions: Busy-Idle CyclesM/M/N+M (Erlang-A) with Many Servers: N ↑ ∞M/M/N+M (Erlang-A) with Many Servers: N ↑ ∞

0 1 N-1 N N+1

Busy Period

µ 2µNµ(N-1)µ Nµ +

Q(0) = N : all servers busy, no queue.

Let TN,N−1 = Busy Period (down-crossing N ↓ N − 1 )

TN−1,N = Idle Period (up-crossing N − 1 ↑ N )

Then P (Wait > 0) =TN,N−1

TN,N−1 + TN−1,N=

[1+

TN−1,N

TN,N−1

]−1

.

Calculate TN−1,N =1

λNE1,N−1∼ 1

Nµ× h(−β)/√N

∼ 1√N

· 1/µ

h(−β)

TN,N−1 =1

Nµπ+(0)∼ 1√

N· β/µ

h(δ) /δ, δ = β

√µ/θ

Both apply as√N (1− ρN) → β, −∞ < β < ∞.

Hence, P (Wait > 0) ∼[1+

h(δ)/δ

h(−β)/β

]−1

.

1

Q(0) = N : all servers busy, no queue.

Let TN,N−1 = E[Busy Period] down-crossing N ↓ N − 1

TN−1,N = E[Idle Period] up-crossing N − 1 ↑ N )

Then P (Wait > 0) =TN,N−1

TN,N−1+TN−1,N=[1 +

TN−1,NTN,N−1

]−1.

97

QED Intuition via Excursions: Asymptotics


λNE1,N−1∼ 1

Nµ× h(−β)/√

N∼ 1√

N· 1/µ

h(−β)

TN,N−1 =1

Nµπ+(0)∼ 1√

N· β/µ

h(δ)/δ, δ = β

√µ/

Both apply as√

N(1− ρN)→ β,−∞ < β <∞.

Hence, P(Customer Wait > 0) ∼[1 +

h(δ)/δ

h(−β)/β)

]−1

, and

P(Server Wait > 0) = P(Customer Wait = 0)

Special case: µ = θ (Impatient):

Then Q d= M/M/∞, since sojourn-time is exp(µ = θ).

If also β = 0 (Prevalent): P{Wait > 0} ≈ 1/2.

98

QED Intuition via Excursions: Asymptotics


λNE1,N−1∼ 1

Nµ× h(−β)/√

N∼ 1√

N· 1/µ

h(−β)

TN,N−1 =1

Nµπ+(0)∼ 1√

N· β/µ

h(δ)/δ, δ = β

√µ/

Both apply as√

N(1− ρN)→ β,−∞ < β <∞.

Hence, P(Customer Wait > 0) ∼[1 +

h(δ)/δ

h(−β)/β)

]−1

, and

P(Server Wait > 0) = P(Customer Wait = 0)

Special case: µ = θ (Impatient):

Then Q d= M/M/∞, since sojourn-time is exp(µ = θ).

If also β = 0 (Prevalent): P{Wait > 0} ≈ 1/2.98

QED Erlang-X (Markovian Q’s: Performance Analysis)I Pre-History, 1914: Erlang (Erlang-B = M/M/n/n, Erlang-C = M/M/n)I Pre-History, 1974: Jagerman (Erlang-B)I History Milestone, 1981: Halfin-Whitt (Erlang-C, GI/M/n)I Erlang-A (M/M/N+M), 2002: w/ Garnett & ReimanI Erlang-A with General (Im)Patience (M/M/N+G), 2005: w/ ZeltynI Erlang-C (ED+QED), 2009: w/ ZeltynI Erlang-B with Retrial, 2010: Avram, Janssen, van LeeuwaardenI Refined Asymptotics (Erlang A/B/C), 2008-2011: Janssen, van Leeuwaarden,

Zhang, ZwartI Production Q’s, 2011: Reed & ZhangI Universal Erlang-A, ongoing: w/ Gurvich & HuangI Queueing Networks:

I (Semi-)Closed: Nurse Staffing (Jennings & de Vericourt), CCs with IVR (w/Khudiakov), Erlang-R (w/ Yom-Tov)

I CCs with Abandonment and Retrials: w. Massey, Reiman, Rider, StolyarI Markovian Service Networks: w/ Massey & Reiman

I Leaving out:I Non-Exponential Service Times: M/D/n (Erlang-D), G/Ph/n, · · · , G/GI/n+GI,

Measure-Valued DiffusionsI Dimensioning (Staffing): M/M/n, · · · , time-varying Q’s, V- and Reversed-V, · · ·I Control: V-network, Reversed-V, · · · , SBRNets

99

Operational Regimes: Q(uality) vs. E(fficiency)

CC in a Large Israeli Bank

P{Wq > 0} vs. (R, N) R-Slice: P{Wq > 0} vs. N

• Intercepting plane of the previous plot for a "constant" offered load (actually

18 18.5R≤ ≤ ) • Smoother line was created using smoothing splines. • General shape of the smoothing line is as the Garnett delay functions! • In 2-d view, we get the following:

3 Operational Regimes:I QD: ≤ 25%

I QED: 25%− 75%

I ED: ≥ 75%

100

Operational Regimes: Conceptual Framework

R: Offered LoadDef. R = Arrival-rate × Average-Service-Time = λ

µ

eg. R = 25 calls/min. × 4 min./call = 100

N = #Agents ? Intuition, as R or N increase unilaterally.

QD Regime: N ≈ R + δR , 0.1 < δ < 0.25 (eg. N = 115)I Framework developed in O. Garnett’s MSc thesisI Rigorously: (N − R)/R → δ, as N, λ ↑ ∞, with µ fixed.I Performance: Delays are rare events

ED Regime: N ≈ R − γR , 0.1 < γ < 0.25 (eg. N = 90)I Essentially all customers are delayedI Wait same order as service-time; γ% Abandon (10-25%).

QED Regime: N ≈ R + β√

R , −1 < β < +1 (eg. N = 100)I Erlang 1913-24, Halfin & Whitt 1981 (for Erlang-C)I %Delayed between 25% and 75%I E[Wait] ∝ 1√

N× E[Service] (sec vs. min); 1-5% Abandon.

101



µ








101



µ








101



µ







N× E[Service] (sec vs. min); 1-5% Abandon.101

Asymptotic Landscape: 9 Operational Regimes, and then someErlang-A, w/ I. Gurvich & J. Huang

Mandelbaum Part B2 / Wednesday 15th February, 2012 / 17:38 ServiceNetworks

Table 1: (Part of the) Asymptotic Landscape of Erlang-A = 9 Operational Regimes

Erlang-A Conventional scaling Many-Server scaling NDS scalingµ & θ fixed Sub Critical Over QD QED ED Sub Critical OverOffered load 1

1+δ1− β√

n1

1−γ1

1+δ1− β√

n1

1−γ1

1+δ 1− βn

11−γper server

Arrival rate λ µ1+δ

µ− β√nµ µ

1−γnµ1+δ

nµ− βµ√n nµ1−γ

nµ1+δ

nµ− βµ nµ1−γ

# servers 1 n nTime-scale n 1 n

Impatience rate θ/n θ θ/n

Staffing level λµ

(1 + δ) λµ

(1 + β√n

) λµ

(1− γ) λµ

(1 + δ) λµ

+ β√λµ

λµ

(1− γ) λµ

(1 + δ) λµ

+ β λµ

(1− γ)

Utilization 11+δ

1−√θµh(β)√n

1 11+δ


1 11+δ

1−√θµh(β)n

1

E(Q) 1δ(1+δ)

√ng(β) nµγ

θ(1−γ)1δ%n

√ng(β)α nµγ

θ(1−γ)o(1) ng(β) n2µγ

θ(1−γ)

P(Ab) 1n

1δθµ

θ√nµg(β) γ 1

n(1+δ)δ

θµ%n

θ√nµg(β)α γ o( 1

n2 ) θnµg(β) γ

P(Wq > 0) 11+δ

≈ 1 %n α ∈ (0,1) ≈ 1 ≈ 0 ≈ 1

P(Wq > T ) 11+δ

e− δ

1+δµT 1 +O( 1√

n) 1 +O( 1

n) ≈ 0 f(T ) ≈ 0 Φ(β+

√θµT )

Φ(β)1 +O( 1

n)

CongestionEWqES

1δ

√ng(β) nµγ/θ 1

n(1+δ)δ

%nα√ng(β) µγ

θo( 1n

) g(β) nµγ/θ

1

I Conventional: Ward & Glynn (03, G/G/1 + G)I Many-Server:

I QED: Halfin-Whitt (81), Garnett-M-Reiman (02)I ED: Whitt (04)I NDS: Atar (12)

I “Missing": ED+QED; Hazard-rate scaling (M/M/N+G); Time-Varying,Non-Parametric; Moderate- and Large-Deviation; Networks; Control

102

Asymptotic Landscape: 9 Operational Regimes, and then someErlang-A, w/ I. Gurvich & J. Huang

Mandelbaum Part B2 / Wednesday 15th February, 2012 / 17:38 ServiceNetworks

Table 1: (Part of the) Asymptotic Landscape of Erlang-A = 9 Operational Regimes

Erlang-A Conventional scaling Many-Server scaling NDS scalingµ & θ fixed Sub Critical Over QD QED ED Sub Critical OverOffered load 1

1+δ1− β√

n1

1−γ1

1+δ1− β√

n1

1−γ1

1+δ 1− βn

11−γper server

Arrival rate λ µ1+δ

µ− β√nµ µ

1−γnµ1+δ

nµ− βµ√n nµ1−γ

nµ1+δ

nµ− βµ nµ1−γ

# servers 1 n nTime-scale n 1 n

Impatience rate θ/n θ θ/n

Staffing level λµ

(1 + δ) λµ

(1 + β√n

) λµ

(1− γ) λµ

(1 + δ) λµ

+ β√λµ

λµ

(1− γ) λµ

(1 + δ) λµ

+ β λµ

(1− γ)

Utilization 11+δ


1 11+δ


1 11+δ

1−√θµh(β)n

1

E(Q) 1δ(1+δ)

√ng(β) nµγ

θ(1−γ)1δ%n

√ng(β)α nµγ

θ(1−γ)o(1) ng(β) n2µγ

θ(1−γ)

P(Ab) 1n

1δθµ

θ√nµg(β) γ 1

n(1+δ)δ

θµ%n

θ√nµg(β)α γ o( 1

n2 ) θnµg(β) γ

P(Wq > 0) 11+δ

≈ 1 %n α ∈ (0,1) ≈ 1 ≈ 0 ≈ 1

P(Wq > T ) 11+δ

e− δ

1+δµT 1 +O( 1√

n) 1 +O( 1

n) ≈ 0 f(T ) ≈ 0 Φ(β+

√θµT )

Φ(β)1 +O( 1

n)

CongestionEWqES

1δ

√ng(β) nµγ/θ 1

n(1+δ)δ

%nα√ng(β) µγ

θo( 1n

) g(β) nµγ/θ

1

I Conventional: Ward & Glynn (03, G/G/1 + G)I Many-Server:

I QED: Halfin-Whitt (81), Garnett-M-Reiman (02)I ED: Whitt (04)I NDS: Atar (12)

I “Missing": ED+QED; Hazard-rate scaling (M/M/N+G); Time-Varying,Non-Parametric; Moderate- and Large-Deviation; Networks; Control

102

Universal Approximations: Erlang-A (M/M/N + M)agents

arrivals

abandonment

λ

µ

1

2

n

…

queue

θ

w/ I. Gurvich & J. Huang

I QNet: Birth & Death Queue, with B - D rates

F (q) = λ− µ · (q ∧ n)− θ · (q − n)+, q = 0,1, . . .

I FNet: Dynamical (Deterministic) System – ODEdxt = F (xt )dt , t ≥ 0

I DNet: Universal (Stochastic) Approximation – SDE

dYt = F (Yt )dt +√

2λ dBt , t ≥ 0

eg. µ = θ : x = λ− µ · x , Y = OU process

Accuracy increases as λ ↑ ∞ (no additional assumptions)

103


arrivals

abandonment

λ

µ

1

2

n

…

queue

θ



F (q) = λ− µ · (q ∧ n)− θ · (q − n)+, q = 0,1, . . .




2λ dBt , t ≥ 0



103


arrivals

abandonment

λ

µ

1

2

n

…

queue

θ



F (q) = λ− µ · (q ∧ n)− θ · (q − n)+, q = 0,1, . . .




2λ dBt , t ≥ 0



103


arrivals

abandonment

λ

µ

1

2

n

…

queue

θ



F (q) = λ− µ · (q ∧ n)− θ · (q − n)+, q = 0,1, . . .




2λ dBt , t ≥ 0



103


arrivals

abandonment

λ

µ

1

2

n

…

queue

θ



F (q) = λ− µ · (q ∧ n)− θ · (q − n)+, q = 0,1, . . .




2λ dBt , t ≥ 0


Accuracy increases as λ ↑ ∞ (no additional assumptions)103

Value of Universal Approximation

I Tractable - closed-form stable expressionsI Accurate - more than heavy traffic limitsI Robust - all many-server regimes, and beyond, with hardly any

assumptionsI Value

I Performance AnalysisI Optimization (Staffing)I Inference (w/ G. Pang)I Simulation (w/ J. Blanchet)

I Limitation: Steady-State (but working on it)

Why does it work so well?

Coupling “Busy" + “Idle" Excursions of B&D and the correspondingDiffusion (durations order 1√

λ)

104

Universal Diffusion: Tractability

I Density function of Y (∞)− n:

π(x) =

√µ√λ

φ(√µ(x/

√λ+β/µ))

Φ(β/√µ) p(β, µ, θ), if x ≤ 0,

√θ√λ

φ(√θ(x/√λ+β/θ))

1−Φ(β/√θ)

(1− p(β, µ, θ)), if x > 0,

Here β := (nµ− λ)/√λ

and

p(β, µ, θ) =

[1 +

√µ

θ

φ(β/√µ)

Φ(β/√µ)

1− Φ(β/√θ)

φ(β/√θ)

]−1

.

105

Universal Approximation: Accuracy

I ∆λ is the “balancing" state, obtained by solving

λ = µ(n ∧∆λ) + θ(∆λ − n)+.

Solution: ∆λ = λµ −

(λµ − n

)+ (1− µ

θ

).

Specifically: QD = λµ ; ED = n + 1

θ (λ− nµ); QED = n +O(√λ))

I Centered processes (excursions):

Qλ(·) = Q(·)−∆λ, Yλ(·) = Y (·)−∆λ.

TheoremFor f bounded by an m-degree polynomial (m ≥ 0):

Ef (Qλ(∞))− Ef (Yλ(∞)) = O(√λ

m−1).

I Accuracy: higher than heavy-traffic limits

106

Universal Approximation: Accuracy

I ∆λ is the “balancing" state, obtained by solving

λ = µ(n ∧∆λ) + θ(∆λ − n)+.

Solution: ∆λ = λµ −

(λµ − n

)+ (1− µ

θ

).

Specifically: QD = λµ ; ED = n + 1

θ (λ− nµ); QED = n +O(√λ))

I Centered processes (excursions):

Qλ(·) = Q(·)−∆λ, Yλ(·) = Y (·)−∆λ.

TheoremFor f bounded by an m-degree polynomial (m ≥ 0):

Ef (Qλ(∞))− Ef (Yλ(∞)) = O(√λ

m−1).

I Accuracy: higher than heavy-traffic limits106

Universal Approximation: Why 2λ?

I Semi-martingale representation of the B&D process:Fluid + Martingale

I Predictable quadratic variation:∫ t

0[λ+ µ(Qs ∧ n) + θ(Qs − n)+]ds

I In steady-state, arrival rate ≡ departure rate:

λ = E[µ(Qs ∧ n) + θ(Qs − n)+]

I Expectation of the predictable quadratic variation:

E∫ t

0[λ+ µ(Qs ∧ n) + θ(Qs − n)+]ds = 2λt

I dMartingalet ≈√

2λ · dBrowniant

107

Reconciling Steady-State and Time-Varying ModelsI Challenge: Accommodate time-varying demand (routine)I Prerequisite: Flexible Capacity

I As in Call Centers and to a degree in Healthcare,I In contrast to rigid (fixed) staffing level during a shift: doomed to

alternate between overloading and underloading

I Idea/Goal: In the face of time-varying demand, designtime-varying staffing which accommodates demand such thatperformance is stable over time

I Solution: In fact, a time-varying system with Steady-Stateperformance, at all times, via (Modified) Offered-Load(Square-Root) Staffing.

I History:I Jennings, M., Reiman, Whitt (1996): Emergence of the

phenomenon, via infinite-server heuristicsI Feldman, M., Massey, Whitt (2008): Stabilize delay probability via

QED staffing (justified theoretically only for Erlang-A with µ = θ)I Liu and Whitt (ongoing): Stabilize abandonment probability by ED

staffing, via a corresponding network, theoretically and empiricallyI Huang, Gurvich, M. (ongoing): QED theory

108



alternate between overloading and underloadingI Idea/Goal: In the face of time-varying demand, design

time-varying staffing which accommodates demand such thatperformance is stable over time






108



alternate between overloading and underloadingI Idea/Goal: In the face of time-varying demand, design

time-varying staffing which accommodates demand such thatperformance is stable over time






108

The Offered-Load R(t), t ≥ 0 (R(t)↔ R)

Empirically (in SEEStat):I Process: L(·) = Least number of servers that guarantees no delay.I Offered-Load Function R(·) = E [L(·)]

ILTelecom , Private12.05.2004

0.005.00

10.0015.0020.0025.0030.0035.0040.0045.0050.0055.0060.00

07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


Num

ber o

f cas

es

Offered load Abandons Av_agents_in_system

109

The Offered-Load R(t), t ≥ 0 (R(t)↔ R)

Empirically (in SEEStat):I Process: L(·) = Least number of servers that guarantees no delay.I Offered-Load Function R(·) = E [L(·)]

ILTelecom , Private12.05.2004

0.005.00

10.0015.0020.0025.0030.0035.0040.0045.0050.0055.0060.00

07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


Num

ber o

f cas

es

Offered load Abandons Av_agents_in_system

109

Time-Varying Arrival Rates

Square-Root Staffing:N(t) = R(t) + β

√R(t) , −∞ < β <∞.

R(t) is the Offered-Load at time t ( R(t) 6= λ(t)× E[S] )

Arrivals, Offered-Load and Staffing

0

50

100

150

200

250

0 1 2 4 5 6 7 8

10

11

12

13

14

16

17

18

19

20

22

23

0

500

1000

1500

2000

Arr

iva

ls p

er

ho

ur

beta 1.2 beta 0 beta -1.2 Offered Load Arrivals

QDQED

ED

110

Time-Stable Performance of Time-Varying Systems

Delay Probability = as in the Stationary Erlang-A / RDelay Probability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 1 2 4 5 6 7 8

10

11

12

13

14

16

17

18

19

20

22

23

beta 2 beta 1.6 beta 1.2 beta 0.8 beta 0.4 beta 0

beta -0.4 beta -0.8 beta -1.2 beta -1.6 beta -2

111

Time-Stable Performance of Time-Varying SystemsWaiting Time, Given Waiting:

Empirical vs. Theoretical Distribution

Waiting Time given Wait > 0:

beta = 1.2 QD ( 0.1)

0

0.05

0.1

0.15

0.2

0.25

0.0

00

0.0

02

0.0

04

0.0

06

0.0

08

0.0

10

0.0

12

0.0

14

0.0

16

0.0

18

0.0

20

ho

urs

Simulated Theoretical (N=191)


beta = 0 QED ( 0.5)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.0

00

0.0

02

0.0

04

0.0

06

0.0

08

0.0

10

0.0

12

0.0

14

0.0

16

0.0

18

0.0

20

0.0

22

0.0

24

0.0

26

0.0

28

ho

urs



beta = -1.2 ED ( 0.9)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.0

00

0.0

04

0.0

08

0.0

12

0.0

16

0.0

20

0.0

24

0.0

28

0.0

32

0.0

36

0.0

40

0.0

44

ho

urs


- Empirical: Simulate time-varying Mt/M/Nt + M(λ(t),N(t) = R(t) + β

√R(t))

- Theoretical: Naturally-corresponding stationary Erlang-A, with QEDβ-staffing (some Averaging Principle?)

- Generalizes up to a single-station within a complex network (eg.Doctors in an Emergency Department, modeled as Erlang-R).

112

Calculating the Offered-Load R(t), Theoretically

I Offered-Load Process: L(·) = Least number of servers thatguarantees no delay.

I Offered-Load Function R(t) = E [L(t)], t ≥ 0.Think Mt/G/N?

t + G vs. Mt/G/∞: Ample-Servers.

Four (all useful) representations, capturing “workload before t":

R(t) = E [L(t)] =

∫ t

−∞λ(u) · P(S > t − u)du = E

[A(t)− A(t − S)

]=

= E[∫ t

t−Sλ(u)du

]= E [λ(t − Se)] · E [S] ≈ ... .

I {A(t), t ≥ 0} Arrival-Process, rate λ(·);I S (Se) generic Service-Time (Residual Service-Time).I Relating L, λ,S (“W ”): Time-Varying Little’s Formula.

Stationary models: λ(t) ≡ λ then R(t) ≡ λ× E[S].

QED-c: Nt = Rt + βRct , 1/2 ≤ c < 1; (c = 1 separate analysis).

113






R(t) = E [L(t)] =

∫ t

−∞λ(u) · P(S > t − u)du = E

[A(t)− A(t − S)

]=

= E[∫ t

t−Sλ(u)du

]= E [λ(t − Se)] · E [S] ≈ ... .

I {A(t), t ≥ 0} Arrival-Process, rate λ(·);I S (Se) generic Service-Time (Residual Service-Time).

I Relating L, λ,S (“W ”): Time-Varying Little’s Formula.Stationary models: λ(t) ≡ λ then R(t) ≡ λ× E[S].


113






R(t) = E [L(t)] =

∫ t

−∞λ(u) · P(S > t − u)du = E

[A(t)− A(t − S)

]=

= E[∫ t

t−Sλ(u)du

]= E [λ(t − Se)] · E [S] ≈ ... .




113






R(t) = E [L(t)] =

∫ t

−∞λ(u) · P(S > t − u)du = E

[A(t)− A(t − S)

]=

= E[∫ t

t−Sλ(u)du

]= E [λ(t − Se)] · E [S] ≈ ... .




113

Estimating / Predicting the Offered-Load

Must account for “service times of abandoning customers".

I Prevalent Assumption: Services and (Im)Patience independent.I But recall Patient VIPs: Willing to wait longer for more services.

Survival Functions by Type (Small Israeli Bank)

31

Service Time (cont’)Survival curve, by types

Time

Surv

ival

Service times stochastic order: SNew

st< SReg

st< SVIP

Patience times stochastic order: τNew

st< τReg

st< τVIP

114

Dependent Primitives: Service- vs. Waiting-Time

Average Service-Time as a function of Waiting-TimeU.S. Bank, Retail, Weedays, January-June, 2006

Introduction Relationship Between Service Time and Patience Workload and Offered-Load Empirical Results Future Research

Motivation

Mean Service-Time as a Function of Waiting-TimeU.S. Bank - Retail Banking Service - Weekdays - January-June, 2006

190

210

230

250

270

290

150

170

190

210

230

250

270

290

0 50 100 150 200 250 300

Waiting Time

Fitted Spline Curve E(S|τ>W=w)

⇒ Focus on ( Patience, Service-Time ) jointly , w/ Reich and Ritov.E [S |Patience = w ], w ≥ 0: Service-Time of the Unserved.

115

Dependent Primitives: Service- vs. Waiting-Time

Average Service-Time as a function of Waiting-TimeU.S. Bank, Retail, Weedays, January-June, 2006

Introduction Relationship Between Service Time and Patience Workload and Offered-Load Empirical Results Future Research

Motivation

Mean Service-Time as a Function of Waiting-TimeU.S. Bank - Retail Banking Service - Weekdays - January-June, 2006

190

210

230

250

270

290

150

170

190

210

230

250

270

290

0 50 100 150 200 250 300

Waiting Time

Fitted Spline Curve E(S|τ>W=w)

⇒ Focus on ( Patience, Service-Time ) jointly , w/ Reich and Ritov.E [S |Patience = w ], w ≥ 0: Service-Time of the Unserved.

115

(Imputing) Service-Times of Abandoning Customers

w/ M. Reich, Y. Ritov:

1. Estimate g(w) = E [S |Patience > Wait = w ], w ≥ 0:Mean service time of those served after waiting exactly w unitsof time (via non-linear regression: Si = g(Wi ) + εi );

2. Calculate

E [S |Patience = w ] = g(w)− g′(w)

hτ (w);

hτ (w) = hazard-rate of (im)patience (via un-censoring);

3. Offered-load calculations: Impute E [S |Patience = w ](or the conditional distribution).

Challenges: Stable and accurate inference of g,g′,hτ .

116

Extending the Notion of the “Offered-Load"

I Business (Banking Call-Center): Offered Revenues

I Healthcare (Maternity Wards): Fetus in stressI 2 patients (Mother + Child) = high operational and cognitive loadI Fetus dies⇒ emotional load dominates

I ⇒I Offered Operational Load

I Offered Cognitive Load

I Offered Emotional Load

I ⇒ Fair Division of Load (Routing) between 2 Maternity Wards:One attending to complications before birth, the other tocomplications after birth, and both share normal birth

117

Server Networksw/ A. Senderovic: Planning

then joined A. Gal, M. Weid, Y. Goldberg: Process Mining

ILDUBank January 24, 2010 Agent #043 Shift: 16:00 - 23:45

Inbound Call-Backs

Outgoing

Available Idle

Private Call

Break

I As Challenging - in theory and practice - as Customer NetworksI Uncharted territory: e.g. Gnedenko/Palm’s Machine Repair model,

Armony and Ward (Asymptotic Little & ASTA)118

Individual Agents: Service-Duration, Variabilityw/ Gans, Liu, Shen & Ye

Agent 14115

Service-Time Evolution: 6 month Log(Service-Time)

I Learning: Noticeable decreasing-trend in service-durationI LogNormal Service-Duration, individually and collectively

119

Individual Agents: Learning, Forgetting, Switching

Daily-Average Log(Service-Time), over 6 monthsAgents 14115, 14128, 14136

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

0 20 40 60 80 100 120 1404.2

4.4

4.6

4.8

5.0

5.2

5.4

Day IndexM

ean

Log(

Ser

vice

Tim

e)

a 102−day break

0 20 40 60 80 100

4.4

4.6

4.8

5.0

5.2

5.4

5.6

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

switch to Online Banking after 18−day break

0 50 100 150

4.5

5.0

5.5

6.0

Weakly Learning-Curves for 12 Homogeneous(?) Agents

5 10 15 20

34

56

Tenure (in 5−day week)

Ser

vice

rat

e pe

r ho

ur

120

Individual Agents: Learning, Forgetting, Switching

Daily-Average Log(Service-Time), over 6 monthsAgents 14115, 14128, 14136

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

0 20 40 60 80 100 120 1404.2

4.4

4.6

4.8

5.0

5.2

5.4

Day IndexM

ean

Log(

Ser

vice

Tim

e)

a 102−day break

0 20 40 60 80 100

4.4

4.6

4.8

5.0

5.2

5.4

5.6

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

switch to Online Banking after 18−day break

0 50 100 150

4.5

5.0

5.5

6.0

Weakly Learning-Curves for 12 Homogeneous(?) Agents

5 10 15 20

34

56

Tenure (in 5−day week)

Ser

vice

rat

e pe

r ho

ur

120

Tele-Service Process (Beyond present SEE Data)

RetailService(IsraeliBank)

StatisticsORIEPsychol.MIS

START

Hello14 / 20

I.D.24 / 23Request

15 / 8

Stock17 / 21

Question14 / 20

Password creation62 / 42

Processing49 / 24

Confirmation29 / 9

Answer32 / 19

END202/190

Dead time18 / 17

Paperwork22 / 12

End of call5 / 3

Credit34 / 32

Others21 / 21

Checking21 / 9

1

0.65

0.050.27

0.950.03

0.62

0.29

0.17

0.28

0.17

0.11

0.05

0.05 0.17

0.23 0.08

0.38

0.15

0.15

0.93

0.14

0.03

0.5

0.03 0.26

0. 4

0.23

0.590.09

0.05

0.67

0.11

0.17

0.67

0.330.7

0.25

0.66

0.43

0.57

0.130.2

0.93

0.04

0. 6

Password creation62 / 42

0.67

0.33

STDAVG

121

Why Bother?I Server Networks: Unchartered Research TerritoryI In large call centers:

+One Second to Service-Time implies +Millions in costs,annually

⇒ Time and "Motion" Studies (Classical IE with New-age IT)

I Service-Process Model: Customer-Agent InteractionI Work Design (w/ Khudiakov)

eg. Cross-Selling: higher profit vs. longer (costlier) services;Analysis yields (congestion-dependent) cross-selling protocols

I “Worker" Design (w/ Gans, Liu, Shen & Ye)eg. Learning, Forgetting, . . . : Staffing & individual-performanceprediction, in a heterogenous environment

I IVR-Process Model: Customer-Machine Interaction75% bank-services, poor design, yet scarce research;Same approach, automatic (easier) data (w/ N. Yuviler)

122








122








122

ServNets: Data-Based Online Automatic Creationw/ V. Trofimov, E. Nadjharov, I. Gavako = Technion SEELab

I ServNets = QNets, SimNets, FNets, DNets

I SimNets of Service Systems = Virtual Realities

I SimNets also of QNEts, FNets, DNetseg. ED MD (Physics): Where are the Differential Equations?

I Ultimately: Research Labs, offering universal access to dataand ServNets, will become necessary (hence must be funded!)

I Data-based Research: Tradition in Physics, Chemistry, Biology;Psychology (now also in Transportation (Science) and(Behavioral) Economics)

I Why not in Service Science / Engineering / Management ?I Moreover, address the Reproducibility Crisis in Scientific

Research (Computation, Massive-data, . . .)

123








Research (Computation, Massive-data, . . .)

123







I Why not in Service Science / Engineering / Management ?

I Moreover, address the Reproducibility Crisis in ScientificResearch (Computation, Massive-data, . . .)

123








Research (Computation, Massive-data, . . .)123

Data-Based Creation ServNets: some Technicalities

I ServNets = QNets, SimNets, FNets, DNetsI Graph Layout: Adapted from but significantly extends Graphviz

(AT&T, 90’s); eg. edge-width, which must be restricted topoly-lines, since there are “no parallel Bezier (Cubic) curves(Bn(p) = EpF [B(n,p)],0 ≤ p ≤ 1)

I Algorithm: Dot Layout (but with cycles), based on Sugiyama,Tagawa, Toda (’81): “Visual Understanding of HierarchicalSystem Structures"

I Draws data directly from SEELab data-bases:I Relational DBs (Large! eg. USBank Full Binary = 37GB, Summary

Tables = 7GB)I Structure: Sequence of events/states, which (due to size)

partitioned (yet integrated) into days (eg. call centers) or months(eg. hospitals)

I Differs from industry DBs (in call centers, hospitals, websites)

124

Data-Based Creation ServNets: some Technicalities

I ServNets = QNets, SimNets, FNets, DNetsI Graph Layout: Adapted from but significantly extends Graphviz

(AT&T, 90’s); eg. edge-width, which must be restricted topoly-lines, since there are “no parallel Bezier (Cubic) curves(Bn(p) = EpF [B(n,p)],0 ≤ p ≤ 1)

I Algorithm: Dot Layout (but with cycles), based on Sugiyama,Tagawa, Toda (’81): “Visual Understanding of HierarchicalSystem Structures"

I Draws data directly from SEELab data-bases:I Relational DBs (Large! eg. USBank Full Binary = 37GB, Summary

Tables = 7GB)I Structure: Sequence of events/states, which (due to size)

partitioned (yet integrated) into days (eg. call centers) or months(eg. hospitals)

I Differs from industry DBs (in call centers, hospitals, websites)

124

Documents

Data-Based Service Networks - Technionie.technion.ac.il/serveng/References/0_SAMSI_Workshop.pdf · Data-Based Service Networks: A Research Framework for Asymptotic Inference, Analysis