Exploi'ng  Mobility  in  Propor'onal  Fair  Cellular  Scheduling:  Measurements  and  Algorithms  

Robert  Margolies1,  Ashwin  Sridharan2,    Vaneet  Aggarwal2,  Ri8wik  Jana2,  Vinay  Vaishampayan2,    

N.  K.  Shankaranarayanan2,  and  Gil  Zussman1  

 1  Columbia  University,  New  York,  NY  

2  AT&T  Labs  -­‐    Research,  Florham  Park,  NJ  

Mobile  Scheduling  in  Cellular  Networks  

•  Cellular  users  are  constantly  on  the  move,  many  Omes  with  predictable  mobility  (i.e.,  buses,  trains,  commuOng,  etc)  

 •  ExisOng  scheduling  algorithms  do  not  take  predictable  

mobility  into  account  

We  develop  a  cellular  scheduling  framework  to  leverage  cases  with  predictable  mobility  

Cellular  Scheduling  Background  •  3G  UMTS  Cellular  Network  –  WCDMA  •  Pilot  signals  used  to  esOmate  the  

channel  quality  (Ec/Io)  for  each  basestaOon  

Sector 1

Ec/Io:1

Pilot-1

Pilot-2

Ec/Io:2 Ec/Io:3

Pilot-3

Sector 2

Sector 3

Start

Time Slot 1 2 3 4 5 6 Allocation for User 0 1 1 1 0 0

Sign

al S

treng

th, E

c/Io

Measured  Immobile  User  –  Fast  Fading  

Time (s)

0 1000 2000 3000 4000 5000ï25

ï20

ï15

ï10

ï5Sector 1 Sector 2 Sector 3

Distance (m)

Sign

al Q

ualit

y, E

c/I o (dB

)

Drive 1Drive 2Drive 3

Distance (m)

Sign

al S

treng

th, E

c/Io

Measured  Mobile  User  -­‐    Slow  Fading  Sector 1 Sector 2 Sector 3

Finish

[1]  M.  Andrews,  L.  Qian,  and  A.  Stolyar.  OpOmal  uOlity  based  mulO-­‐user  throughput  allocaOon  subject  to  throughput  constraints.  In  Proc.  IEEE  INFOCOM’05,  Mar.  2005.    [2]  A.  Stolyar.  On  the  asymptoOc  opOmality  of  the  gradient  scheduling  algorithm  for  mulOuser  throughput  allocaOon.  Opera4ons  Research,  53:12–25,  2005.  

Finite  ProporOonal  Fair  (FPF)  Scheduling  max↵ C =

XK

i=1log(

XT

j=1↵ijrij)

subject to

XK

i=1↵ij = 1 8j = 1 . . . T

↵ij 2 {0, 1}.

•  Follows  [1,2]  but  has  a  finite  4me  horizon    •  Users  always  have  data  to  send  •  T  slot  Ome  horizon  •  K  users  •  rij  is  the  feasible  data  rate  for  user  i  in  slot  j •  αij= 1 for  the  scheduled  user  i  in  slot  j

1 2 3 4 5 .  .  .  .  .    T

1 5 6 4 8 6

2 2 3 4 1 2

3 1 4 3 4 5 .  .  .    K

User  i

Time  Slot  j  

Data  Rate, rij (Mbps)  

Scheduling  Decisions    

αij =1

αij =0

(User  scheduled)  

•  Exploits  fast  fading  and  mulO-­‐user  diversity  •  Ri[j]  is  the  exponenOal  average  of  user  i’s  throughput  at  slot  j

Deployed  ProporOonal  Fair  Scheduler  

[3]  M.  Andrews.  Maximizing  profit  in  overloaded  networks.  In  Proc.  IEEE  INFOCOM’05,  Mar.  2005.  

Sign

al S

treng

th, E

c/Io

Measured  Immobile  User  –  Fast  Fading  

Time (s)

OpOmal  for  long  associaOon  Omes  with  staOonary  channel  condiOons  

ExponenOal  ProporOonal    Fairness  Algorithm  (PF-­‐EXP)    

0 1000 2000 3000 4000 5000ï25

ï20

ï15

ï10

ï5Sector 1 Sector 2 Sector 3

Distance (m)

Signal

Qual

ity, E

c/I o (dB)

Drive 1Drive 2Drive 3

Sign

al S

treng

th, E

c/Io

Measured  Mobile  User  -­‐    Slow  Fading  Sector 1 Sector 2 Sector 3

Distance (m)

Not  opOmal  for  mobile  scenarios  [3]  

PredicOve  FPF  SoluOon  Framework  •  Consider  the  gradient  of  the  cost  funcOon:    

•  Requires  past,  present,  and  future  knowledge  of  channel  rate  and  scheduled  alloca4ons  

•  Online  Scheduling  Framework  

EsOmate  Future  Channel  Rates      

EsOmate  Future  Channel  AllocaOons  

   

Online  Scheduler  for  Ome  slots  1  to  T:  

schedule  the  user  with  the  highest  gradient  

Outline  

EsOmate  Future    Channel  Rates  

     

EsOmate  Future  Channel  AllocaOons  

     

Framework  EvaluaOon    

Online  Scheduler  for  Ome  slots  1  to  T:  schedule  the  user  with  

the  highest  gradient  {rij}K⇥T {↵ij}K⇥Trij

j�1X

t=1

↵itrit + ↵ijrij +TX

t=j+1

↵itrit

Experimental  Measurement  Campaign        

Measurement  Campaign  

•  Qualcomm  Toolkit  (QXDM)  •  Measuring  parameters  from  

physical  layer  of  smartphone  •  Fine  granularity  (milliseconds)  •  3G  data  network  Control,

Monitoring, and Logging System

Samsung Galaxy Phone

USB Connection

Courtesy  of  Google  Maps  

Summary  of  Measurements  

•  4  separate  drive  routes  •  1  set  of  non-­‐mobile  

tests    

Route  1  10  drives  

10  km  

Route  2  4  Drives  

Route  3  6  Drives  

Route  4  7  Drives  

Rob’s  Place   AT&T  

•  Significant  data  set  logged  v ~1400  minutes  v 810km  distance  traveled  v ~522  serving  sectors  v 3+GB  of  data  

Measurements  •  Received  Signal  Strength  Indicator  (RSSI):  Total  in-­‐band  power  •  Received  Signal  Code  Power  (RSCP):  Total  power  in  each  pilot  

channel  •  Ec/Io:  EffecOve  signal  to  noise  raOo  for  pilot  channel  

–  Ec/Io(dB) = RSSI(dBm) – RSCP (dBm) R

SSI (

dBm

)

RSC

P (d

Bm

)

Ec/Io

(dB

)

Freq

uenc

y

Association Time (s)

Modeling  Slow  Fading  •  Developed  a  slow-­‐fading  metric  

 •  Slow-­‐fading  showed  li8le  correlaOon    

to  line-­‐of-­‐sight  parameters  

11  

0 10 20 300

0.05

0.1

0.15

0.2

0.25

Average Velocity (m/s)

Slow

ïFad

ing,

S

PT

j=1 Ec

/Io

[j]2/T

Slow

-Fad

ing

Met

ric

Static Rt. 1 Rt. 2 Rt. 3 Rt. 4

3000 3500 4000 4500ï30

ï20

ï10

0

Distance Along Route (m)

E c/I o (dB

)

Start

Finish Sign

al S

treng

th, E

c/Io

Reproducibility  of  Slow  Fading  

Start   Finish  

Outline  

EsOmate  Future    Channel  Rates  

     

EsOmate  Future  Channel  AllocaOons  

     

Framework  EvaluaOon    

Online  Scheduler  for  Ome  slots  1  to  T:  schedule  the  user  with  

the  highest  gradient  {rij}K⇥T {↵ij}K⇥Trij

j�1X

t=1

↵itrit + ↵ijrij +TX

t=j+1

↵itrit

Experimental  Measurement  Campaign        

LocalizaOon  using  Dynamic  Time  Warping  

Sign

al S

treng

th

His

tory

Time

Sign

al S

treng

th

Patte

rn o

f Rou

te

Distance Along Route

LocalizaOon  using  Dynamic  Time  Warping  c(b, j) = (RSSI[j]� RSSIhbi)2+X

u2Ub

(Ec

/Io

u

[j]� Ec

/Io

u

hbi)2 + (RSCPu

[j]� RSCPu

hbi)2

Dynamic  programming  soluOon    •  Leverages  predictable  mobility  •  RSSI  –  Received  Signal  Strength  •  RSCP  –  Received  Signal  Code  Power  •  Ec/Io –  EffecOve  signal  to  noise    raOo  for  pilot  channel  

LocalizaOon  Error  (m)  Freq

uency  

Coverage  Map  PredicOon  Mechanism  

•  Leverages  predictable  route  trajectory  •  Uses  locaOon  and  velocity  from  localizaOon  scheme  •  Extrapolates  current  velocity  for  T  Ome  slots    •  Determine  future  grid  locaOons  •  Coverage  map  used  to  map  locaOon  into  feasible  data  rate.  

Coverage Map Grid (25m x 25m) 0 5 10 150

5

10

15

20

Time (s)

Dat

a Ra

tes (

Mbp

s)

ActualPredictedLocaOon+  

Velocity  

Outline  

EsOmate  Future    Channel  Rates  

     

EsOmate  Future  Channel  AllocaOons  

     

Framework  EvaluaOon    

Online  Scheduler  for  Ome  slots  1  to  T:  schedule  the  user  with  

the  highest  gradient  {rij}K⇥T {↵ij}K⇥Trij

j�1X

t=1

↵itrit + ↵ijrij +TX

t=j+1

↵itrit

Experimental  Measurement  Campaign        

Channel  AllocaOon  (α)  EsOmaOon  HeurisOcs  

•  Round  Robin  EsOmaOon  (RRE):  Each  user  receives  and  equal  fracOon  of  each  Ome  slot  

•  Blind  Gradient  EsOmaOon  (BGE):  In  each  slot  j,  select  a  user  using  the  gradient  with  no  future  component  

•  Local  Search  EsOmaOon  (LSE):  Begin  with  a  random  allocaOon  and  conOnue  swapping  to  improve  the  cost  funcOon  

Framework  Performance  EvaluaOon  •  Test  cases  generated  from  random  segments  of  measured  traces  

 •  Benchmarks  

v Numerical  Solver  (CVX)  –  solves  convex  relaxaOon  without  integer  constraints  on  α.  

v Deployed  Scheduler  (PF-­‐EXP)  

0 10 20 300

2

4

6

8 x 106

Time (s)

r ijD

ata

Rat

es (M

bps)

Test  Case  Example  

Time (s)

Fairness  and  Throughput  Results  

Clairvoyant Using GPS Using Warping

Fairness  gains  confirm  we  are  improving  overall  network  fairness  in  addiOon  to  throughput  

Rate  predicOon    mechanisms  

Channel  allocaOon  heurisOcs  

Clairvoyant Using GPS Using Warping

Fairness  and  Throughput  Results  

Rate  predicOon    mechanisms  

Channel  allocaOon  heurisOcs  

Network  throughput  improvements  of  15  to  55%  over  exisOng  scheduling  algorithm  

0 0.2 0.4 0.6

0.2

0.4

0.6

0.8

1

Delay (s)

CD

F

ClairvoyauntCMPMïGPSCMPMïCHLSPFïEXP

Fairness  and  Throughput  Results  

Network  throughput  improvements  of  15  to  55%  over  exisOng  scheduling  algorithm  

Clairvoyant Using GPS Using Warping PF-EXP

SensiOvity  Results  

Performance  improves  with  number  of  users,  K

3 5 7 101

1.01

1.02

1.03

Fairn

ess G

ains

Number of Users, K1

1.25

1.5

1.75

Thh

tGi

FairnessThroughput

Fairn

ess G

ains

Thro

ughp

ut G

ains

SensiOvity  Results  

Performance  improves  with  Ome  horizon,  T

5 15 30 601

1.01

1.02

1.03

1.04

Fairn

ess G

ains

Time Horizon, T (s)1

1.25

1.5

1.75

2

2.25

Thh

tGi

FairnessThroughput

Fairn

ess G

ains

Thro

ughp

ut G

ains

Conclusions  •  Proposed  a  predicOve  scheduling  framework    •  Characterized  the  repeatability  of  mobility  through  an  

extensive  channel  measurement  campaign  •  Developed  a  localizaOon  scheme  uOlizing  user  channel  quality  

history  •  Evaluated  the  framework’s  performance  using  traces  

collected  from  an  operaOonal  3G  network  and  demonstrated  throughput  improvements  of  15-­‐55%  

•  Extendable  for  4G  scheduling  models    •  Contact  Info  

v Robert  Margolies  v robm@ee.columbia.edu