Lecture 17. ATM VPs, circuit-switching

D. Moltchanov, TUT, Spring 2008

D. Moltchanov, TUT, Spring 2015

OutlineATM virtual path designTelephone network: single BHTelephone network: multiple BH

ATM virtual path design

ATM virtual path designAsynchronous transfer mode (ATM)

Concept of virtual paths (VP) and virtual circuits (VC)VP: permanent/semi-permanent connectionsSeveral VC multiplexed into one VPSimilar to MPLS but completely separate from IP networkStill used mainly in US

Could be: IP/ATM/SONET or something like this…

ATM virtual path designProblem we consider

Analysis is as usualGet demands constraints: how demands are realized over pathGet capacity constraints: which flows are using links (link loads)

Analyzing the problemWe have set of paths for demand d: Unsplittable (non-bifurcated) solution is neededWe need a binary variable Tells us whether a path is chosen or not

which gives us demand constraint

How to determine the link capacity such that the total link cost is minimized given a set of unsplittable demands and modular link units of 155Mbps?

{0,1}dpu

1,2, , dp P

1

1, 1,2, ,dP

dpp

u d D

ATM virtual path designContinuing

Total number of VPs using link e

At most one flow will use link e for each demand due to

If a flow uses link then full demand is realized over this linkThe link load is then

Assume that demand volume and link rates are in units of 155Mbps

where link rate for link e is an integer

1

dP

edp dpp

u

1

1, 1,2, ,dP

dpp

u d D

1 1

, 1,2, .dPD

d edp dp ed p

h u y e E

1 1

, 1,2, .dPD

d edp dp ed p

h u y e E

ey

ATM virtual path designObjective function

We are to minimize costLet unit cost of 155Mbps be in link e

The whole problemMinimizeSubject to

where is binary, are integers

Integer programming (IP) problem! Complex to solve!Applicable to MPLS directly…

e

1

E

e ee

y

1

E

e ee

F y

1

1, 1,2, ,dP

dpp

u d D

1 1

, 1,2, .dPD

d edp dp ed p

h u y e E

dpu ey

ATM virtual path design: LP vs. IP problem

Recall similar problem

minimize subject to

We have here IP version of LP problem

minimize subject to

binary integers

Note: way more complex to solve compared to LP

1

E

e ee

F y

1

, 1,2, ,dP

dp dp

x h d D

1 1

, 1,2, ,dPD

edp dp ed p

x y e E

0, 0y x

1

E

e ee

F y

1

1, 1,2, ,dP

dpp

u d D

1 1

, 1,2, .dPD

d edp dp ed p

h u y e E

dpu ey

Circuit-switched telephony: single BH

Telephony: single busy hour designNodes in telephony networks

End nodesTransit nodes

End nodes (access nodes)Digital exchanges generating demandDemand is expressed in ErlangsDuring the busy hourNetwork is underloaded at other times

Transit nodes: do not generate demands, act as relaysThe describe the load we need

be the average arrival rate be the average duration of a callthe offered traffic load is then

1 Erl:

,a Erlangs

Telephony: circuits/trunksCircuits/trunks

Calls require 64KbpsCalls require path for the whole duration of a sessionPath may traverse se sequence of transit nodesLinks between nodes: trunk-groups or circuit-groups

Installation of trunksTypically installed in moduleUS/Japan T1 (1.5Mbps) – 24 trunksRest of the world: E1 (2.048Mbps) – 30 trunks (+2 signaling, 0 and 16)Modular link capacity: a number of E1 trunks, 30,60,90,…!1 LCU = 30, DVU are arbitrary integers

Telephony: problem and GoSProblem we are to solve

What is grade-of-service (GoS)?Set of metrics attributed to traffic performance in the networkSimply: allowed call dropping probability (CDP)Dropping: all resources are busy

Telephone networksGoS is different for different type of callsLocal: 5-8% CDP during BHInternational: 1-3% during BHCellular? 5-8% during BH

Networks are always designed for BH!

How to determine the modular capacity needed in the network so that the offered traffic is carried with some acceptable grade of service (GoS)?

Telephony: call routingCall routing

According to fixed rulesUsing a set of predefined routes

Exampledemand d: end nodes 1 and 2there are three available routes, Pd=3

(1,3,7,6,2), (1,3,7,6,4,2) uses end-node 7 which is not allowedroute (1,2,6,4,2) just prohibited

Possible routing ruleSplit demand between routes such that

and we are getting demand constraintsImplemented using load sharing: route p with probability

1

2

3 4

5

6

7

(1,3,4,2) (1,3,5,4,2) (1,3,6,2)

1

, 1,2, ,dP

dp dd

x h d D

dp dx h

Telephony: call routingLinks load (taking into account load sharing) are

where is 1 if link e belongs to path p of demand d

Important noteslink load: average offered traffic to link e (Erl.)average number of calls in progress given no losses on a link!given that the link has infinite capacity!

Let be the call blocking probability for link e, i.e.

a is the offered loadc is the number of trunks (circuits)probability that all servers are busy in M/M/c/c queue

1 1

, 1,2, ,dPD

edp dp ed p

x y e E

edp

eb

0

!( , )

!

c

c k

k

a cb B a c

a k

Telephony: call routing

However, we want to get c for a certain (a,b)Forward formula gives b for certain (a,c)Let c=C(a,b) be inverse of Erlang-B loss formulaFunction C(a,b) is concave in a for any b

( , )B a c

, .a Erl

20c

10c

5c2c

1c

( , )B a c

, .a Erl

1,3,5,10,25,50,100,1000c

1000c

1c

Telephony: call routingLink dependent dimensioning function

where is a certain dimensioning constant (e.g. 1% of losses) gives real number of circuits to carry offered load a

The whole problemFor offered demands, blocking and unit modular capacity costMinimizeSubject to

where continuous non-negative, integers

Concave-integer dimensioning problem

( ) ( , )e eF a C a b

eb( )eF a

1

E

e eeF y

1

, 1,2, ,dP

dp dd

x h d D

1 1

, 1,2, ,dPD

e edp dp ed p

F x My e E

dpx ey

Circuit-switched telephony: multiple BHs

Telephony: multiple BHsWe considered the case

Busy hours of all demands coincideE.g. all happen at, say 15:00-16:00May only happen in local proximitySame time-zone, small country inside a single time-zone

US as an example8:00 AM Eastern time zone (NY, Boston, Washington)5:00 AM Pacific time zone (LA, San-Francisco, Seattle)BHs do not coincide due to time difference

Beneficial for large carriersDecrease the capacity needed Route via “still” or “already” lightly loaded regions

Why call prices are that high? Network is unloaded anyway!

Telephony: routing of calls againRouting in 1970-1980

Fixed-order of routes + load sharing

Routing 1980 onwardsDynamic non-heirarchial routing (DBHR)Dynamically controlled routing (DCR)Dynamic alternative routing (DAR)Real-timer network routing (RTNR)Common: free capacity due to non-coincidence of BHsOne time zone is used as a reference

Applied to core network, e.g. transit nodes

1

2

3 4

5

6

7

Telephony: routing of calls againProblem we consider

New demand representationPartition a day into several “traffic hours” t=1,2,…,TFor each demand its traffic is different at different intervalsSet of demand volume vectors

Paths is real networksMay contain at most two linksIn other words may traverse at most one intermediate hopWe do not even need an algorithm to get them…

How to do modular capacity design given that traffic volume is different for different times of a day and by taking into account functional characteristics of a routing scheme.

1 2 1 2, , , , ( , , , )T t t t Dth h h h h h h

Telephony: routing of calls againDynamic nature of a flow

Routing should be different at different traffic hours, t=1,2,…,TDemand d for path p at time t is denoted as

The whole problemFor demands, blocking, modular capacity cost and t=1,2,…,TMinimizeSubject to

where are non-negative continuous, are integers

Similar concave-integer programming problem

, 1,2, , , 1,2, , , 1,2, ,dpt dx d D p P t T

1

E

e eeF y

1

, 1,2, , , 1,2, ,dP

dpt dtd

x h d D t T

1 1

, 1,2, , , 1,2, ,dPD

et edpt dpt ed p

F x My e E t T

dptx ey

Telephony: routing of calls againNodes on dynamic routing

Add another dimension of flexibilitySolution is only slightly more complex can be made time-dependentSlightly higher blocking during the links’ busy period

Multi-BH scenario for packet-switchingDynamic routing is good for packet networksDependence of time zones is also evidentSimilar to voice trafficDifferent traffic matrices for different time of a dayMay result in substantial cost savingsAdds implementation complexity

( )etF a