1 presented by sarbagya buddhacharya. 2 increasing bandwidth demand in telecommunication networks is...

Dimensioning of optical Networks with Alternate Routing Using Absorption

Probability

1

Presented by

Sarbagya Buddhacharya

2

Introduction• Increasing bandwidth demand in telecommunication networks is satisfied by WDM networks.

• Dimensioning of WDM networks with conventional steady state blocking probability results in overprovisioning problem (Nayak et al., 2002).

• To minimize the overdimensioning problem in WDM network various approaches are being introduced.

Introduction

Absorption probability model (Nayak et al., 2002) Time dependent blocking probability model (Tian, 2006)

3

Problem Statement

• All the approaches (Nayak et al., 2002; Tian, 2006) to reduce the overdimensioning problem have considered fixed routing.

• Several literatures (Lin et al., 1978; Birman 1996; Zhu et al., 2000) have discussed different methods for the computation of blocking probability with alternate routing.

• We propose a method to compute the absorption probability with fixed alternate routing, and demonstrate its use in network capacity dimensioning.

Introduction

4

Objectives• To develop a method for the computation of absorption probability with fixed alternate routing.

• To compare the value of absorption probability obtained from fixed alternate routing with previously used fixed routing.

• To study the impact of alternate routing on the first passage time ( network upgrade time) of the network.

• To analyze capacity allocation of a network using the absorption probability with fixed alternate routing.

Introduction

5

Scope and Limitations• We consider only full wavelength conversion, although there are other wavelength conversion techniques such as sparse wavelength conversion.

• We do not analyze dynamic alternate routing techniques and focus on fixed alternate routing.

• We do not include traffic growth model.

Introduction

Methodology

6

Computation and simulation of absorption probability for

• A single link• Fixed routing• Fixed alternate outing

Methodology

7

Absorption probability for a single link

• Assumptions: Poisson arrival rate and exponential service time.

• Absorption probability for a single link with capacity K at a given time t (Nayak et al., 2002).

where are the negative eigenvalues of

(K +2) ×(K+2) matrix A, arranged in the descending order.

where and

Methodology

8

Absorption Probability for Fixed Routing

• For the given network topology, fixed route for each S-D pair is obtained using shortest path algorithm.

• Shortest path is selected based on the number of hop counts.

• Arrival rate for each link is thinned using Erlang fixed point approximation.

Methodology

where,R = set of all possible routes.Ajr {0, 1}: equal to one if and only if a lightpath on route uses a circuit from link j. = Poisson arrival rate of lightpath requests on route.

• Using link absorption probability, absorption probability of route can be obtained.

9

Methodology

• For the given link capacity and arrival rate, absorption probability of all the links at time t, can be obtained using single link formula.

• The average absorption probability of the whole network can be obtained using equation (1).

(1)

10

Absorption Probability for Fixed Alternate Routing• Augmented route tree for each S-D pair is obtained and path-loss sequence is represented in terms of link set Ui.

A

E

B D

C E

L

D

DC

P1(ABD) P2(ACED) P3(AECD) L(AL)

U1 U2 U3 U4

• Pr {Ui. used} is obtained based on the call completion rule.

Pr {Ui. used}= Pr {Ui. is available and U1, U2. ,…, Ui-1. are unavailable } = Pr {Ui. available}× Pr{U1 U2., …, Ui.-1 are unavailable| Ui. available} (2)• To solve equation 2 reliability formulae are used (Lin et al.,1978).

Methodology

• We define following terms

• Using these terms following reliability formulae are defined

where,

11

Methodology

• Link absorption probability calculated using an iterative method. Initialize Pasb,j,n (t ) = 0

Calculate Pr { P s,k used } for each alternate path of each S-D pair using equation 2.

Find carried traffic of each alternate routes

Find carried traffic for each link

Find offered traffic for each link

Calculate Pasb,j,n+1 (t ) using single link formula.

Taking Pasb,j,n+1 (t ) as the starting point start next iteration.

12

Methodology

Compute carried traffic of each link

Compute offered traffic of each

link

Absorption Probability(Initially assumed)

Compute Pr { P s,k used }

Compute carried traffic of each alternate route

13

Methodology

We continue iteration until the difference between Pasb,j,n (t ) and Pasb,j,n+1 (t ) for each link is below certain threshold value.

• Absorption probability of S-D pair s can be computed as,

14

Methodology

• The average absorption probability of the whole network can be obtained using equation (1).

Simulation Model

• MATLAB software is used.

• Event based simulation.

• Simulation outputs are used to validate the computational results.

• Poisson arrival rate and exponential service time are assumed.

• Simulation is done for Single link. Fixed routing. Fixed alternate routing.

Methodology: Simulation

15

For each event (arrival or termination): Update link status.

When link status is greater than the link capacity : Increment the number of blocked call.

At the end of time t : if the number of blocked call is greater than zero, then increment the

number of absorption count.

Absorption probability=absorption count/number of iteration

For a Single Link

Methodology : Simulation

16

For each event (arrival or termination):Find the path on which event take place and update the link status.

For each path: if the link status of any one of its link is greater than the link capacity, then increment the number of

blocked call on that path.

For each path: if the number of blocked call is greater than zero at time t, then increment the number of absorption

count on that path.

Absorption probability of a path= absorption count of the path/ number of iterations.

For Fixed Routing


17

For each event (arrival or terminations): Find the S-D pair on which event takes place and update the link status.

If Arrival on S-D: search for the free path

If the path is not found, then increment the number of blocked call on the S-D pair.

For each S-D pair: if blocked call is greater than zero, then increment the absorption count on the S-D pair.

Absorption probability for S-D pair = Absorption count on S-D pair/ number of iterations.

For Fixed Alternate Routing


18

Simulation ResultsFor a single link

• Capacity K =32, arrival rate l=24 arrival/year and mean service time 1/m =1 year (Nayak et al., 2002).

• Outputs obtained from our method are close to output of (Nayak et al., 2002).

Simulation results

19

Plot of absorption probability for a single link (a) Using our simulation program (b) Plot from (Nayak et al., 2002).

For Fixed Routing• Network Topology : Pan-European COST 239 (O’Mahony et al., 1996)

• The numerical value above each link indicates the link capacity (in wavelength channels).

9

11

10

6

8 7

3

2 4

5

1

40

40

40

40

40

4141

41

41

41

41 4343

4343

43

43

44

44

44

44

44

44

Simulation results

20

• Average absorption probability of the whole network is obtained using equation(1).

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Time(Years)

Absorp

tion P

robabili

ty

Computation

Simulation

Plot of absorption probability for fixed routing

Simulation results

21

Parameters Value

S-D pairs 20 pairs randomly selected

Arrival rate (l) 10 arrival/yearmean service time (1/m) 1 yearRouting Shortest path routing based on hop count

Computational values are higher than the simulation output due to link independence assumptions in EFPA

For Fixed Alternate Routing

Simulation results

22

Parameters Value

Network topology Pan-European COST 239 (O’Mahony et al., 1996)


Number of sets of S-D pairs 5

Arrival rate (l) 10 arrival/year

mean service time (1/m) 1 year

Routing Fixed alternate routingAlternate path calculation k-shortest path algorithm (Yen, 1971).Number of alternate routes (P) 2

1 1.5 2 2.5 3 3.5 4 4.5 5

10-4

10-3

10-2

10-1

100

Time (Years)

Abs

orpt

ion

Pro

babi

lity

Computation

Simulation

Plot of absorption probability for P=2

Simulation results

23

Comparison of absorption probability with Fixed Routing and Fixed Alternate Routing

Results Obtained

24

Results obtained

Parameters Value




Arrival rate (l) 8 arrival/year,10 arrival/year and 12 arrival/yearmean service time (1/m) 1 year

Number of alternate routes (P) 1, 2, 3

• Absorption probability calculated using purposed computational method .

• Absorption probability is reduced as the number of alternate paths are increased.

1 1.5 2 2.5 3 3.5 4

10-10

10-5

100

Time(Years)

Abso

rptio

n Pr

obab

ility

1 1.5 2 2.5 3 3.5 4

10-10

10-5

100

Time(Years)

Abso

rptio

n Pr

obab

ility

1 1.5 2 2.5 3 3.5 4

10-10

10-5

100

Time(Years)

Abso

rptio

n Pr

obab

ility

P=1P=2P=3

P=1P=2P=3

P=1P=2P=3

(a) (b)

(c)

Plot of absorption probability with 20 SD pairs for (a) l=8 arrival/year (b) l=10 arrival/year (c) l=12 arrival/year

25

Results Obtained

26

Results Obtained

Parameters Value


S-D pairs 10 , 15 , 20 (randomly selected)Number of sets of S-D pairs 5 Arrival rate (l) 10 arrival/yearmean service time (1/m) 1 yearNumber of alternate routes (P) 1, 2, 3

• Absorption probability calculated using purposed computational method .

• Absorption probability is reduced as the number of alternate paths are increased.

• Plot is obtained for different number of S-D pairs

Plot of absorption probability with arrival rate l=10 arrival/year for (a) 10 S-D pairs (b)15 S-D pairs (c) 20 S-D pairs

27

Results Obtained

1 1.5 2 2.5 3 3.5 4

10-10

10-5

100

Time(Years)

Abso

rptio

n Pr

obab

ility

1 1.5 2 2.5 3 3.5 4

10-10

10-5

100

Time(Years)

Abso

rptio

n Pr

obab

ility

1 1.5 2 2.5 3 3.5 4

10-10

10-5

100

Time(Years)

Abso

rptio

n Pr

obab

ility

P=1P=2P=3

P=1

P=2P=3

P=1

P=2P=3

(a) (b)

(c)

• Refers to the time period during which there is high probability that at least one lightpath request will not be served (Nayak et al., 2002).

• At the end of this time, operators need to upgrade the capacity of the network.

• Alternate routing increase first passage time as compared to fixed routing.

• First passage time is plotted for 3 different arrival rates.

First Passage TimeResults Obtained

28

Parameters Value




Arrival rate (l) 8 arrival/year,10 arrival/year and 12 arrival/yearmean service time (1/m) 1 yearNumber of alternate routes (P) 1, 2, 3Absorption probability 0.01, 0.001

0.01 0.0010

2

4

6

8

10

12

14

Absorption Probability

Tim

e (Y

ears

)

0.01 0.0010

2

4

6

8

10

12

14


Tim

e (Y

ears

)

0.01 0.0010

2

4

6

8

10

12

14


Tim

e (Y

ears

)

P=1P=2P=3

P=1P=2P=3

P=1P=2P=3

(c)(a) (b)

Plot of first passage time with 20 SD pairs for (a) l=8 arrival/year (b) l=10 arrival/year (c) l=12 arrival/year

29

Results Obtained

30

Results Obtained

• First passage time is also computed for 3 different numbers of S-D pairs

Parameters ValueNetwork topology Pan-European COST 239 (O’Mahony et al., 1996)

S-D pairs 10 , 15 , 20 (randomly selected)Number of sets of S-D pairs 5 Arrival rate (l) 10 arrival/yearmean service time (1/m) 1 yearNumber of alternate routes (P) 1, 2, 3Absorption probability 0.01, 0.001

0.01 0.0010

2

4

6

8

10

12

14

16


Tim

e (Y

ears

)

0.01 0.0010

2

4

6

8

10

12

14

16


Tim

e (Y

ears

)

0.01 0.0010

2

4

6

8

10

12

14

16


Tim

e (Y

ears

)

P=1P=2P=3

P=1P=2P=3

P=1

P=2P=3

(a) (b) (c)

Plot of first passage time with arrival rate l=10 arrival/year for (a) 10 S-D pairs (b) 15 S-D pairs (c) 20 S-D pairs

31

Results Obtained

Capacity Allocation

• Capacity allocation is done based on a heuristic algorithm from (Gunawardena et al., 2009)

• This algorithm has mainly two phase : capacity increment phase and capacity decrement phase.

• In capacity increment phase, links are selected based on three link criticalities given below and link capacity of the selected links is incremented by 1.

Nj : number of S-D pairs which use link j that have the absorption probability greater than the threshold value .

• In capacity decrement phase, all the links are selected in some random order and capacity is decremented by 1. This is repeated until any route absorption probability exceeds the threshold.

Results Obtained

32

Capacity allocation for Pan-European COST 239

• Network parameters for capacity allocation of Pan-European COST 239 network are given below.

Parameters Numerical values

Arrival rate (l) 6 arrival/yearService time (1/m) 1 yearS-D pairs 55Absorption probability threshold ( Pth ) 0.01, 0.001

Time period (years) 0.5, 1, 1.5, 2

Number of routes (P ) 1, 2, 3

Results Obtained

33

t 0.5 1Pth 0.01 0.001 0.01 0.001

Link P=1 P=2 P=3 P=1 P=2 P=3 P=1 P=2 P=3 P=1 P=2 P=31 24 20 21 30 26 22 38 29 30 41 30 342 21 20 18 25 24 19 32 31 29 35 34 303 26 24 21 28 27 26 36 36 33 41 40 43

Total 425 394 367 485 455 404 613 588 567 694 635 590

• Results of capacity allocation are shown below

Pth : Absorption probability thresholdt: Observation period

Results Obtained

34

t 1.5 2Pth 0.01 0.001 0.01 0.001

Link P=1 P=2 P=3 P=1 P=2 P=3 P=1 P=2 P=3 P=1 P=2 P=31 44 37 35 49 39 41 49 44 40 54 41 452 38 36 37 43 40 36 42 40 40 46 45 393 44 43 39 48 47 41 48 47 43 54 52 46

Total 734 712 683 807 745 697 814 777 756 888 833 779

• Total capacity is reduced as the number of alternate paths are increased.

• Capacity allocation is done based on the absorption probability obtained from the simulation program.

• Results obtained are shown below.

t 1Pth 0.01 (Comp) 0.01 (Sim) 0.001(Comp) 0.001(Sim)

Link P=1 P=2 P=3 P=1 P=2 P=3 P=1 P=2 P=3 P=1 P=2 P=31 38 29 30 35 27 32 41 30 34 38 34 332 32 31 29 29 30 26 35 34 30 31 28 31

3 36 36 33 36 33 35 41 40 43 39 36 37

Total 613 588 567 578 527 505 694 635 590 641 560 548

Pth : Absorption probability thresholdt : Observation periodComp: ComputationSim: Simulation

Results Obtained

35

0.5 1 1.5 20

100

200

300

400

500

600

700

Time(Years)

Tot

al c

apac

ity

0.5 1 1.5 20

100

200

300

400

500

600

700

Time(Years)

Tot

al c

apac

ity

P=1

P=2P=3

P=1

P=2P=3

(b)(a)

• Plots are obtained for the capacity allocation with arrival rate of = 4 l arrival/year, = 6 l arrival/year, and = 8 l arrival/year using computational method.

l = 4 arrival/year (a) Pth =0.01 (b) Pth = 0.001

36

Results Obtained

0.5 1 1.5 20

200

400

600

800

1000

1200

Time(Years)

Tot

al c

apac

ity

0.5 1 1.5 20

200

400

600

800

1000

1200

Time(Years)

Tot

al c

apac

ity

P=1

P=2P=3

P=1

P=2P=3

(b)(a)

1 2 3 40

100

200

300

400

500

600

700

800

900

Time(Years)

Tota

l capacity

1 2 3 40

100

200

300

400

500

600

700

800

900

Time(Years)

Tota

l capacity

P=1

P=2P=3

P=1

P=2P=3

(a) (b)



37

Results Obtained

Discussions• Absorption probability of the network is reduced with fixed alternate routing as compared to the fixed routing.

• First passage time of the network is increased with the implementation of fixed alternate routing instead of fixed routing.

• The capacity required to maintain the absorption probability of the network below certain threshold is reduced with the increased number of alternate paths.

38

Summary of Contributions• A numerical computational method for calculating the absorption probability with fixed alternate routing.

• Simulation program for the computation of the absorption probability with fixed routing and fixed alternate routing.

• Fixed alternate routing is better than the fixed routing for network dimensioning based on absorption probability.

Decrease absorption probability of the Network Increase first passage time of the Network Reduce the capacity allocation

39

Recommendations

• We have considered full wavelength conversion. This work can be further explored with several other wavelength conversion techniques such as sparse wavelength conversion technique.

• We have considered fixed alternate routing so this work can be further extended for adaptive routing.

• We have considered constant traffic, so this thesis can be further explored with traffic growth model.

40

Thank You

41

1 presented by sarbagya buddhacharya. 2 increasing bandwidth demand in telecommunication networks is...

Documents