route optimization in optical burst switched networks considering the streamline effect

Computer Networks 52 (2008) 2033–2044

Contents lists available at ScienceDirect

Computer Networks

journal homepage: www.elsevier .com/ locate/comnet

Route optimization in optical burst switched networksconsidering the streamline effect q

Qian Chen *, Gurusamy Mohan, Kee Chaing ChuaDepartment of Electrical and Computer Engineering, National University of Singapore, ONE Lab, E4-06-20, Singapore 117576, Singapore

a r t i c l e i n f o

Article history:Received 24 May 2007Received in revised form 12 February 2008Accepted 13 February 2008Available online 16 March 2008

Keywords:Optical burst switchingRoute optimizationLoss estimationStreamline effect

1389-1286/$ - see front matter � 2008 Elsevier B.Vdoi:10.1016/j.comnet.2008.02.017

q Earlier version of part of this work appeared in2006.

* Corresponding author. Tel.: +65 94324606.E-mail addresses: [email protected] (Q. Chen

(G. Mohan), [email protected] (K.C. Chua).

a b s t r a c t

Route optimization in optical burst switching (OBS) networks is investigated in this paper.Two route optimization problems are studied. The first problem considers the network inthe normal working state where all the links are working properly. The route for each flowis decided so as to minimize the overall network burst loss. The second problem considersthe failure states apart from the normal working state. The primary and backup paths foreach flow are determined in such a way to minimize the expected burst loss over the nor-mal and failure states. We argue that route selection based on load balancing or the tradi-tional Erlang B formula is not efficient because of an important feature called thestreamline effect. We analyze the streamline effect and propose a more accurate loss esti-mation formula which considers the streamline effect. Based on this formula, we developmixed integer linear programming (MILP) formulations for the two problems. Since theMILP-based solutions are computationally intensive, we develop heuristic algorithms.We verify the effectiveness of our algorithms through numerical results obtained by solv-ing the MILP formulations with CPLEX and also through simulation results.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Optical burst switching (OBS) is a promising technologyto transmit bursty traffic over wavelength division multi-plexing (WDM) networks [1]. To reduce the burst loss inOBS networks, many scheduling algorithms [2] and lossreduction techniques, such as burst segmentation [3], traf-fic distribution [4], route deflection [5] and burst resched-uling [6], have been proposed. In this paper, we considerusing offline route optimization to reduce burst loss inOBS networks. We assume that the network has multipleprotocol label switching (MPLS) control. We use the term‘flow’ to refer to the stream of bursts sent on a labelswitching path (LSP) from an ingress node to an egress

. All rights reserved.

ICC 2006 and HPSR

), [email protected]

node. We also assume that each node has full wavelengthconversion, which is widely adopted in the OBS researchcommunity. Offline route optimization determines theroutes of the flows in such a way to minimize the overallnetwork burst loss, assuming the estimated traffic demandis known. We assume the traffic demand is quasi-station-ary, as the measurements in Internet traffic indicate thatthe aggregated load on links changes relatively slowly[8]. Due to the large amount of data carried by an OBS net-work, a failure would cause huge data loss. Therefore, wealso consider the selection of backup routes.

We study two route optimization problems in this pa-per. The first problem considers the usual case of normalstate where all the links are working properly, and oneroute is determined for each flow to minimize the overallburst loss. The second problem considers the failures, andthe primary and backup paths for each flow are deter-mined in such a way to minimize the expected burst lossover the normal and the failure states. We refer the firstproblem as the normal state route (NSR) optimization

mailto:[email protected]



http://www.sciencedirect.com/science/journal/13891286

http://www.elsevier.com/locate/comnet

2034 Q. Chen et al. / Computer Networks 52 (2008) 2033–2044

problem and the second problem as the failure recoveryroute (FRR) optimization problem.

For the FRR problem, we consider a failure recoverymechanism as below. For each flow, two link-disjoint LSPs,the primary LSP and backup LSP, are set up. When the net-work is in the normal working state, the bursts are trans-mitted on the primary LSP. When a link failure occurs,the end nodes of the failed link detect the failure and notifythe end nodes of the failed LSPs. After receiving the notifi-cation, the source node transfers the affected flows to thepre-configured backup LSP. We assume single link failure,which has been commonly used in the literature. So whena failure occurs the affected traffic could be transferred tothe backup path without searching for a new route. Sucha recovery scheme is fast since it is exempted from thesearching and setup of a new route after a failure occurs,and it is also efficient as the routes have been optimized.There has been some work done on OBS fault manage-ments [9–11], but none deals with primary/backup routeselection to minimize the expected burst loss.

There are works [12] for offline route optimization inOBS networks where the Erlang B formula is used to esti-mate the loss. Our work differs from those in that we con-sider the special feature of OBS networks, called thestreamline effect. This effect is that, in OBS networks, dueto the bufferless core nodes, if some flows share a link,there will be no contention among these flows in the out-going link. We present a loss estimation formula consider-ing the streamline effect. Based on our formula, we presentmixed integer linear programming (MILP) formulations forthe NSR and the FRR problems. Because of the intensivecomputation needed to solve MILP formulations, heuristicalgorithms are developed.

The rest of the paper is organized as follows. Section 2analyses the streamline effect, presents a new loss estima-tion formula, and illustrates how it can help find a betterroute layout. Section 3 gives the MILP formulations forthe NSR and the FRR problems based on the new formula.The heuristic algorithms are described in Section 4. Section5 presents the performance study. Section 6 makes con-cluding remarks.

A B C

Flow 1

Flow 2

Fig. 1. Illustration of the streamline effect.

2. The streamline effect and its impact on routeoptimization

2.1. Streamline effect and loss estimation

We assume that the burst arrivals follow a Poisson dis-tribution. Such an assumption is reasonable since a flowin OBS networks is the aggregation of many independentIP streams. The Erlang B formula is usually used to esti-mate burst loss in OBS networks. The Erlang B formula as-sumes that all the flows are independent and contendwith each other. However, since there is no buffering atthe core nodes in OBS networks, if two or more flowsshare more than one consecutive link along their paths,the relative temporal relationship among the bursts ofthese flows will not change along these links. As a result,the contention among these flows can only take place atthe first shared link. Due to this effect, the loss on a sub-

sequent link is likely to be less than that computed by theErlang B formula. Consider the example shown in Fig. 1.Suppose that two flows merge at node A and share linkAB and link BC. There should be no loss in link BC, be-cause link AB has removed all the contentions betweenthe two flows. However, the estimated loss given by theErlang B formula,

Gða;WÞ ¼ a� Erlang Bða;WÞ ¼ aaW

W!PWm¼0

am

m!

!ð1Þ

where W is the number of wavelengths over the link and ais the offered load on link BC (a ¼ k=l, where k and 1=l arethe arrival rate and the mean burst length, respectively. Thecorresponding normalized load can be derived by dividing aover W), is greater than zero. Therefore, to estimate the lossmore accurately, we need to take the following effect intoconsideration: if some flows share a link, there will be nocontention among these flows if they traverse the samenext link. We call this effect the streamline effect.

We now derive the loss estimation formula with thestreamline effect taken into consideration. We note thatan intuitive explanation of the streamline effect has beengiven in [7], and here we give a detailed mathematicalanalysis. Consider two systems with the same input flows,as shown in Fig. 2. In System 1, all the flows enter link L1from different input links and are independent, which isthe case assumed by the Erlang B formula. In System 2,flows are divided into N groups, and the flows of the ithgroup merge at the ith input link Ki before reaching linkL2. System 2 is the case in OBS networks. The offered loadof the ith group is qi. The total offered load is given byq ¼

PNi¼1qi.

First we show that the total losses in the two systemsare approximately equal when W tends to be large. Thethroughput in System 1, denoted by C1, is

C1 ¼ q� Gðq;WÞ ¼ q

PW�1m¼0

qm

m!PWm¼0

qm

m!

!ð2Þ

In System 2, suppose that the propagation delay of the ithinput link Ki is si. We also suppose that, when a burst ar-rives at the jth input link at time t, the number of burstsbeing served at the ith input link at time t þ sj � si is Si.So we have the following observations:

1. IfPN

i¼1Si

� �< W , the newly arrived burst survives since

it can always find a free wavelength either on the inputlink Kj or link L2.

2. IfPN

i¼1Si

� �P W , the newly arrived burst is dropped. If

Sj ¼W , it will be dropped on the input link Kj. If Sj < W ,but

PNi¼1Si

� �P W , it will be dropped on link L2.

Link L1

Flows

System 1

Link L2

System 2

Flows of

Group 1

Flows ofGroup N

Flows

K1

KN

Fig. 2. Comparison of two systems.

Q. Chen et al. / Computer Networks 52 (2008) 2033–2044 2035

As a result, the throughput in System 2, denoted by C2,is equal to q� Pr

PNi¼1Si

� �< W

� �. Because the traffic in

each input link Ki are independent, and the burst arrivalprocess is Poisson, we have

C2 ¼ q� PrXN

i¼1

Si < W

!

¼ q�XW�1

m¼0

XS1þS2þ��þSN¼m; 06Si6W

YNi¼1

PrðSiÞ ! ! !

¼ q�XW�1

m¼0

PS1þS2þ��þSN¼m; 06Si6m

QNi¼1

qSii

Si !

� �QN

i¼1

PWk¼0

qki

k!

� �0BB@

1CCA0BB@

1CCA ð3Þ

According to the formula,

XN

i¼1

ai

!M

¼X

b1þb2þ��þbN¼M; 06bi6M

YNi¼1

M!ðaiÞbi

bi!

!ð4Þ

we have

XS1þS2þ��þSN¼m; 06Si6m

YN

i¼1

qSii

Si!

!¼

PNi¼1qi

� �m

m!¼ qm

m!ð5Þ

Using Eq. (5) in Eq. (3), we have

C2 ¼ q�XW�1

m¼0

qm

m!QNi¼1

PWk¼0

qki

k!

� �0B@

1CA0B@

1CA ð6Þ

SinceP1

k¼0qk

ik!¼ eqi , for a large value of W (which is the

usual case in OBS networks), we havePW

k¼0qk

ik!

� �u eqi . So,

C2 u q�XW�1

m¼0

qm

m!QNi¼1eqi

! !¼ q�

XW�1

m¼0

qm

m!

eq

! !ð7Þ

Using the same approximation technique in Eq. (7), wehave

C1 u q�XW�1

m¼0

qm

m!

eq

! !ð8Þ

The above analysis shows C1 u C2. So the overall burst lossin System 2 is also Gðq;WÞ. Since the burst loss at the ithinput link Ki is Gðqi;WÞ; the loss at link L2 is given by

Gðq;WÞ �XN

i¼1

Gðqi;WÞ ð9Þ

Eq. (9) gives the loss estimation formula considering thestreamline effect. The loss is equal to the loss estimatedby the Erlang B formula with the contentions betweenthe flows from the same upstream link removed. We cansee that the new formula gives the correct loss estimationin the case illustrated in Fig. 1.

2.2. Impact of streamline effect on route optimization

With the new loss estimation formula, a better routelayout can be found by making good use of the streamlineeffect. The Erlang B based route optimization minimizesthe summation of losses on the links traversed estimatedby the Erlang B formula. The load balancing route optimi-zation would make the loads distributed as balanced aspossible. However, such route layouts may not be optimalin OBS networks due to the streamline effect. Consider thenetwork topology shown in Fig. 3. Assume that there arefour flows, with the loads as shown, all destined for nodeF. Note that these flows have no choice on the part ofroutes before node C, so we focus on the part of routeselection after node C.

With the Erlang B formula based or the load balancingroute optimization, the following route layout is selected.This layout makes the loads in the route C ? D ? F andC ? E ? F equal, and the summation of the Erlang B esti-mated loss in the links of CD, CE, DF and EF is minimized:

Flow 1: A ? C ? D ? F Flow 2: A ? C ? E ? FFlow 3: B ? C ? E ? F Flow 4: B ? C ? D ? F

A

C

E

D

F

B

Flow 1 (0.5)

Flow 4 (0.1)

Flow 3 (0.2)

Flow 2 (0.4)

Fig. 3. Illustration of the benefit of considering the streamline effect inroute optimization.


With the new loss estimation formula, the followinglayout is selected. In this layout, the summation of the lossestimated by the new formula is minimized. There is nocontention between Flow 1 and Flow 2 after node C dueto the streamline effect, and thus they take the same routeafter node C. And so are Flow 3 and Flow 4:

Flow 1: A ? C ? D ? F Flow 2: A ? C ? D ? FFlow 3: B ? C ? E ? F Flow 4: B ? C ? E ? F

For the two layouts, the burst losses in link AC and linkBC are the same. The burst loss over the links of CD, DF, CEand EF in the first layout is larger than zero. However, inthe second layout, the burst loss over these links is 0, be-cause of the streamline effect. Therefore, the route layoutobtained by the streamline effect based loss formula re-sults in lower burst loss.

3. The MILP formulation

In this section, we develop MILP formulations for theNSR and the FRR problems based on the new loss estima-tion formula.

The NSR problem can be stated as follows:Given an OBS network topology and a traffic demand, it

is required to determine a route for each flow so as to min-imize the overall burst loss.

The FRR problem can be stated as follows:Given an OBS network topology and a traffic demand, it

is required to determine a pair of link-disjoint primary andbackup paths for each flow to minimize the expected burstloss over the normal and failure states. The expected burstloss, E, is defined as below:

E ¼XL

i¼0

Prðstate iÞ � Lossðstate iÞ

where L is the number of links in the network, and the linksare numbered from 1 to L, state 0 is the normal state,state ið1 6 i 6 LÞ is the state where the ith link fails,Lossðstate iÞ is the overall burst loss in state i, andPrðstate iÞ is the probability that the network is in state i:We assume the values of Prðstate iÞ are known.

3.1. Notation

The following notations are used in the MILP formula-tion for the NSR problem:

� links: The set of links in the network. The links are num-ber from 1 to L.

� nodes: The set of nodes in the network.� states: The set of all the normal and failure states. The

states are number from 0 to L.� F: The set of flows. Each flow is identified by a pair hs; di,

where s and d are the source and destination node,respectively.

� HeadðvÞ: The links starting from node v.� TailðvÞ: The links ending at node v.� UpðlÞ: The upstream end node of link l.� DownðlÞ: The downstream end node of link l.� qs;d: The traffic load of flow hs; di.� xk

s;d: Is 1 if the primary path of flow hs; di traverses linkkð1 6 k 6 LÞ, otherwise it is 0. Note that xk

s;d indicatesthe route the flow uses in state k. The flow uses thebackup route in state k if xk

s;d ¼ 1 and the primary routeif xk

s;d ¼ 0. To describe the route selection in the normalstate, we additionally define x0

s;d ¼ 0.� PrevðkÞ: The set of the links whose downstream end

node is UpðkÞ.

The following notations are added for the MILP formu-lation for the NSR problem:

� yks;d: Is 1 if the backup path of flow hs; di traverses link k,

otherwise it is 0.� ak;i

s;d: Is 1 if the flow hs; di traverses link k in state i, other-wise it is 0.

� bk;is;d; ck;i

s;d: Two auxiliary boolean variables used in thedefinition of ak;i

s;d.� qk

i : The load over link k in state i.� bl;k;i

s;d : Is 1 if flow hs; di traverses the concatenation of link land link k in state i, otherwise it is 0. Note thatl 2 PrevðkÞ.

� hl;ki : The load over the link concatenation of l and k in

state i. Note that l 2 PrevðkÞ.� L lossk

i : The burst loss over link k in state i.� Lossðstate iÞ: The burst loss in state i.

3.2. MILP1: NSR problem formulation

Objective: Minimize the burst loss in the normal stateLossðstate 0Þ.Constraints: The problem is subject to the followingconstraints:1. Flow conservation demand:
X
k2tailðvÞxk

s;d �X

k2headðvÞxk

s;d

¼1 if v ¼ s

�1 if v ¼ d

0 otherwise

8><>: 8hs; di 2 F; 8v 2 nodes ð10Þ

2. By definition, bl;k;0s;d ¼ xk

s;d � xls;d. However, this expres-

sion is non-linear. So the following linear constraintsare defined. They give the same results when all thevariables are boolean:

bl;k;0s;d 6 ðxk

s;d þ xls;dÞ=2 8hs; di 2 F; 8k 2 links;

8l 2 prevðkÞ ð11Þ


bl;k;0s;d P ðxk

s;d þ xls;dÞ=2� 0:5 8hs; di 2 F; 8k 2 links;

8l 2 prevðkÞ ð12Þ

3. The definition of qk0; hl;k

0 and L lossk0:

qk0 ¼

Xhs;di2F

qs;d � xks;d 8k 2 links ð13Þ

hl;k0 ¼

Xhs;di2F

qs;d � bl;k;0s;d 8k 2 links; 8l 2 prevðkÞ ð14Þ

L lossk0 ¼ dþ bGðqk

0;WÞ �X

l2prevðkÞ

bGðhl;k0 ;WÞ 8k 2 links

ð15Þ

Lossðstate 0Þ ¼X

k2links

L lossk0 ð16Þ

d is a small value (set to 10�8 in this paper) that keeps thelink cost greater than zero and prevents a loop in the routefound. bGðq;WÞ is a piecewise linear function to approxi-mate the non-linear Gðq;WÞ with interpolation:

bGðq;WÞ ¼ Gðqm;WÞ � Gðqm�1;WÞqm � qm�1

ðq� qm�1Þ; qm

> q P qm�1; m ¼ 1;2; . . . ;K ð17Þ

3.3. MILP2: FRR problem formulation

Objective: Minimize the expected burst loss E.Constraints: The problem is subject to the followingconstraints:1. Flow conservation demand for the primary and the

backup routes:
Xk2tailðvÞ
xks;d �

Xk2headðvÞ

xks;d

¼1 if v¼ s

�1 if v¼ d0 otherwise

8><>: 8hs;di 2 F; 8v 2 nodes ð18Þ

Xk2tailðvÞ

yks;d �

Xk2headðvÞ

yks;d

¼1 if v¼ s

�1 if v¼ d

0 otherwise

8><>: 8hs;di 2 F; 8v 2 nodes ð19Þ

2. The primary and backup paths are link-disjoint:

xks;d þ yk

s;d 6 1 8hs; di 2 F; 8k 2 links ð20Þ

3. By definition, ak;is;d ¼ xk

s;d � ð1� xis;dÞ þ yk

s;d � xis;d. We

use the following linear constraints to replace themultiplication expression. These constraints givethe same results if the variables involved are allboolean:

bk;is;d 6 ðx

ks;d þ 1� xi

s;dÞ=2 8hs; di 2 F;

8k 2 links; 8i 2 states ð21Þ

bk;is;d P ðxk

s;d þ 1� xis;dÞ=2� 0:5 8hs; di 2 F;


ck;is;d 6 ðy

ks;d þ xi

s;dÞ=2 8hs; di 2 F; 8k 2 links;

8i 2 states ð23Þ

ck;is;d P ðyk

s;d þ xis;dÞ=2� 0:5 8hs; di 2 F;


ak;is;d ¼ bk;i

s;d þ ck;is;d 8hs; di 2 F; 8k 2 links; 8i 2 states

ð25Þ

4. We have bl;k;is;d ¼ ak;i

s;d � al;is;d by definition. By the same

technique as above, we use the following linear con-straints to replace the non-linear multiplicationexpression:

bl;k;is;d 6 ða

k;is;d þ al;i

s;dÞ=2 8hs; di 2 F; 8k 2 links;

8i 2 states ð26Þ
bl;k;i
s;d P ðak;is;d þ al;i

s;dÞ=2� 0:5 8hs; di 2 F; 8k 2 links;

8i 2 states ð27Þ

5. The definition of qki and hl;k

i :

qki ¼

Xhs;di2F

qs;d � ak;is;d 8hs; di 2 F; 8k 2 links;

8i 2 states ð28ÞX
hl;k
i ¼hs;di2F

qs;d � bl;k;is;d 8k 2 links; 8l 2 prevðkÞ;

8i 2 states ð29Þ

6. The definition of L losski ; Lossðstate iÞ and E:

Losski ¼ dþ bGðqk

i ;WÞ �X

l2prevðkÞ

bGðhl;ki ;WÞ 8k 2 links;

8i 2 states ð30ÞX
Lossðstate iÞ ¼
k2links

Losski 8i 2 states ð31Þ

E ¼XL

i¼0

Prðstate iÞ � Lossðstate iÞ ð32Þ

The definition of d and bGðq;WÞ are the same as that in theMILP1 formulation.

4. Heuristic algorithms

Since solving an MILP problem is computationallyintensive, heuristic algorithms are developed. SLNS-Heur(streamline effect based normal state route optimizationheuristic) is developed to solve the NSR problem, whileSLFR-Heur (streamline effect based failure recovery routeoptimization heuristic) is developed to solve the FRRproblem.

4.1. Streamline effect based normal state route optimizationheuristic (SLNS-Heur)

SLNS-Heur works in two steps. The first step performsinitialization, where each flow is assigned the shortestpath. The second step adopts iterative techniques to im-prove the route layout. In each iteration, some flows arerandomly chosen to have their routes re-computed. If thenew routes help reduce the overall burst loss, these flows


will have their routes updated. Otherwise, the originalroutes are kept. The details of SLNS-Heur are described asbelow:

1. Each flow is assigned the path with the minimum-cost.The cost of a link is the loss introduced by the new flowaccording to the loss estimation formula proposed. Thedetails of the link cost calculation are given at the end ofthe algorithm description.

2. M flows are randomly selected and their traffic loadsremoved along the routes. Then the same link cost cal-culation method as that in step 1 is used to find a min-imum-cost path for each of the M flows. If the re-routing reduces the overall burst loss, the routes forthese M flows are updated. Otherwise the originalroutes are kept.

3. Step 2 is repeated until the stopping criterion is met.The stopping criterion could be that no improvementis observed for a specific number of iterations or themaximal permitted iterations are reached.

The cost of link hm;ni, costðm;nÞ, is computed asfollows:

new ¼ Gðqðm;nÞE þ q0;WÞ � GðhPðmÞ;ðm;nÞE þ q0;WÞ ð33Þ

old ¼ Gðqðm;nÞE ;WÞ � GðhPðmÞ;ðm;nÞE ;WÞ ð34Þ

costðm;nÞ ¼ new� oldþ d ð35Þ

The notations used above are:

� q0: The traffic load of the flow whose route is to bedetermined.

� qðm;nÞE : The existing traffic load over link hm;ni.� PðmÞ: The node prior to node m in the shortest path from

the source node to node m.� new and old: The difference between new and old is the

increase in the burst loss over the link if the new flow isintroduced. The burst loss over link hm;ni with andwithout the flow going through are Gðqðm;nÞE þq0;WÞ � GðhPðmÞ;ðm;nÞ

E þ q0;WÞ �P

p6¼PðmÞGðhp;ðm;nÞE ;WÞ and

Gðqðm;nÞE ;WÞ � GðhPðmÞ;ðm;nÞE ;WÞ �

Pp6¼PðmÞGðh

p;ðm;nÞE ;WÞ, res-

pectively. Since we are concerned with the loss differ-ence between these two values, we remove the commonitem of �

Pp 6¼PðmÞGðh

p;ðm;nÞE ;WÞ and have the expression of

new and old as given above.

Computational complexity: Let the number of flows be F,the maximum node degree be D, the number of nodes be V ,the number of wavelengths per link be W , the maximalpermitted number of iterations be I, and the number offlows whose routes are re-computed each iteration be M.Since the complexity of Erlang B formula is OðWÞ, the com-plexity of one link cost computation is OðD �WÞ. The com-plexity of the shortest route search for each flow is OðV2Þ.So the complexity of the first and the second steps areOðF � V2 � D �WÞ and OðI �M � V2 � D �WÞ, respectively. Sothe complexity of SLNS-Heur is OðF � V2 � D �W þ I�M � V2 � D �WÞ. We note that this complexity is reasonableand acceptable since the route optimization is done offline.

4.2. Streamline effect based failure recovery routeoptimization heuristic (SLFR-Heur)

SLFR-Heur is composed of two phases. In the first phase,the primary path of each flow is decided using SLNS-Heurproposed above. In the second phase, the primary pathsare fixed, and we determine the backup paths to minimizethe expected loss in failure states, which is given byPL

i¼1Prðstate iÞ

1�Prðstate 0Þ � Lossðstate iÞ� �

. The second phase of

SLFR-Heur is as follows:

1. For each flow, assign the minimum-cost path link-dis-joint to its primary path as the backup path. The linkcost function is given later.

2. M flows are randomly selected. For each of the M flows,the minimum-cost path link-disjoint to the primarypath is determined as the backup path, using the samelink cost function as step 1. If the re-routing reduces theexpected burst loss in failure states, the backup routesfor these M flows are updated. Otherwise the originalroutes are kept.

3. Step 2 is repeated until the stopping criterion is met.The stopping criterion could be that no improvementis observed for a specific number of iterations or themaximal permitted iterations are reached.

In the second phase, the cost of link hm;ni, costðm;nÞ, iscomputed as follows. The notations used in the descriptionof SLNS-Heur are kept:

1. The value of qðm;nÞi , the traffic load over link hm;ni instate ið1 6 i 6 LÞ, and the value of hðPðmÞ;ðm;nÞÞi , the trafficover the link concatenation of hPðmÞ;mi and hm;ni instate ið1 6 i 6 LÞ, are calculated.

2. If link hm;ni is in the primary path, set the cost to infin-ity to exclude the backup path from traversing it. Other-wise, estimate the additional loss caused by the newflow if this link is taken as the next hop. Note that weare only concerned with the failure states where oneof the links in the primary path fails. The pseudo-codefor computation is as follows:

If (link hm;ni is on the primary path of the flow)costðm;nÞ ¼ 1;

else{ costðm;nÞ ¼ d;

for (every failure state i){ if (link i is on the primary path)

{ new ¼ Gðqðm;nÞi þ q0;WÞ � GðhðPðmÞ;ðm;nÞÞi þq0;WÞ;

old ¼ Gðqðm;nÞi ;WÞ � GðhðPðmÞ;ðm;nÞÞi ;WÞ;costðm;nÞþ ¼ Prðstate iÞ

1�Prðstate 0Þ � ðnew� oldÞ;} } }

Computational complexity: We use the same notations asin the analysis of SLNS-Heur. In SLFR-Heur, the complexityof the first phase is the same as SLNS-Heur. The secondphase is L times more complex than SLFR-Heur, since thelink cost computation involves L failure states. Therefore,the complexity of SLFR-Heur is OðF � V2 � D �W � Lþ I�M � V2 � D �W � LÞ. We note that this complexity is reasonableand acceptable since the route optimization is done offline.

0

1

2

5

3

4 6

9

7

8

13

12

10

11

Fig. 6. NSFNET topology.

0

1

2

3

4

5

6

7

8 x 10–5

Loss

Rat

e

StreamlineSimulationErlangB


5. Performance study

In this section, we present numerical results. We firststudy the accuracy of the streamline loss estimation for-mula. Then the performance of routing algorithms pro-posed in this paper are compared with other knownalgorithms.

5.1. Accuracy of the streamline estimation formula

We validate the streamline loss estimation formula ontwo networks. First, we validate the formula on a six-nodenetwork shown in Fig. 4. We consider three flows. Flow 1:A ? C ? E ? F, Flow 2: B ? C ? E ? F and Flow 3:D ? E ? F. The loads of the Flow 1 and Flow 2 are 0.3,respectively, and the load of Flow 3 is varied from 0 to0.15. Fig. 5 compares the loss rates on link EF given bythe simulation and that estimated by the Erlang B formulaand the streamline formula. We can observe that the esti-mation given by the streamline formula is closer to thesimulation result than that by the Erlang B formula.

Next, we validate the formula on the NSFNET networkshown in Fig. 6. We assume there is a flow between eachnode pair. We assume that each flow takes the shortestpath. The load of each flow (except the one from node 11to node 1) is randomly chosen between 0 and 0.32. Wevary the load of the flow from node 11 to node 1 and ob-serve the end-to-end loss rate of this flow. Fig. 7 showsthe result obtained from the simulation and that estimated

A

B

C

D

E F

Fig. 4. Six-node netwok for estimation formula comparison.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

0.005

0.01

0.015

0.02

0.025

Load of Flow 3

Loss

Rat

e on

Lin

k E

–>F

streamlinesimulationErlang B

Fig. 5. Comparions of burst loss rates estimated by different formulas inthe six-node network (Fig. 4).

1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28average load

Fig. 7. Comparions of burst loss rates estimated by different formulas inthe NSFNET network (Fig. 6).

by Erlang B formula and the streamline formula. We canobserve that the estimation given by the streamline for-mula is closer to the simulation result.

5.2. Performance study for the proposed routing algorithms

Experiments are conducted over three network topolo-gies, a 10-node network shown in Fig. 8, the 14-node NSF-NET topology and the 33-node Pan-European topology (seehttp://www.geant.net). In the Pan-European topology,some links are added to make the network bi-connected.Each link carries 32 wavelengths. Two traffic load scenariosare considered. The first one is the identical scenario,where the traffic load of each flow is equal. The secondone is the non-identical scenario where the traffic load ofeach flow is uniformly randomly chosen between 0:5cand 1:5c, where c is the average load of flows. The arrivalof bursts in each flow follows Poisson distribution. In theexperiments, after the route layouts are computed, weuse the simulator developed by us to measure the burstloss rates of different route layouts.

5.2.1. Performance study for the NSR problemThe following algorithms are implemented to solve the

NSR problem and the performance of the route layoutsfound by them is compared:

http://www.geant.net

0

1 2

53

4

6

9

7

8

Fig. 8. A 10-node network topology.


1. MILP1 presented in this paper to solve the NSR problem.The interpolation points of q in the piecewise functionbGðq;WÞ are 6.4, 12.8, 19.2 and 25.6. Note that the loadsare the offered load. The value of corresponding nor-malized load can be derived by division over the num-ber of wavelengths on a link.

2. SLNS-Heur presented in this paper. The optimizationprocess stops when the objective value reduction is lessthan 0.1% in the past 100 iterations or the number ofiterations reaches 1000, whichever is satisfied first.

3. The Erlang B based route layout MILP presented in [12](referred as Erl-MILP), where the streamline effect isnot considered and Erlang B formula is used to estimatethe loss. The parameters are set as in [12].

4. The Erlang B based route layout heuristic presented in[12] (referred as Erl-Heur), where the streamline effectis not considered and Erlang B formula is used to esti-mate the loss. The parameters are set as in [12].

5. The widest shortest path algorithm (referred as WSP).Here the flows are considered in a non-increasing orderof their traffic load. We found that such an orderachieves the best performance compared with the otherrouting order we have tested, including the randomorder, the least-load-first order, the longest-flow-firstorder and the shortest-flow-first order.

6. An MILP formulation to minimize the maximal load onany link (referred as Min–max).

7. The shortest path first algorithm (referred as SPF),which assigns the minimum-hop path to each flow.

In the experiments on the 10-node network, all thealgorithms are evaluated. In the experiments over the NSF-NET and the Pan-European topologies, only four algo-rithms, SLNS-Heur, Erl-Heur, WSP and SPF, are evaluated,because the MILPs are computationally intensive in theselarger networks:

(a) Results for 10-node network: We consider three sce-narios, where 10-, 11- and 12-node pairs are chosen

Table 1Burst loss rates of different algorithms in the 10-node network

Number of flows MILP1 SLNS-Heur Erl-MILP

8 2.71e�7 2.71e�7 6.79e�510 2.26e�6 2.83e�6 6.12e�412 5.10e�4 5.10e�4 2.03e�3

to be ingress–egress pairs, respectively. The load ofeach flow q ¼ 6:4. In SLNS-Heur, the routes for fourflows are re-computed in each iteration. The resultsare listed in Table 1. As the results show, the MILP1and SLFR-Heur methods give lower overall burst lossthan the other methods. Thus, the route layoutscomputed by our methods are better.

(b) Results for NSFNET topology: There is a flow betweeneach node pair, thus there are a total of 182 flows.Both the identical and the non-identical load sce-narios are tested. In SLNS-Heur, the routes of 15flows’ are re-computed in each iteration. Weobserve that SLNS-Heur gives lower overall burstloss than the other methods for both the identicaland the non-identical load scenario as shown inFigs. 9 and 10. We also observe that when the trafficload is light the performance gain of SLNS-Heur overthe other methods is greater. The gain decreases asthe load increases. We will discuss this phenome-non later.

(c) Results for Pan-European opology: There is a flowbetween each node pair, and thus there are a totalof 1056 flows. Both the identical and the non-identi-cal load scenarios are tested. In SLNS-Heur, theroutes for 15 flows are re-computed in each itera-tion. We see that SLNS-Heur gives lower overallburst loss than the other methods for both the iden-tical and non-identical load scenarios as shown inFigs. 11 and 12. We also observe that when the traf-fic load is light the performance gain of SLNS-Heurover the other methods is greater. It is due to the fol-lowing reason. In the Erlang B formula, the firstderivative is positive and the second derivative isnegative, so the loss rate increases more slowlywhen the load increases. Similarly, when estimatingwith the streamline effect formula, the loss rate willincrease more slowly as the load increases. As aresult, when the load is heavier, the differencecaused by different route layouts are smaller. Sothe performances of the different algorithms tendto be closer. Such behavior has been observed byother researchers [12].

5.2.2. Performance study for the FRR problemThe following algorithms are implemented to solve the

FRR problem and the performance of the route layoutsfound by them is compared:

� MILP2 proposed in this paper to solve the FRR problem.The interpolation points of q in the piecewise functionbGðq;WÞ are 6.4, 12.8, 19.2 and 25.6.

� SLFR-Heur proposed in this paper. In both phases, theoptimization process stops when the objective value

Erl-Heur WSP Min–max SPF

6.79e�5 2.03e�3 1.35e�4 7.79e�36.12e�4 1.20e�2 1.27e�3 1.28e�22.13e�3 3.78e�2 4.79e�3 5.90e�2

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8average load

SLNS–HeurErl–HeurWSPSPF

10–7

10–6

10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 10. Burst loss rates of different algorithms (NSFNET topology, non-identical load scenario).

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.3210

–7

10–6

10–5

10–4

10–3

10–2

10–1

average load

Loss

Rat

e


Fig. 11. Burst loss rates of different algorithms (Pan-European topology,identical load scenario).

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32average load


10–7

10–6

10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 12. Burst loss rates of different algorithms (Pan-European topology,non-identical load scenario).

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.810

–7

10–6

10–5

10–4

10–3

10–2

10–1

average load

Loss

Rat

e


Fig. 9. Burst loss rates of different algorithms (NSFNET topology, identicalload scenario).


reduction is less than 0.1% in the past 100 iterations orthe number of iterations reaches 1000, whichever is sat-isfied first.

� The Erlang B based failure recovery route layout MILPformulation extended from Teng and Rouskas [12](referred as Ext-Erl-MILP), where the loss estimation isbased on the Erlang B formula. The parameters are setas in [12].

� The Erlang B based failure recovery route layout heuris-tic algorithm extended from Teng and Rouskas [12](referred as Ext-Erl-Heur). In Ext-Erl-Heur, first the heu-ristic in [12] is used to determine the primary paths.Then, an algorithm similar to the second phase ofSLFR-Heur, except that the link cost estimation is basedon the Erlang B formula, is used to determine the backuppaths. The parameters of the first phase are set as in[12], and the parameters of the second phase are setthe same as the second phase of SLFR-Heur.

� An MILP formulation to minimize the maximal load inany link in any states (referred as Min–max).

� The shortest path algorithms (referred as SPF), wherethe minimum-hop path is selected as the primary path,and the minimum-hop path disjoint to the primary pathis chosen as the backup path.

In each topology, the probability of the normal state is99.9% and the 0.1% failure probability is evenly distributedamong all the links in the network. In the experiments overthe 10-node network, all the algorithms are evaluated. Inthe experiments over the NSFNET and the Pan-Europeantopologies, only three algorithms, SLFR-Heur, Ext-Erl-Heur,SPF, are evaluated, as the MILPs are computationally inten-sive for these larger networks:

(a) Results for 10-node network: We consider three traf-fic scenarios, where four-, five- and six-node pairsare chosen to be ingress–egress pairs, respectively.The load of each flow q ¼ 6:4. In both phases ofSLFR-Heur and the second phase of Ext-Erl-Heur,the routes for three flows are re-computed in eachiteration. The results are listed in Tables 2 and 3.

Table 2Expected burst loss rate over normal and failure states of different algorithms in the 10-node network

Number of flows MILP2 SLFR-Heur Ext-Erl-MILP Ext-Erl-Heur Min–max SPF

4 2.72e�10 2.72e�10 3.26e�10 3.26e�10 5.99e�10 1.33e�95 3.05e�10 3.05e�10 1.13e�7 1.13e�7 9.57e�7 1.13e�66 5.08e�10 6.38e�10 1.02e�6 8.61e�5 9.43e�5 2.08e�6

Table 3Expected burst loss rate in failures of different algorithms in the 10-node network

Number of flows MILP2 SLFR-Heur Ext-Erl-MILP Ext-Erl-Heur Min–max SPF

4 2.72e�7 2.72e�7 3.26e�7 3.26e�7 5.98e�7 1.31e�65 3.04e�7 3.04e�7 1.21e�6 1.21e�6 2.13e�6 1.71e�46 5.07e�7 6.37e�7 7.92e�5 1.02e�4 1.27e�4 1.97e�4

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8average load

SLFR–HeurExt–Erl–HeurSPF

10–6

10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 14. Expected burst loss rates over normal and failure states of diff-erent algorithms (NSFNET, non-identical load scenario).

10–1


As the results show, the proposed MILP2 and SLFR-Heur methods give lower expected burst loss overnormal and failure states and expected burst lossin failure states than the other methods. Thus, theprimary route layouts and also the backup route lay-outs computed by our methods are better.

(b) Results for NSFNET topology: Each node pair is aningress–egress pair, i.e., there are 182 flows. Boththe identical and the non-identical load scenariosare tested. In both phases of SLFR-Heur and the sec-ond phase of Ext-Erl-Heur, the routes for 15 flowsare re-computed in each iteration. It is observed thatSLFR-Heur gives the lowest expected burst loss overnormal and failure states for both the identical andthe non-identical load as shown in Figs. 13 and 14.Figs. 15 and 16 show that SLFR-Heur gives the low-est expected burst loss in failure states for bothidentical and non-identical load scenarios. So boththe primary and the backup route layouts deter-mined by SLFR-Heur are better. We also observe thatwhen the traffic load is light the performance gain ofSLFR-Heur over the Ext-Erl-Heur is greater. Besides,the gain of our algorithm is less in terms of expected

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8average load


10–7

10–6

10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 13. Expected burst loss rates over normal and failure states of diff-erent algorithms (NSFNET, identical load scenario).

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.810

–5

10–4

10–3

10–2

average load

Loss

Rat

e


Fig. 15. Expected burst loss rates in failure states of different algorithms(NSFNET, non-identical load scenario).

burst loss over failure states than in terms of theexpected burst loss over normal and failure states.We will discuss these observations later.

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

average load


10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 16. Expected burst loss rates in failure states of different algorithms(NSFNET, identical load scenario).

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32average load


10–7

10–6

10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 18. Expected burst loss rates over normal and failure states of diff-erent algorithms (Pan-European, non-identical load scenario).

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32average load


10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 19. Expected burst loss rates in failure states of different algorithms(Pan-European, identical load scenario).


(c) Results for Pan-European topology: Each node pair isan ingress–egress node, i.e, there are a total of1056 flows. Both the identical and the non-identicalload scenarios are tested. In both phases of SLFR-Heur and the second phase of Ext-Erl-Heur, theroutes for 15 flows are re-computed in eachiteration.

We see that SLFR-Heur gives the lowest expected burstloss over normal and failure states for both load scenariosin Figs. 17 and 18. Figs. 19 and 20 show that SLFR-Heurgives the lowest expected burst loss in failure states forboth load scenarios. So both the primary and the backuproute layouts determined by SLFR-Heur are better. We alsoobserve that when the traffic load is light the performancegain of SLFR-Heur over Ext-Erl-Heur is greater. This phe-nomenon has been discussed earlier in the performancestudy for the NSR problem. Besides, the gain of our algo-rithm over the others in terms of the expected burst loss

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32average load


10–7

10–6

10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 17. Expected burst loss rates over normal and failure states of diff-erent algorithms (Pan-European, identical load scenario).

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32

average load


10–5

10–4

10–3

10–2

10–1

Loss

Rat

e

Fig. 20. Expected burst loss rates in failure states of different algorithms(Pan-European, non-identical load scenario).


over failure states is less than in terms of the expectedburst loss over normal and failure states. The reason is thatwhen we choose two link-disjoint paths instead of one (i.ethe primary path only), the space to optimize the backuppath is smaller. Similar observations were made in [13].In [13], the performance enhancement is much less in pri-mary-backup path selection than in primary route selec-tion, though similar route selection techniques are used.However, the difference in this topology is not so large asin the case of the NSFNET topology. This is because thePan-European network is larger and denser and there aremore choices to select the backup path for a given primarypath.

6. Conclusions

Two problems of route optimization in OBS networkshave been studied in this paper. The first problem is todetermine a route for each flow to minimize the overallburst loss. The second problem considers the failure statesand determines the primary and backup paths for eachflow to minimize the expected burst loss over the normaland the failure states. We have discussed the streamline ef-fect, a special feature of OBS networks. We have alsoshown that the route selection based on Erlang B formulaor load balancing is inadequate due to the ignorance ofthe streamline effect. A new loss estimation formula whichconsiders the streamline effect has been developed. Basedon the new formula, we have developed MILP formulationsfor the two problems. Since MILP-based solutions are com-putationally intensive, we have proposed heuristic algo-rithms to solve the two problems. The simulation resultsshow that our algorithms are very effective in finding theroute layouts that yield lower burst loss than other knownalgorithms.

References

[1] C. Qiao, M. Yoo, Optical burst switching – a new paradigm for anoptical internet, Journal of High Speed Networks, Special Issue onOptical Networks 8 (1) (1999) 69–84.

[2] Y. Xiong, M. Vandenhoute, H.C. Cankaya, Control architecture inoptical burst-switched WDM networks, IEEE Journal on SelectedAreas in Communications 18 (10) (2000) 1838–1851.

[3] V.M. Vokkarane, J.P. Jue, Prioritized burst segmentation andcomposite burst assembly techniques for QoS support in opticalburst-switched networks, IEEE Journal on Selected Areas inCommunications: Special Issue on High-Performance Optical/Electronic Switches/Routers for High-Speed Internet 21 (7) (2003)1198–1209.

[4] J. Li, G. Mohan, K.C. Chua, Dynamic load balancing in IP-over-WDMoptical burst switching networks, Computer Networks Journal 47 (3)(2005) 393–408.

[5] X. Wang, H. Morikawa, T. Aoyama, Burst optical deflection routingprotocol for wavelength routing WDM networks, in: Proceedings ofthe SPIE/IEEE OPTICOMM 2000, Dallas, TX, USA, 2000.

[6] S.K. Tan, G. Mohan, K.C. Chua, Algorithms for burst rescheduling inWDM optical burst switching networks, Computer Networks Journal41 (1) (2003) 41–55.

[7] M.H. Phung, K.C. Chua, G. Mohan, M. Motani, T.C. Wong, Thestreamline effect in OBS networks and its application in loadbalancing, in: Proceedings of the BroadNets, Boston, MA, USA, 2005.

[8] K. Thompson, G.J. Miller, R. Wilder, Wide-area internet traffic’s andcharacteristics, IEEE Network 11 (6) (1997) 10–23.

[9] E. Kozlovski, Survivability of wavelength-routed optical burst-switched networks with guaranteed IP services, in: Proceedings ofFifth International Conference on Transparent Optical Networks,Warsaw, Poland, 2003.

[10] Y. Xin et al., Fault management with fast restoration for opticalnetworks, in: Proceedings of the Broadnets, San Jose, CA, USA, 2004.

[11] D. Griffithand, S. Lee, A 1 + 1 protection architecture for optical burstswitched networks, IEEE Journal on Selected Areas inCommunications 21 (9) (2003) 1384–1398.

[12] J. Teng, G.N. Rouskas, A traffic engineering approach to pathselection in OBS networks, OSA Journal of Optical Networking 4(11) (2005) 759–777.

[13] K. Gopalan, T. Chiueh, Y. Lin, Load balancing routing withbandwidth-delay guarantees, IEEE Communications Magazine 42(6) (2004) 108–113.

Qian Chen received her B.E. degree fromBeijing University of Posts and Telecommu-nications, China in 1996. She received her M.E.degree in Electrical and Computer Engineer-ing from National University of Singapore in2003. Now she is working towards her Ph.D.degree. Her research interests focus on opticalburst switching.

Gurusamy Mohan received the Ph.D. degree
in Computer Science and Engineering fromthe Indian Institute of Technology (IIT),Madras in 2000. He joined the National Uni-versity of Singapore in June 2000, where he iscurrently an associate professor in theDepartment of Electrical and Computer Engi-neering. He has held a visiting position atIowa State University, USA, during January–June 1999. His current research interests arein WDM OCS networks, WDM OBS networks,MPLS switching networks, wireless sensor
networks and grid networks.

Kee Chaing Chua received his Ph.D. degree in
Electrical Engineering from the University ofAuckland, New Zealand, in 1990. Followingthis, he joined the Department of ElectricalEngineering at the National University ofSingapore (NUS) as a lecturer, became a seniorlecturer in 1995, an associate professor in1999 and professor in 2006. From 1995 to2000, he was seconded to be the DeputyDirector of the Center for Wireless Commu-nications (now Institute for InfocommResearch), a National Telecommunication
R&D Institute funded by the Singapore Agency for Science, Technologyand Research. From 2001 to 2003, he was on leave of absence from NUS towork at Siemens Singapore where he was the founding head of the ICM
Mobile Core R&D Department. He is a director for the Singapore NationalResearch Foundation now. He has carried out research in various areas ofcommunication networks. His current interests are in ensuring end-to-end quality of service in wireless and optical networks. He is a recipient ofan IEEE Third Millennium Medal.

route optimization in optical burst switched networks considering the streamline effect

Documents