Multi-class Service Based on the Adaptive routing Algorithm in WDM

networks Zichun Le1, Zhijun Zhu2, Ran Zhu2, Minglei Fu2

1College of Sciences, Zhejiang University of Technology, Hangzhou 310032, China

2College of Information Engineering, Zhejiang University of Technology, Hangzhou 310032, China

ABSTRACT

It is important to analyse blocking probability in the WDM networks. In this paper, we present an analytical model for supporting multi-class service with the blocking probability analysis and adaptive routing algorithm to solve the potential shortcomings in the real network. We make the use of the idea of segmented routes according to the finite wavelength conversion resources. We then combine the each segment to get the whole blocking probability. The results show that, by adopting the adaptive routing algorithms, the network can calculate the blocking probability for all the candidate routes, and the request which takes the highest priority will choose the minimum blocking probability route. There are two features in our paper. First, a method of segmented route is designed. Second, use k-shortest routing algorithm to get the minimum blocking probability routing between source node and destination node.

Keywords: optical networks; adaptive routing algorithms; blocking probability; quality of service.

1. INTRODUCTION

As the trend of service differentiation and quality of service require multi-class services [1] for efficiency purposes. In particular, as wavelength division multiplexing (WDM) technique emerges as a promising method to meet the rapidly growing demands on bandwidth in present communication networks, supporting multi-class service at the WDM become a significant issue. Routing problem is a key issue in optical networks. It can be divided into three types of algorithms, including fixed routing, alternate routing [2] and adaptive routing algorithms [3-4]. The adaptive routing algorithms can dynamically cater for the real need of network requests. Hence, the adaptive routing algorithms have been studied extensively. However, based on the previous studies on blocking probability [5-7], we know that it is difficult to calculate the blocking probability in the adaptive routing algorithms directly. Moreover, to our best knowledge, current approaches for calculating the whole network blocking probability don’t take the quality of service (QoS) into consideration.

In this paper we present an analytical model for supporting multi-class service with the blocking probability analysis and adaptive routing algorithm to solve the potential shortcoming stated above. We make the use of the idea [3] [8] of segmented routes according to the finite wavelength conversion resources. The NSF net is chosen as the simulation network. It is an irregular network with 14 nodes and 21 links. We intend to design three wavelength convertible nodes in the NSF net count on our algorithm. The task of this algorithm is to find out three nodes that are traversed most times. In this solution, a route is divided into numbers of segments by wavelength convertible nodes, and then combines the

Optical Transmission, Switching, and Subsystems V,edited by Dominique Chiaroni, Wanyi Gu, Ken-ichi Kitayama, Chang-Soo Park,

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(a) a route

(b) divide into two segments

single-link part and overflow part to get the whole network blocking probability. The adaptive routing algorithm for multi-class service we define in the present paper including three kinds of service request can flexibly choose the minimum blocking probability route for the call. When the call arrival is coming, first of all, we use two different shortest path algorithms to get a route, at the same time calculate the blocking probability of this selected route. Secondly, getting a second-rate shortest route for the call, and calculate the blocking probability as well. Finally, to get a third shortest route and it’s blocking probability. Adopting this measurement the first-class request can certainly reach it’s destination via the minimum blocking probability route. We choose two approaches to select routing for calculating blocking probability that can accommodate for the need of multi-class requests. One is k-shortest routing algorithm, the other is shortest routing algorithm based on coloring graph (CG). For the numerical applications, we take the NSF net as the simulation network and compare two approaches listed above. The numerical results show that, by adopting the adaptive routing algorithms, the network can calculate the blocking probability for all the candidate routes, and the request which takes the highest priority will choose the minimum blocking probability route.

2. THE NETWORK MODEL IN THIS PAPER

2.1 The model for segmented routing

Figure.1 an example of dividing a route into segments

It is simple to separate a route into segments by wavelength convertible node. For example, suppose in Fig.1 (a) node1 is wavelength convertible node, while other nodes are inconvertible. We divided route (a) into two segments. The aim to separate each route is to simply calculate the blocking probability at the wavelength convertible nodes. However, there is a special case out of the assumption that seems to be source and destination nodes, s and d. They have no opportunity to be blocked. Therefore, every segment must abide by wavelength continuity constraint. The call setups that arrive at each node are divided into k classes. )...2,1( kiCi = is used to denote each class and the priority is lower from

1C to kC .The arrival rate of each class follows the same Poisson distribution.

2.2 Notations and assumptions

The network is assumed as full light splitting capability, however only finite wavelength conversion capability. Consequently, blocking happens not only on links, but also at nodes.

2.3 Network and traffic

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● In the network, there are N nodes, L links, and W wavelengths. Every link has an identical wavelength.

● A lightpath setup request is denoted by two ends (s,d), where s and d are the source node and the destination node.

● There are at most N×(N-1) pairs, since all connections are directional.

●We assume that the arrival rate of each class is with identical Poisson distribution with rate iλ . The service time is

exponentially distributed with a unit mean.

● The cost of each link is assumed as one unit. Therefore, the cost of a path is its hop distance.

The assumptions listed above are to simplify the calculation.

2.4 symbols and notations

●P stands for probability, depending on the context. For example, rp is the blocking probability of route r, sp

indicates the probability of segment and Bp is the probability of the whole network.

● The offered load for s-d pair i is iT while irT is the load to route r of s-d pair i. one bar (-) is added at the top of

the offered load to indicate the corresponding carried load. For instance, irT is the carried load on route r of s-d pair i.

● For a link l, lF is the variable that indicates the number of free wavelengths on that link. F is also used as a

segment or a path, depending on the context.

2.5 Analytical model

The models are chose to simplify the calculation of blocking probability of the candidate routes. It is significant to decide the overflow traffic to the queue of wavelength convertible node, and then get the blocking probability at that node. After that, calculate the blocking probabilities of segments. Finally, combine the blocking probabilities of each segment into the blocking probabilities of the whole network.

1

00 1

( ) [ 0] ( ) [ ]s s i im i

p s p F p m p F mΓ+

≥ =

= = = =∑ ∏ (1)

Where 0sF = means there is no free wavelength in the segment. Then we turn to focus on Eq.(2)

1

1 1

1- (1- ( )) (1- ( ))r r

r s wci n

p p si p nΓ + Γ

= =

= ×∏ ∏ (2)

Where rΓ stands for the number of convertible nodes in the route r. ( )wcp n is the blocking probability of the

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wavelength converter queue at node n.

1 1

,,( ) [ 0 | 0, 0]

n n n n

i rof S S S Sp n p F F F

+ += = > > (3)

Where , ( )i rofp n denotes the probability that the traffic stream r of s-d pair overflowing to the converter queue at

node n. Finally, the whole network blocking probability is: ( 1)

1( 1)

1

1N N i

iB N N i

i

p TT

× −

=× −

=

= − ∑∑

(4)

Where irT and i

rT is the offered load and carried load to route r of s-d pair i. Suppose in the network has N nodes,

and there are at most ( 1)N N× − pairs, since all connections are directional. The detailed process refer to [3][8].

3. THE STATEMENT OF MULTI-CLASS

The idea of segmented routes is firstly presented in reference [8]. However, it does not take the quality of service into consideration. We use k -shortest algorithm and coloring graph algorithm to solve the problem and get a series of candidate routes for each request from different classes. We choose two approaches to select routing. One is k-shortest route algorithm, the other is shortest route algorithm based on coloring graph. In the following table we demonstrate the candidate route for the i-class calls according to the ways mentioned above. Where, node 3, 7 and 10 are selected as wavelength convertible node.

Table.1 .candidate routes (k -shortest algorithm)

s-d pair Route1 Route2 Route3

0-13 0-7-10-13 0-1-3-9-13 0-7-10-12-11-13 1-11 1-3-9-12-11 1-3-9-13-11 1-2-5-11 2-12 2-5-11-12 2-5-8-10-12 2-5-4-6-7-10-12

Table.2 candidate routes (coloring graph)

s-d pair Route1 Route2 Route3 0-13 0-7-10-13 0-1-3-9-13 0-2-5-11-13 1-11 1-3-9-12-11 1-2-5-11 1-0-7-10-13-11 2-12 2-5-11-12 2-1-3-9-12 2-0-7-10-12

In the following, we take some routes for example to calculate the rp (blocking probability of the route).

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Table.3 comparison of two routing approaches

s-d (k-shortest) ( rp )

(k-shortest)

s-d (coloring graph) ( rp )

(coloring graph) 0-1-3-9-13 0.0336 0-1-3-9-13 0.0336

0-7-10-12-11-13 41.00 10−× 0-2-5-11-13 0.1327 1-3-9-13-11 0.0671 1-2-5-11 0.0336

1-2-5-11 0.0336 1-0-7-10-13-11 0.0671 2-5-8-10-12 0.0336 2-1-3-9-12 0.0336

2-5-4-6-7-10-12 0.0671 2-0-7-10-12 41.00 10−×

After the calculation shown in Table 3, we will choose the minimum blocking probability route for the first-class

request. In other words, we get a proper route to cater for the need of quality of service.

4. THE STATEMENT OF ADAPTIVE ROUTING ALGORITHM

The adaptive routing algorithm has the following procedures.

Step1: set 0Bp =0, and set number of iterations counter α =1. Choose an error tolerance valueε .

Step2: Determine the blocking probability of each segment using (1)

Step3: Determine the blocking probability of a wavelength convertible node using (3).

Step4: Determine the blocking of a route using (2).

Step5: Obtaining three routes from k-shortest path algorithm. Meanwhile, calculate the blocking probability for these three routes respectively, Then selecting the minimum blocking probability route for first-class request.

Step6: Reuse the k-shortest path algorithm to update the network situation and to depict the routing table in

real-time. Calculate the overall blocking probability Bpα using (4).

Step7: If | 1B Bp pα α−− |<ε , the algorithm stops, and the whole network blocking probability is acquired. Otherwise,

1α α= + , go to step 2.

5. NUMERIC RESULT

5.1 Simulation Networks

We take the NSFNET as the simulation network. The NSFNET is an irregular network with 14 nodes and 21 links (Figure.2).

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1100.

2 40800

300

Figure 2: The 14-node NSFNET

5.2 Traffic model

The requests which arrive at every node are divided into 3 classes. And requests of the 3 classes have identical Poisson arrival rate. The arrival rate of class r -request that originate at node i to node j is denoted

by ( ) 31,, ≤≤≥ rijrijλ . The mean of the exponentially distributed service time of class r -requests that originate at

node i to node j is denoted by ( )rijµ1 . Therefore, the load unit between node i to node j is ( ) ( ) ( )r

ijr

ijr

ij µλρ = .

5.3Calculation of fairness

The network fairness ratio is given by:

jir BBf = (5)

Where iB and jB are the highest and lowest blocking probabilities respectively. The closer rf to 1 is, the

better the fairness is.

5.4 Blocking probability analysis

Figure 3 show that k-shortest and coloring graph algorithm improves the blocking probability compared against the shortest-cost strategy ( SP). In the 14-node NSFNET, figure 3 show that the mean of blocking probability of coloring graph class 1 reduces 29.9% and the mean of blocking probability of k-shortest class 1 reduces 36.9%, meanwhile the mean of blocking probability of coloring graph class 2 reduces 20.2% and the mean of blocking probability of k-shortest class 2 reduces 27.49%. However, a certain wavelengths which belong to the high classes are probably used by the lower class-requests and those wavelengths might not be allocated for the higher-class requests at the same time. Hence, the blocking probability of the lowest class increases little. Coloring graph algorithm assume last routing selection is blocked, so it will need a longer routing to reach the destination node than k-shortest algorithm. When the scale of networks is not large enough the performance of coloring graph algorithm can not reach the best effect. In conclusion, the blocking probability of the whole network improves by adopting the k-shortest and coloring graph algorithm.

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bloc

king

pro

babi

lity

C

C

C

C

C

C

C

C

C

t t

t '

t t

h h

h

= =

=

-L

a a

a

S

UJ

N-)

—

F- =

m

i b

U

I I I I I—e— :sp

j —4— :k-shortest8

—- :coloring graph

7

8

8?

4

3

2

20 30 40 80 80 70 80 90

Load (in Erlang)

Figure 3: Comparison of Blocking Probability in NSFNET

5.5 Fairness analysis

Figure 4 show that k-shortest and coloring graph algorithm improves the network fairness compared against the

shortest-cost strategy (SP). The value of rf reduces 26.9% and 32% in NSFNET respectively. Numerical results

show that the adaptive routing algorithm reduces the blocking probability of the whole network. And although the blocking probability of the lower-class requests increase little, the BP of the high-class requests reduce to a larger extend. Therefore, the fairness of the whole network improves.

Figure 4: Comparison of fairness in NSFNET

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6 THE CONCLUSION

In this paper, we present an analytical model and for the blocking probability analysis on adaptive routing over the WDM networks with finite wavelength conversion capability. It is difficult to calculate blocking probability analytically on adaptive routing. The key problem is how to model the finite nature of wavelength conversion. We make use of the idea of segmented route to deal with the finite wavelength conversion. According to this method, a route is divided into a series of segments separated by wavelength convertible nodes. We use the analytical model to calculate the blocking probability of the link, the blocking probability of the segments. Finally, get the blocking probability of the whole network. We then proposed an adaptive routing method in finite wavelength conversion optical networks. This method seeks the path with minimum hop distance while with the minimum blocking probability to consider the problem of multi-class service; this is more realistic in practice as the need of quality of service.

Acknowledgements

This work is performed with support from the fund of Science and Technology Department of Zhejiang Province, People’s Republic of China (No.2005C21010). Zichun Le is the author to whom the correspondence should be addressed.

References:

1 Sridhar Ramesh, George N. Rouskas, Harry G. Perros, "Computing Blocking Probabilities in Multi-Class Wavelength Routing Networks ," ACM Transactions on Modeling and Computer Simulation, Vol.10, 87-103 (2000).

2 Ramu Ramamurthy, Biswanath Mukherjee, "Fixed-alternate routing andwavelength conversion in wavelength-routed optical networks," IEEE/ACM Transactions on Networking, 2002;6

3 C. F. Hsu, T. L. Liu, and N. F. Huang, "Performance of Adaptive Routing Strategies in Wavelength-Routed Networks," IEEE IPCCC 2001, April 4-6, 2001, Phoenix, Arizona, USA

4 Xingbo Gao, Mostafa A. Bassiouni, "Conversion cascading constraint-aware adaptive routing for WDM optical networks, " Journal of Optical Networking, vol.6, No.3. 278-294 (2007) 5 Yuanoiu Luo, Ansari Nirwan, "A computational model for estimating blocking probabilities of multifiber WDM

optical networks, " IEEE Communications Letter, 60-62 (2004)

6 Syed Muhammad Hassan Zaidi, Amjad Mahmood. "Blocking optimization in dynamic traffic all-optical WDM networks without wavelength conversion," Proceedings IEEE INMIC 170-175 (2003)

7 O. Gusak and E. Karasan, "Analysis of blocking probability in WDM all-optical networks with non-Poisson traffic statistics ," Proceedings of The First International Conference on Transparent Optical Networks, 8-11 June 1999, Kielce, Poland, 27-32.

8 Gee-swee Poo, Aijun Ding, Sun-Teck Tan, "Blocking Performance Analysis on Adaptive Routing over WDM Networks with Sparse Wavelength Conversion ," Photon Netw Commun , 211-218 (2006)

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