- Email: [email protected]
Static and dynamic routing and wavelength assignment algorithms for future transport networks
ARTICLE IN PRESS
Optik
Optics
Optik 121 (2010) 702–710 www.elsevier.de/ijleo
Static and dynamic routing and wavelength assignment algorithms for future transport networks Rajneesh Randhawaa,, J.S. Sohalb a
Department of Computer Sciences, Regional Institute of Management and Technology, Mandi Govindgarh, Punjab, India Ludhiana College of Engineering and Technology, Ludhiana, Punjab, India
b
Received 10 August 2008; accepted 20 November 2008
Abstract In this paper, two static and three dynamic routing algorithms have been proposed and compared to some of the existing algorithms on the basis of blocking probability. The two proposed static routing and wavelength assignment (RWA) algorithms reduce the blocking probability to maximize the utilization of network. For dynamic algorithms, first a model with no weights assignments is presented and then three algorithms are proposed and analysed with weight assignment resulting in reduction of blocking probability. All these algorithms are analysed and compared with four wavelength assignment schemes which are first-fit, random, most used and least used. It is shown that our proposed static algorithms give the best performance for first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate routing algorithm gives the lowest blocking probability. For dynamic routing, it has been shown that our proposed algorithm ‘‘less weight to maximum empty and nearest’’ gives the least blocking probability as compared to the other dynamic routing algorithms for random, most used and least used wavelength assignment strategies. r 2008 Elsevier GmbH. All rights reserved. Keywords: Routing; Wavelength assignment; Algorithms; WDM
1. Introduction Today’s global communications world has many different definitions for optical transport networks (OTNs) and many different technologies that support them. An optical transport network is composed of a set of optical network elements connected by optical Corresponding author.
E-mail addresses: [email protected] (R. Randhawa), [email protected] (J.S. Sohal). 0030-4026/$ - see front matter r 2008 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2008.11.004
fibre links, able to provide functionality of transport, multiplexing, routing, management, supervision and survivability of optical channels carrying client signals, according to the requirements given in Recommendation G.872. Presently optical fiber technology is used to transmit gigabits of data per second over thousands of kilometres with extremely low loss. The demand of these high speed applications, however, has put a question mark on possibility of the traditional approach of building faster time division multiplexed (TDM) networks. This has increased interest in building all-optical
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
networks where wavelengths, rather than timeslots, are switched. The routing and wavelength assignment (RWA) [1] problem in wavelength routed WDM networks consists of choosing a route and a wavelength for each connection so that no two connections using the same wavelength share the same fiber. The requirement that connections sharing the same fiber must use different wavelength channels is often referred as distinct channel assignment requirement [2]. Routing [3,4] can be subdivided in these two categories: static routing and dynamic routing. In static routing, all the strategy for routing has to be decided offline. There are two strategies which are mainly mentioned in this category. The first is fixed routing [5] in which fixed routing path between the source and the destination is calculated offline using algorithm, just like Dijkstra algorithm. If path is empty, then route the incoming on this path; otherwise call is blocked. The second is fixed alternate routing [6] in which one has to calculate one more alternate path in addition to fixed path. If fixed channel is empty, then route the incoming call through fixed paths. If the fixed channel is not empty then incoming call is routed through alternate predefined paths. Dynamic routing [7] is a method for efficient use of given resources. In this method all the routing schemes are decided online according to present network state. Deciding factors in dynamic routing can be number of empty channels, distance between source destination and more. One example for dynamic routing can be adaptive algorithm. Connections sharing with common fiber must use different wavelengths [8]. A violation of the distinct channel assignment constraint is often referred to as a wavelength conflict. Furthermore, if the wavelength conversion is not possible in the network nodes, then an additional constraint, called wavelength continuity, must be satisfied, i.e., each connection must use the same wavelength on every link. This constraint together with distinct channel assignment gives the RWA problem in all-optical network its special characteristics. If the traffic is not static but lightpath requests arrive randomly following some traffic process [9–12], the RWA constitutes a typical decision making problem. When a certain event occurs, one has to decide on some action. The set of possible actions is finite, i.e., first block the call and second route it by assigning the best available combination of route and wavelength. A feasible RW (routing and wavelength) combination is such that along the route from the source to destination the wavelength is not being used on any of the links. If no feasible RW combination exists, the call is unconditionally rejected. Furthermore, the accepted connections cannot be interrupted. RWA algorithms in optical communication was initially presented by Mukherjee [1] and validated by
703
Ramamurthy and Mukherjee [13]. Various routing algorithms in wavelength-routed optical networks have been analysed [5–10] and it has been shown that dynamic routing schemes [7] such as least-loaded routing achieve significantly better blocking performance when compared with fixed shortest-path routing, in wavelength-continuous and wavelength-convertible networks. The analytical model for alternate routing has also been investigated [6] and the effect of blocking probability of paths with different numbers of hops and different wavelength-assignment policies has been reported. Although, a few algorithms have been reported for control mechanisms of the RWA problem. Some static algorithms have been analysed in where fixed and alternate fixed path algorithms has been reported to reduce the blocking probability. Also some dynamic algorithms have been reported for reduction of blocking probability for better utilization of bandwidth and resources but very less work has been reported for routing with wavelength assignment techniques like random, least used and most used. In this paper, we propose two new static and two dynamic algorithms to reduce the blocking probability further. We have shown that our algorithms have better blocking probability as compared to the existing algorithms. Further, we analyse our routing algorithms for random, most-used and least-used wavelength assignments. For static algorithms, we assume that the traffic is static, i.e., the problem is to configure a given static set of connections between the given nodes in the network. The network itself can be a single or multi-fiber network and this kind of approach is relevant in the backbone networks, where it may be reasonable to assume that the traffic is static. First, some assumptions are to be taken for calculating the blocking probability in Section 2 and then analytical model is proposed in Section 3 based on these assumptions. The wavelength assignment techniques are discussed in Section 4. After giving brief introduction to algorithms in Section 5, the existing and proposed static algorithms are implemented in Sections 6 and 7, respectively. The dynamic algorithms are proposed in Section 8 and results and discussion have been given in Section 9 by comparing all these algorithms. Finally conclusions are made in Section 10.
2. Assumptions In our proposed model, following are the assumptions: 1. Call arrives at each node following poisson distribution. 2. Call holding time is exponentially distributed with unit means. 3. Calls which cannot be established are blocked. 4. Capacity of all the links is equal.
ARTICLE IN PRESS 704
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
5. Wavelengths are assigned using first-fit and random methods. 6. N is the variable used to define no of time calls have to arrive, as we increase the value of N we get results more close to reality. 7. Nodes are not having wavelength conversion capability.
3. Analytical model 1. Link is the set of links numbered from 1 to L. Link ¼ f1; 2; . . . . . . . . . ; Lg 2. Channels is the number of channels from 1 to C.
3. 4.
5. 6.
Channels ¼ f1; 2; . . . . . . . . . ; Cg Load is kept 13 Erlang except from varying load case. Connection matrix is a matrix used to store the status of each channel (busy/empty) and also holding time information. Call arrival rate is l. P is the set of all possible paths between source and destination Path ¼ fP1 ; P2 ; . . . . . . . . . ; Pn g
Let XP be the random variable representing the number of idle wavelengths on path P. If path consist a single link E and it may be written as XE. We will have blocking in this case by the condition on a Path PE link from source to destination as X Pr ½X E ¼ 0jX 1 ¼ m1 ; . . . . . . ; X k ¼ mk blocking ¼ mX0
Pr ½X 1 ¼ m1 ; . . . . . . ; X k ¼ mk ¼
X
p0 ðmÞ
k Y
Pr ½X j ¼ mj
j¼1
mX0
If oL is the common set of empty wavelengths over some Path with hope length L. Suppose Wij is the available wavelength bank for jth link when ith call arrive. We can say Aði; jÞ ¼
N X k X
oL 2 W ij
i¼1 j¼1
for a fixed i, if oL is empty, then incoming call will be blocked as no availability of the wavelength for the path f1; 2; . . . . . . . . . ; kg. If there is a common wavelength present over the path, then the call will be routed and connection will be successful. In this way blocking can also be calculated as blocking ð%Þ ¼
Successful attemts to establish a call Total attempts
4. Wavelength assignment strategies In this work, these wavelength assignment strategies are followed. (1) First-fit wavelength assignment: let w0 ; w1 ; . . . . . . . . . ; wW be the wavelengths in the network. The wavelength chosen for a connection has the smallest index among the wavelengths which are available along the path. The first-fit heuristic is proposed in [6] and shown to be very effective. Here the first available wavelength in the available wavelength bank will be assigned to the incoming call. (2) Random wavelength assignment: a wavelength to be used for a connection is chosen randomly among wavelengths which are presently not in use. If oL is the wavelengths bank for a path and its length is l than assigned wavelength with number ceil (rand*l). Ceil is a function in MATLAB to assign next higher integer for a fraction and same value for an integer. (3) Most used wavelength assignment: in this algorithm a counter is used to monitor how frequently a channel is being used; here a channel is selected from the empty channels list with the highest number of frequency. (4) Least used wavelength assignment: same as the above algorithm, we choose the least frequently used channel from the empty channels list instead of the most frequently used one in the above case.
5. Algorithms In order to demonstrate that how our approach is performing in comparison with existing approaches, it is imperative to analyse the existing algorithms using our model for the proposed algorithms. In absence of a suitable simulator that could support our proposed heuristics, some codes have been developed in MATLAB to run the simulation. It accepts input parameters such as the number of nodes in the network, link information with weight, number of wavelengths per fibre, connection requests. Some of the calls may be blocked because of the unavailability of free wavelength on links along the route from the source to the destination. The ratio of the total number of calls blocked to the total number of light path requests in the network determines the blocking probability of the technique.
6. Analysed static routing algorithms (1) Shortest path algorithm (SRW1). Here shortest path algorithm is used for routing with first-fit and random wavelength assignment strategy is used for wavelength assignment. For each incoming call, first of all try to establish the connection on first wavelength using shortest
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
705
Fig. 1. Shortest path between nodes 1 and 10.
route. If unsuccessful, then connection is tried on second wavelength and so on up to the last wavelength. If unsuccessful than call is said to be blocked. Dijkastra algorithm can be used to calculate the shorted path between a given source-destination pair. Also algorithm used is given below as per the setup consisting of 10 nodes as shown in Fig. 1.
Fig. 2. Alternate shortest path 1.
Algorithm 1. 1. for link 1 to L 2. for generation_request 1 to N 3. for loop 1 to link 4. Calculate call arrival rate 5. Calculate holding time 6. If (check for some empty wavelength) 7. If (check for wavelength assignment method) 8. Method ¼ 1 then first-fit assignment 9. elseif (Random) 10. Random assignment 11. elseif (Most-used) 12. Most-used assignment 13. else 14. Least-used assignment 15. Assign busy status and holding time in the connection matrix to the selected parameters 16. end 17. Decrement holding times for all non-free channels 18. end 19. Check whether there is some free channel in connection matrix 20. If no free channel then 21. blocked_call ¼ blocked_call+1 22. end 23. Clear temporary variables 24. end 25. blocking ¼ blocked_call*100/gen 26. end (2) Alternate shortest path algorithm (SRW2). In alternate shortest path algorithm, for each incoming
Fig. 3. Alternate shortest path 2.
call first, try to establish the connection on channels with shortest route. If unsuccessful, then we try to establish connection on alternate shortest path channels. If again unsuccessful, then call is said to be blocked. Here we monitor the status of channels. In case there is minimum one channel empty, then the call can be successful. But if all channels are occupied, then incoming call will be blocked. The alternate shortest paths 1 and 2 are shown in Figs. 2 and 3, respectively. Alternate shortest path routing 1. Initialize all the parameters 2. If there is at least one empty channel on shortest path 3. Route the call through shortest path using Algorithm 1 4. elseif there is at least one empty channel on alternate shortest path 5. Route the call through alternate shortest path using Algorithm 1 6. else 7. Block the call
ARTICLE IN PRESS 706
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
8. Repeat up to number of times as given by number of generation one wish to test
7. Proposed static algorithms (3) Maximum empty channel routing (SRW3). In this algorithm, it is required to monitor all the paths between a source and destination pair. When a call arrives first we check status of all paths and route the call through the channel with maximum number of empty channels. Maximum empty channel routing 1. Initialize all the parameters 2. Calculate the number of empty channels on each path 3. Select one with maximum empty channels 4. If at least one empty channel is there on any path 5. Route the call through that path using Algorithm 1 6. else 7. Block the call 8. Repeat up to number of times as given by number of generation one wish to test (4) Combined path algorithm (SRW4). In this algorithm, all the channels are combined which belongs to shortest path and alternate shortest path. This combination makes a bank of all the channels (wavelengths); also some wavelength assignment strategy is used for wavelength assignment. For each incoming call first of all, try to establish the connection on first wavelength (first-fit) using any route. If unsuccessful, then connection is tried on second wavelength and so on up to the last wavelength. If unsuccessful then call is said to be blocked. Combined path algorithm: 1. Initialize all required parameters 2. Combine channels of all the given paths and consider them as one common channel 3. If at least one channel is empty 4. Route the call using Algorithm 1 5. else 6. Block the call 7. Repeat up to number of generation
8. Dynamic algorithms Proposed Algorithm 1: no weight assignment (DRW1). In this algorithm no weights are assigned and all the links have same weight. So in this dynamic (on-line) routing, first calculate shortest path then alternate shortest path and then as per the availability of empty wavelengths on links as the call arrive in the network, calculate all available paths. We have designed a MATLAB programme to calculate all possible path of
Fig. 4. Graph with 10 nodes and 21 edges.
the given network. The setup with 10 nodes for this algorithm is shown in Fig. 4. The algorithm is 1. Generate a source and destination pair 2. Calculate all possible path between this pair 3. If there is empty wavelength on shortest path 4. Route the call through shortest path using Algorithm 1 5. elseif there is an empty wavelength on alternate path than 6. Route the call through this path using Algorithm 1 7. else 8. Call is blocked 9. Repeat up to number of generation Proposed Algorithm 2: less weight to less used (DRW2). In this algorithm, first we calculate the number of times each link is being used, then we assign lower load to these nodes to make the network full utilization of each node. The setup is shown in the Fig. 5. The algorithm is 1. By running a programme calculate number of times each link was used 2. Assign lower weight to the nodes which are used lesser times 3. Generate a source and destination pair 4. Calculate all possible path between this pair 5. If there is empty wavelength on the path with lowest weight 6. Route the call through this path using Algorithm 1 7. elseif there is an empty wavelength on the path with next higher weight 8. Route the call through this path using Algorithm 1 9. else 10. Call is blocked Repeat up to number of generation
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
707
alternate shortest path (with 1 fixed and 2 alternate) algorithm, 2-combined path algorithm, 3-combined path algorithm, max empty channel path (3 alternate paths) algorithm with different wavelength assignment strategies have been shown in Figs. 7–13. It is observed that for all these algorithms, first-fit wavelength assignment technique gives the least blocking probability. There is difference in all the routing techniques and wavelength assignment strategy except for the alternate
Fig. 5. Network with static weight assignment.
Fig. 7. Performance of shortest path algorithm with different wavelength assignment strategies.
Fig. 6. Network shows a link distance from source and destination.
Proposed Algorithm 3: less weight to max empty and nearest (DRW3). In this algorithm, the weights are assigned dynamically, i.e., the weights are inversely proportional to the sum of its distances of its end nodes to the source and destination and directly proportional to the no of empty wavelengths on that link: W¼
Fig. 8. Performance of alternate shortest path algorithm with different wavelength assignment strategies.
No of empty wavelengths available on that link Sum of distances of link from source and destination
In Fig. 6, we can see that the total distance of above graphs node f7; 9g to source destination pair f1; 10g is 2+1 ¼ 3.
9. Results and discussion The performance of existing and proposed algorithms with different wavelength assignment algorithms have been investigated first. For static algorithms, the shortest path algorithm, alternate shortest path algorithm,
Fig. 9. Performance of alternate shortest path (with 1 fixed and 2 alternate) algorithm with different wavelength assignment strategies.
ARTICLE IN PRESS 708
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
Fig. 10. Performance of 2-combined path algorithm with different wavelength assignment strategies.
Fig. 11. Performance of 3-combined path algorithm with different wavelength assignment strategies.
path, where all wavelength assignments give close blocking probabilities. Let us now investigate these algorithms together with individual wavelength assignment strategies. The performance of analysed and proposed static algorithms as the load in increased with first-fit wavelength assignment, random wavelength assignment, most-used wavelength assignment and least-used wavelength assignment has been shown in Figs. 13–16, respectively. By the analysis of graphs obtained by the simulation of the above algorithms we can again say that the combined path algorithm with first-fit wavelength strategy is working well. We can see the reduced
Fig. 14. Performance of static algorithms with random wavelength assignment as load in increased.
Fig. 12. Performance of max empty channel path (3 alternate paths) algorithm with different wavelength assignment strategies.
Fig. 15. Performance of static algorithms with most-used wavelength assignment as load in increased.
Fig. 13. Performance of static algorithms with first-fit wavelength assignment as load in increased.
Fig. 16. Performance of static algorithms with least-used wavelength assignment as load in increased.
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
blocking in this case with less complex algorithm. But if we talk about random wavelength assignment then it is found that the performance of alternate shortest path and maximum empty channel algorithms are comparable. So we can say that our proposed algorithms SRWA3 and SRWA4 are good to be used with first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. The blocking probability has been reduced as compared to the existing static algorithms. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate algorithm gives the lowest blocking probability. The performance of proposed dynamic algorithms as load in increased with first-fit wavelength assignment, random wavelength assignment, most-used wavelength assignment and least-used wavelength assignment is shown in Figs. 17–20, respectively. It is shown that our proposed algorithm DRW3 less weight to maximum empty and nearest gives the least blocking probability as compared to the existing dynamic routing algorithm for random, most used and least used wavelength assignment strategies. For first-fit wavelength assignment, our dynamic routing algorithm DRW1 gives the least blocking probability.
709
Fig. 19. Performance of dynamic algorithms with most-used wavelength assignment as load in increased.
Fig. 20. Performance of dynamic algorithms with least-used wavelength assignment as load in increased.
10. Conclusion
Fig. 17. Performance of dynamic algorithms with first-fit wavelength assignment as load in increased.
Fig. 18. Performance of dynamic algorithms with random wavelength assignment as load in increased.
We have proposed two static and three dynamic routing algorithms and these have been compared to some of the existing algorithms on the basis of blocking probability. The two proposed static RWA algorithms reduce the blocking probability to maximize the utilization of network. For dynamic algorithms, first a model with no weights assignments is presented and then three algorithms are proposed and analysed with weight assignment resulting in reduction of blocking probability. All these algorithms are analysed with four wavelength assignment schemes which are first-fit, random, most used and least used and comparison has been made. It is observed that the combined path algorithm with first-fit wavelength strategy is working well. But if we talk about random wavelength assignment then it is found that the performance of alternate shortest path and maximum empty channel algorithms are comparable while blocking in combined is more in this case.
ARTICLE IN PRESS 710
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
Our proposed algorithms SRWA3 and SRWA4 are good to be used with first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. The blocking probability has been reduced as compared to the existing static algorithms. For least used wavelength assignment and random wavelength assignment 1 fixed and 2 alternate algorithm gives the lowest blocking probability. For dynamic routing, it has been shown that our proposed algorithm DRW3 Less weight to maximum empty and nearest gives the least blocking probability as compared to the other dynamic routing algorithm for random, most used and least used wavelength assignment strategies. For first-fit wavelength assignment, our dynamic routing algorithm DRW1 gives the least blocking probability. It can be concluded that different algorithms can be used in different situations but as wavelength assignment strategy plays an important role in blocking, a proper combination has to be chosen to have lowest blocking in the network. Few new algorithms can perform good with a particular wavelength assignment strategy, but it is not essential that it will perform good for any given wavelength assignment algorithm.
References [1] H. Zang, J.P. He, B. Mukherjee, A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks, Optical Network Magazine 1 (1) (2000) 47–60. [2] H. Harai, M. Murata, H. Miyahara, Performance of alternate routing methods in all-optical switching networks, in: Proceedings of IEEE Infocom 97, Kobe, Japan, April 1991, pp. 516–524.
[3] H. Zang, R. Murthy, J.P. Jue, B. Mukherjee, Dynamic light path establishment in wavelength-routed WDM network, IEEE Communication Magazine 39 (9) (2001) 100–108. [4] K. Bala, T.E. Stem, K. Bala, Algorithms for routing in a linear lightwave network, in: Proceeding of IEEE Infocom ’91, Miami, FL, USA, April 1991. [5] A. Birman, A. Kershenbaum, Routing and wavelength assignment methods in single-hop all-optical networks with blocking, in: Proceedings of IEEE Infocom ’95, vol. 2, Boston, MA, USA, April 1995, pp. 431–438. [6] S. Ramamurthy, B. Mukherjee, Fixed-alternate routing and wavelength conversion in wavelength-routed optical networks, in: Proceedings of IEEE Globecorn ’98, Sydney, Australia, November 1998, pp. 2295–2302. [7] H. Zang, R. Murthy, J.P. Jue, B. Mukherjee, Dynamic light path establishment in wavelength-routed WDM network, IEEE Communication Magazine 39 (9) (2001) 100–108. [8] E. Karasan, E. Ayanoglu, Effects of wavelength routing and selection algorithms on wavelength conversion gain in WDM optical networks, IEEE Transactions on Networking 6 (1998) 186–196. [9] K. Chan, T.P. Yum, Analysis of Least congested path routing in WDM lightwave networks, in: INFOCOM ’94. Networking for Global communications, 13th proceedings IEEE, 1994, pp. 962–968. [10] A. Mokhtar, M. Azizocglu, Adaptive wavelength routing in all-optical networks, IEEE/ACM Transactions on Networking 6 (2) (1998). [11] G. Kramer, G. Pesavento, Ethernet passive optical networks (EPON): building a next-generation optical access network, IEEE Communications Magazine 40 (2002) 66–73. [12] B. Mukherjee, Optical Communication Networks, McGraw-Hill, New York, 1997. [13] R. Ramamurthy, B. Mukherjee, Fixed-alternate outing and wavelength conversion in wavelength-routed optical networks, IEEE/ACM Transactions on Networking 10 (3) (2002).
Optik
Optics
Optik 121 (2010) 702–710 www.elsevier.de/ijleo
Static and dynamic routing and wavelength assignment algorithms for future transport networks Rajneesh Randhawaa,, J.S. Sohalb a
Department of Computer Sciences, Regional Institute of Management and Technology, Mandi Govindgarh, Punjab, India Ludhiana College of Engineering and Technology, Ludhiana, Punjab, India
b
Received 10 August 2008; accepted 20 November 2008
Abstract In this paper, two static and three dynamic routing algorithms have been proposed and compared to some of the existing algorithms on the basis of blocking probability. The two proposed static routing and wavelength assignment (RWA) algorithms reduce the blocking probability to maximize the utilization of network. For dynamic algorithms, first a model with no weights assignments is presented and then three algorithms are proposed and analysed with weight assignment resulting in reduction of blocking probability. All these algorithms are analysed and compared with four wavelength assignment schemes which are first-fit, random, most used and least used. It is shown that our proposed static algorithms give the best performance for first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate routing algorithm gives the lowest blocking probability. For dynamic routing, it has been shown that our proposed algorithm ‘‘less weight to maximum empty and nearest’’ gives the least blocking probability as compared to the other dynamic routing algorithms for random, most used and least used wavelength assignment strategies. r 2008 Elsevier GmbH. All rights reserved. Keywords: Routing; Wavelength assignment; Algorithms; WDM
1. Introduction Today’s global communications world has many different definitions for optical transport networks (OTNs) and many different technologies that support them. An optical transport network is composed of a set of optical network elements connected by optical Corresponding author.
E-mail addresses: [email protected] (R. Randhawa), [email protected] (J.S. Sohal). 0030-4026/$ - see front matter r 2008 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2008.11.004
fibre links, able to provide functionality of transport, multiplexing, routing, management, supervision and survivability of optical channels carrying client signals, according to the requirements given in Recommendation G.872. Presently optical fiber technology is used to transmit gigabits of data per second over thousands of kilometres with extremely low loss. The demand of these high speed applications, however, has put a question mark on possibility of the traditional approach of building faster time division multiplexed (TDM) networks. This has increased interest in building all-optical
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
networks where wavelengths, rather than timeslots, are switched. The routing and wavelength assignment (RWA) [1] problem in wavelength routed WDM networks consists of choosing a route and a wavelength for each connection so that no two connections using the same wavelength share the same fiber. The requirement that connections sharing the same fiber must use different wavelength channels is often referred as distinct channel assignment requirement [2]. Routing [3,4] can be subdivided in these two categories: static routing and dynamic routing. In static routing, all the strategy for routing has to be decided offline. There are two strategies which are mainly mentioned in this category. The first is fixed routing [5] in which fixed routing path between the source and the destination is calculated offline using algorithm, just like Dijkstra algorithm. If path is empty, then route the incoming on this path; otherwise call is blocked. The second is fixed alternate routing [6] in which one has to calculate one more alternate path in addition to fixed path. If fixed channel is empty, then route the incoming call through fixed paths. If the fixed channel is not empty then incoming call is routed through alternate predefined paths. Dynamic routing [7] is a method for efficient use of given resources. In this method all the routing schemes are decided online according to present network state. Deciding factors in dynamic routing can be number of empty channels, distance between source destination and more. One example for dynamic routing can be adaptive algorithm. Connections sharing with common fiber must use different wavelengths [8]. A violation of the distinct channel assignment constraint is often referred to as a wavelength conflict. Furthermore, if the wavelength conversion is not possible in the network nodes, then an additional constraint, called wavelength continuity, must be satisfied, i.e., each connection must use the same wavelength on every link. This constraint together with distinct channel assignment gives the RWA problem in all-optical network its special characteristics. If the traffic is not static but lightpath requests arrive randomly following some traffic process [9–12], the RWA constitutes a typical decision making problem. When a certain event occurs, one has to decide on some action. The set of possible actions is finite, i.e., first block the call and second route it by assigning the best available combination of route and wavelength. A feasible RW (routing and wavelength) combination is such that along the route from the source to destination the wavelength is not being used on any of the links. If no feasible RW combination exists, the call is unconditionally rejected. Furthermore, the accepted connections cannot be interrupted. RWA algorithms in optical communication was initially presented by Mukherjee [1] and validated by
703
Ramamurthy and Mukherjee [13]. Various routing algorithms in wavelength-routed optical networks have been analysed [5–10] and it has been shown that dynamic routing schemes [7] such as least-loaded routing achieve significantly better blocking performance when compared with fixed shortest-path routing, in wavelength-continuous and wavelength-convertible networks. The analytical model for alternate routing has also been investigated [6] and the effect of blocking probability of paths with different numbers of hops and different wavelength-assignment policies has been reported. Although, a few algorithms have been reported for control mechanisms of the RWA problem. Some static algorithms have been analysed in where fixed and alternate fixed path algorithms has been reported to reduce the blocking probability. Also some dynamic algorithms have been reported for reduction of blocking probability for better utilization of bandwidth and resources but very less work has been reported for routing with wavelength assignment techniques like random, least used and most used. In this paper, we propose two new static and two dynamic algorithms to reduce the blocking probability further. We have shown that our algorithms have better blocking probability as compared to the existing algorithms. Further, we analyse our routing algorithms for random, most-used and least-used wavelength assignments. For static algorithms, we assume that the traffic is static, i.e., the problem is to configure a given static set of connections between the given nodes in the network. The network itself can be a single or multi-fiber network and this kind of approach is relevant in the backbone networks, where it may be reasonable to assume that the traffic is static. First, some assumptions are to be taken for calculating the blocking probability in Section 2 and then analytical model is proposed in Section 3 based on these assumptions. The wavelength assignment techniques are discussed in Section 4. After giving brief introduction to algorithms in Section 5, the existing and proposed static algorithms are implemented in Sections 6 and 7, respectively. The dynamic algorithms are proposed in Section 8 and results and discussion have been given in Section 9 by comparing all these algorithms. Finally conclusions are made in Section 10.
2. Assumptions In our proposed model, following are the assumptions: 1. Call arrives at each node following poisson distribution. 2. Call holding time is exponentially distributed with unit means. 3. Calls which cannot be established are blocked. 4. Capacity of all the links is equal.
ARTICLE IN PRESS 704
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
5. Wavelengths are assigned using first-fit and random methods. 6. N is the variable used to define no of time calls have to arrive, as we increase the value of N we get results more close to reality. 7. Nodes are not having wavelength conversion capability.
3. Analytical model 1. Link is the set of links numbered from 1 to L. Link ¼ f1; 2; . . . . . . . . . ; Lg 2. Channels is the number of channels from 1 to C.
3. 4.
5. 6.
Channels ¼ f1; 2; . . . . . . . . . ; Cg Load is kept 13 Erlang except from varying load case. Connection matrix is a matrix used to store the status of each channel (busy/empty) and also holding time information. Call arrival rate is l. P is the set of all possible paths between source and destination Path ¼ fP1 ; P2 ; . . . . . . . . . ; Pn g
Let XP be the random variable representing the number of idle wavelengths on path P. If path consist a single link E and it may be written as XE. We will have blocking in this case by the condition on a Path PE link from source to destination as X Pr ½X E ¼ 0jX 1 ¼ m1 ; . . . . . . ; X k ¼ mk blocking ¼ mX0
Pr ½X 1 ¼ m1 ; . . . . . . ; X k ¼ mk ¼
X
p0 ðmÞ
k Y
Pr ½X j ¼ mj
j¼1
mX0
If oL is the common set of empty wavelengths over some Path with hope length L. Suppose Wij is the available wavelength bank for jth link when ith call arrive. We can say Aði; jÞ ¼
N X k X
oL 2 W ij
i¼1 j¼1
for a fixed i, if oL is empty, then incoming call will be blocked as no availability of the wavelength for the path f1; 2; . . . . . . . . . ; kg. If there is a common wavelength present over the path, then the call will be routed and connection will be successful. In this way blocking can also be calculated as blocking ð%Þ ¼
Successful attemts to establish a call Total attempts
4. Wavelength assignment strategies In this work, these wavelength assignment strategies are followed. (1) First-fit wavelength assignment: let w0 ; w1 ; . . . . . . . . . ; wW be the wavelengths in the network. The wavelength chosen for a connection has the smallest index among the wavelengths which are available along the path. The first-fit heuristic is proposed in [6] and shown to be very effective. Here the first available wavelength in the available wavelength bank will be assigned to the incoming call. (2) Random wavelength assignment: a wavelength to be used for a connection is chosen randomly among wavelengths which are presently not in use. If oL is the wavelengths bank for a path and its length is l than assigned wavelength with number ceil (rand*l). Ceil is a function in MATLAB to assign next higher integer for a fraction and same value for an integer. (3) Most used wavelength assignment: in this algorithm a counter is used to monitor how frequently a channel is being used; here a channel is selected from the empty channels list with the highest number of frequency. (4) Least used wavelength assignment: same as the above algorithm, we choose the least frequently used channel from the empty channels list instead of the most frequently used one in the above case.
5. Algorithms In order to demonstrate that how our approach is performing in comparison with existing approaches, it is imperative to analyse the existing algorithms using our model for the proposed algorithms. In absence of a suitable simulator that could support our proposed heuristics, some codes have been developed in MATLAB to run the simulation. It accepts input parameters such as the number of nodes in the network, link information with weight, number of wavelengths per fibre, connection requests. Some of the calls may be blocked because of the unavailability of free wavelength on links along the route from the source to the destination. The ratio of the total number of calls blocked to the total number of light path requests in the network determines the blocking probability of the technique.
6. Analysed static routing algorithms (1) Shortest path algorithm (SRW1). Here shortest path algorithm is used for routing with first-fit and random wavelength assignment strategy is used for wavelength assignment. For each incoming call, first of all try to establish the connection on first wavelength using shortest
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
705
Fig. 1. Shortest path between nodes 1 and 10.
route. If unsuccessful, then connection is tried on second wavelength and so on up to the last wavelength. If unsuccessful than call is said to be blocked. Dijkastra algorithm can be used to calculate the shorted path between a given source-destination pair. Also algorithm used is given below as per the setup consisting of 10 nodes as shown in Fig. 1.
Fig. 2. Alternate shortest path 1.
Algorithm 1. 1. for link 1 to L 2. for generation_request 1 to N 3. for loop 1 to link 4. Calculate call arrival rate 5. Calculate holding time 6. If (check for some empty wavelength) 7. If (check for wavelength assignment method) 8. Method ¼ 1 then first-fit assignment 9. elseif (Random) 10. Random assignment 11. elseif (Most-used) 12. Most-used assignment 13. else 14. Least-used assignment 15. Assign busy status and holding time in the connection matrix to the selected parameters 16. end 17. Decrement holding times for all non-free channels 18. end 19. Check whether there is some free channel in connection matrix 20. If no free channel then 21. blocked_call ¼ blocked_call+1 22. end 23. Clear temporary variables 24. end 25. blocking ¼ blocked_call*100/gen 26. end (2) Alternate shortest path algorithm (SRW2). In alternate shortest path algorithm, for each incoming
Fig. 3. Alternate shortest path 2.
call first, try to establish the connection on channels with shortest route. If unsuccessful, then we try to establish connection on alternate shortest path channels. If again unsuccessful, then call is said to be blocked. Here we monitor the status of channels. In case there is minimum one channel empty, then the call can be successful. But if all channels are occupied, then incoming call will be blocked. The alternate shortest paths 1 and 2 are shown in Figs. 2 and 3, respectively. Alternate shortest path routing 1. Initialize all the parameters 2. If there is at least one empty channel on shortest path 3. Route the call through shortest path using Algorithm 1 4. elseif there is at least one empty channel on alternate shortest path 5. Route the call through alternate shortest path using Algorithm 1 6. else 7. Block the call
ARTICLE IN PRESS 706
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
8. Repeat up to number of times as given by number of generation one wish to test
7. Proposed static algorithms (3) Maximum empty channel routing (SRW3). In this algorithm, it is required to monitor all the paths between a source and destination pair. When a call arrives first we check status of all paths and route the call through the channel with maximum number of empty channels. Maximum empty channel routing 1. Initialize all the parameters 2. Calculate the number of empty channels on each path 3. Select one with maximum empty channels 4. If at least one empty channel is there on any path 5. Route the call through that path using Algorithm 1 6. else 7. Block the call 8. Repeat up to number of times as given by number of generation one wish to test (4) Combined path algorithm (SRW4). In this algorithm, all the channels are combined which belongs to shortest path and alternate shortest path. This combination makes a bank of all the channels (wavelengths); also some wavelength assignment strategy is used for wavelength assignment. For each incoming call first of all, try to establish the connection on first wavelength (first-fit) using any route. If unsuccessful, then connection is tried on second wavelength and so on up to the last wavelength. If unsuccessful then call is said to be blocked. Combined path algorithm: 1. Initialize all required parameters 2. Combine channels of all the given paths and consider them as one common channel 3. If at least one channel is empty 4. Route the call using Algorithm 1 5. else 6. Block the call 7. Repeat up to number of generation
8. Dynamic algorithms Proposed Algorithm 1: no weight assignment (DRW1). In this algorithm no weights are assigned and all the links have same weight. So in this dynamic (on-line) routing, first calculate shortest path then alternate shortest path and then as per the availability of empty wavelengths on links as the call arrive in the network, calculate all available paths. We have designed a MATLAB programme to calculate all possible path of
Fig. 4. Graph with 10 nodes and 21 edges.
the given network. The setup with 10 nodes for this algorithm is shown in Fig. 4. The algorithm is 1. Generate a source and destination pair 2. Calculate all possible path between this pair 3. If there is empty wavelength on shortest path 4. Route the call through shortest path using Algorithm 1 5. elseif there is an empty wavelength on alternate path than 6. Route the call through this path using Algorithm 1 7. else 8. Call is blocked 9. Repeat up to number of generation Proposed Algorithm 2: less weight to less used (DRW2). In this algorithm, first we calculate the number of times each link is being used, then we assign lower load to these nodes to make the network full utilization of each node. The setup is shown in the Fig. 5. The algorithm is 1. By running a programme calculate number of times each link was used 2. Assign lower weight to the nodes which are used lesser times 3. Generate a source and destination pair 4. Calculate all possible path between this pair 5. If there is empty wavelength on the path with lowest weight 6. Route the call through this path using Algorithm 1 7. elseif there is an empty wavelength on the path with next higher weight 8. Route the call through this path using Algorithm 1 9. else 10. Call is blocked Repeat up to number of generation
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
707
alternate shortest path (with 1 fixed and 2 alternate) algorithm, 2-combined path algorithm, 3-combined path algorithm, max empty channel path (3 alternate paths) algorithm with different wavelength assignment strategies have been shown in Figs. 7–13. It is observed that for all these algorithms, first-fit wavelength assignment technique gives the least blocking probability. There is difference in all the routing techniques and wavelength assignment strategy except for the alternate
Fig. 5. Network with static weight assignment.
Fig. 7. Performance of shortest path algorithm with different wavelength assignment strategies.
Fig. 6. Network shows a link distance from source and destination.
Proposed Algorithm 3: less weight to max empty and nearest (DRW3). In this algorithm, the weights are assigned dynamically, i.e., the weights are inversely proportional to the sum of its distances of its end nodes to the source and destination and directly proportional to the no of empty wavelengths on that link: W¼
Fig. 8. Performance of alternate shortest path algorithm with different wavelength assignment strategies.
No of empty wavelengths available on that link Sum of distances of link from source and destination
In Fig. 6, we can see that the total distance of above graphs node f7; 9g to source destination pair f1; 10g is 2+1 ¼ 3.
9. Results and discussion The performance of existing and proposed algorithms with different wavelength assignment algorithms have been investigated first. For static algorithms, the shortest path algorithm, alternate shortest path algorithm,
Fig. 9. Performance of alternate shortest path (with 1 fixed and 2 alternate) algorithm with different wavelength assignment strategies.
ARTICLE IN PRESS 708
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
Fig. 10. Performance of 2-combined path algorithm with different wavelength assignment strategies.
Fig. 11. Performance of 3-combined path algorithm with different wavelength assignment strategies.
path, where all wavelength assignments give close blocking probabilities. Let us now investigate these algorithms together with individual wavelength assignment strategies. The performance of analysed and proposed static algorithms as the load in increased with first-fit wavelength assignment, random wavelength assignment, most-used wavelength assignment and least-used wavelength assignment has been shown in Figs. 13–16, respectively. By the analysis of graphs obtained by the simulation of the above algorithms we can again say that the combined path algorithm with first-fit wavelength strategy is working well. We can see the reduced
Fig. 14. Performance of static algorithms with random wavelength assignment as load in increased.
Fig. 12. Performance of max empty channel path (3 alternate paths) algorithm with different wavelength assignment strategies.
Fig. 15. Performance of static algorithms with most-used wavelength assignment as load in increased.
Fig. 13. Performance of static algorithms with first-fit wavelength assignment as load in increased.
Fig. 16. Performance of static algorithms with least-used wavelength assignment as load in increased.
ARTICLE IN PRESS R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
blocking in this case with less complex algorithm. But if we talk about random wavelength assignment then it is found that the performance of alternate shortest path and maximum empty channel algorithms are comparable. So we can say that our proposed algorithms SRWA3 and SRWA4 are good to be used with first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. The blocking probability has been reduced as compared to the existing static algorithms. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate algorithm gives the lowest blocking probability. The performance of proposed dynamic algorithms as load in increased with first-fit wavelength assignment, random wavelength assignment, most-used wavelength assignment and least-used wavelength assignment is shown in Figs. 17–20, respectively. It is shown that our proposed algorithm DRW3 less weight to maximum empty and nearest gives the least blocking probability as compared to the existing dynamic routing algorithm for random, most used and least used wavelength assignment strategies. For first-fit wavelength assignment, our dynamic routing algorithm DRW1 gives the least blocking probability.
709
Fig. 19. Performance of dynamic algorithms with most-used wavelength assignment as load in increased.
Fig. 20. Performance of dynamic algorithms with least-used wavelength assignment as load in increased.
10. Conclusion
Fig. 17. Performance of dynamic algorithms with first-fit wavelength assignment as load in increased.
Fig. 18. Performance of dynamic algorithms with random wavelength assignment as load in increased.
We have proposed two static and three dynamic routing algorithms and these have been compared to some of the existing algorithms on the basis of blocking probability. The two proposed static RWA algorithms reduce the blocking probability to maximize the utilization of network. For dynamic algorithms, first a model with no weights assignments is presented and then three algorithms are proposed and analysed with weight assignment resulting in reduction of blocking probability. All these algorithms are analysed with four wavelength assignment schemes which are first-fit, random, most used and least used and comparison has been made. It is observed that the combined path algorithm with first-fit wavelength strategy is working well. But if we talk about random wavelength assignment then it is found that the performance of alternate shortest path and maximum empty channel algorithms are comparable while blocking in combined is more in this case.
ARTICLE IN PRESS 710
R. Randhawa, J.S. Sohal / Optik 121 (2010) 702–710
Our proposed algorithms SRWA3 and SRWA4 are good to be used with first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. The blocking probability has been reduced as compared to the existing static algorithms. For least used wavelength assignment and random wavelength assignment 1 fixed and 2 alternate algorithm gives the lowest blocking probability. For dynamic routing, it has been shown that our proposed algorithm DRW3 Less weight to maximum empty and nearest gives the least blocking probability as compared to the other dynamic routing algorithm for random, most used and least used wavelength assignment strategies. For first-fit wavelength assignment, our dynamic routing algorithm DRW1 gives the least blocking probability. It can be concluded that different algorithms can be used in different situations but as wavelength assignment strategy plays an important role in blocking, a proper combination has to be chosen to have lowest blocking in the network. Few new algorithms can perform good with a particular wavelength assignment strategy, but it is not essential that it will perform good for any given wavelength assignment algorithm.
References [1] H. Zang, J.P. He, B. Mukherjee, A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks, Optical Network Magazine 1 (1) (2000) 47–60. [2] H. Harai, M. Murata, H. Miyahara, Performance of alternate routing methods in all-optical switching networks, in: Proceedings of IEEE Infocom 97, Kobe, Japan, April 1991, pp. 516–524.
[3] H. Zang, R. Murthy, J.P. Jue, B. Mukherjee, Dynamic light path establishment in wavelength-routed WDM network, IEEE Communication Magazine 39 (9) (2001) 100–108. [4] K. Bala, T.E. Stem, K. Bala, Algorithms for routing in a linear lightwave network, in: Proceeding of IEEE Infocom ’91, Miami, FL, USA, April 1991. [5] A. Birman, A. Kershenbaum, Routing and wavelength assignment methods in single-hop all-optical networks with blocking, in: Proceedings of IEEE Infocom ’95, vol. 2, Boston, MA, USA, April 1995, pp. 431–438. [6] S. Ramamurthy, B. Mukherjee, Fixed-alternate routing and wavelength conversion in wavelength-routed optical networks, in: Proceedings of IEEE Globecorn ’98, Sydney, Australia, November 1998, pp. 2295–2302. [7] H. Zang, R. Murthy, J.P. Jue, B. Mukherjee, Dynamic light path establishment in wavelength-routed WDM network, IEEE Communication Magazine 39 (9) (2001) 100–108. [8] E. Karasan, E. Ayanoglu, Effects of wavelength routing and selection algorithms on wavelength conversion gain in WDM optical networks, IEEE Transactions on Networking 6 (1998) 186–196. [9] K. Chan, T.P. Yum, Analysis of Least congested path routing in WDM lightwave networks, in: INFOCOM ’94. Networking for Global communications, 13th proceedings IEEE, 1994, pp. 962–968. [10] A. Mokhtar, M. Azizocglu, Adaptive wavelength routing in all-optical networks, IEEE/ACM Transactions on Networking 6 (2) (1998). [11] G. Kramer, G. Pesavento, Ethernet passive optical networks (EPON): building a next-generation optical access network, IEEE Communications Magazine 40 (2002) 66–73. [12] B. Mukherjee, Optical Communication Networks, McGraw-Hill, New York, 1997. [13] R. Ramamurthy, B. Mukherjee, Fixed-alternate outing and wavelength conversion in wavelength-routed optical networks, IEEE/ACM Transactions on Networking 10 (3) (2002).