MWPG - AN ALGORITHM FOR WAVELENGTH REROUTING

Transcription

1 MWPG - AN ALGORITHM FOR WAVELENGTH REROUTING Student Lecture Mohammed Pottayil

2 OUTLINE Review of Wavelength Rerouting Concepts - What is Wavelength Rerouting - Lightpath Migration operations - Rerouting Schemes Algorithms for Wavelength Rerouting The MWPG Algorithm Example Performance Analysis Conclusion 2 2

3 Review of Wavelength Rerouting Concepts Wavelength Rerouting is the migration of existing lightpaths to new wavelengths while maintaining their path to accommodate new connection requests Wavelength continuous, wavelength converters are expensive. Two components of wavelength rerouting Rerouting operation Rerouting algorithm 3 3

4 Review..(cont d) Rerouting Operation Deals with migration of lightpaths Must incur as little disruption of service as possible Simple switching control Types of Rerouting Operations Wavelength Retuning(WR) Retune the wavelength of a lightpath maintaining the path Simple s and easy to control as same switching nodes are used Does not bother if path on the new wavelength is vacant Move-to-vacant(MTV) Reroutes lightpath to vacant route with no other lightpaths Has a complex algorithm and does not necessarily maintain the path Move-to-vacant Wavelength Retuning(MTV-WR) Moves a lightpath to vacant wavelength on the same path Combines the advantages of both while overcoming their drawbacks 4 4

5 Rerouting Schemes: Review..(cont d) Parallel MTV-WR Rerouting of lightpaths happen in parallel overall delay = max delay(all lightpath migrations) Simple algorithms Sequential MTV-WR Lightpath migration is done in passes overall delay = Sum(max delay in each pass) Requires complex algorithms to decide order 5 5

6 Wavelength Rerouting Algorithms Auxiliary Graph(AG) Algorithm [3] Minimizes the weighted number of rerouted lightpaths by choosing a path that intersects a minimum number of existing retunable lightpaths Minimum Weighted-count Path-preserving Graph(MWPG) Algorithm Both algorithms assume the parallel MTV-WR rerouting scheme for lightpath migration. Both algorithms use a dijkstra-like procedure to find the shortest path. 6 6

7 MWPG Algorithm Notations and Definitions: fedge(u,v) free edge between u and v. Weight = ε, a very tiny value ledge(u,v) labeled edge, currently being used by a lightpath q, Weight = retunable cost (infinite if non-retunable, else depends on number of hops in the path) sedge (u,v) segment edge, representing a sequence of ledges labeled q, between nodes u and v. Weight = weight of 1 incident ledge cost(p(u,v)) sum of retunable cost of intersecting lightpaths on p + ε times the number of free edges on the path if cost(p 1 (u,v)) < cost(p 2 (u,v)) then p 1 dist(y,x) cost of the minimum weighted count path from x to y is the minimum weighted count path x is the minimum cost node of path p if dist(x,s) < dist(y,s) where s is the start node 7 7

8 MWPG Algorithm The network is represented as a unidirected graph with W subgraphs that correspond to W wavelengths. The algorithm finds a minimum weighted count path in each of the W subgraphs using a Dijkstra like procedure called min_wt_count_path(). It then chooses the best among these paths,followed by a fixed order wavelength selection for a tie. The min_wt_count_path() procedure : Suppose a request for a connection from node s to d arrives Step 1 node s is marked as the min node min s its distance is updated to 0 dist(min) 0 Step 2 update distances to neighboring nodes of s if connected by fedge then update using ε i.e. for neighbor y dist(y) dist(min) + wt(min,y) 8 8

9 MWPG Algorithm If connected by a ledge, check for retunability from lightpath status information. p label(edge(min,y)); If retunable and minimum cost node not yet found, then update dist() value of every other unmarked node on the lightpath by its retunable cost(rt_cost) value along sedges. for every unmarked node on p do if dist(min) + rt_cost(p) < dist(x) begin end dist(x) dist(min) + rt_cost(p) All ledges corresponding to non retunable lightpaths are ignored as weigth is infinity. This results in the replacement of every ledge corresponding to a retunable lightpath by an equivalent sedge. 9 9

10 MWPG Algorithm Choose a node with the minimum dist() value among the unmarked nodes and mark it as the min node Start the next iteration. End when the destination node is chosen as the min node or when min node has infinite weight

11 Example: MWPG Algorithm Consider the 9 node network as shown in fig 1. There is a lightpath p 1 between node 1 and node 4. There is another lightpath p 2 between nodes 6 and 9. Both lightpaths are assumed to be on the same wavelength plane. A request for connection between nodes 2 and 9 arrives. Assume that there does not exist a finitecost path between nodes 2 and 9 on other wavelengths. Fig 1 Graph G on a wavelength plane Source[1] Finally assume that the 2 lightpaths are retunable 11 11

12 Example: MWPG Algorithm Fig 2 gives the final graph G 2 obtained after the iterations. Note that G 2 and G have the same number of edges. The algorithm chooses path on graph G 2 (equivalent to path on graph G) with cost 6.1 after migrating p 1 and p 2. Fig 2. The minimum weighted count path preserving graph G 2 of G Source[1] 12 12

13 MWPG Algorithm Maintenance of Retunability Status Information Dynamical updating of retunability status of lightpaths on every successful lightpath establishment and release. Type of tracking information maintained number of edges lightpath p uses on wavelength number of free edgfes of p on the remaining wavelengths number of other wavelengths lightpath p can be retuned to Time Complexity The MWPG Algorithm has a best case(route available without retuning) time complexity of O(N 2 W) Under the worst conditions (route available with retuning) the MWPG Algorithm finds a route in O(N 2 W) time

14 Algorithm AG vs MWPG Algorithm Comparison: Unlike the AG Algorithm the MWPG Algorithm does not have separate phases for routing and rerouting. It finds a route with the minimum weighted number of rerouted lightpaths in one phase. Does not check afresh whether existing lightpaths are retunable. It maintains the retunability status which is updated dynamically. So it can determine in constant time whether a lightpath is retunable. Does not construct any auxiliary graph with crossover edges, which is an expensive process. The new graph created by the MWPG algorithm has the same number of edges as the original graph. Time complexity: Best Case Worst Case Algorithm AG O(N 2 W) 2 x O(N 2 W) + O(N 2 W 2 ) + O(N 3 W) MWPG Algorithm O(N 2 W) O(N 2 W) 14 14

15 Performance Analysis Blocking Performance Simulation on the ARPA-2 network 21 nodes 26 bidirectional links 13 wavelengths per link Rerouting schemes considered Equal assigns equal weights as retuning cost to all retunable lightpaths Linear assigns weight proportional to number of hops used in the lightpath as retuning cost Fig 3. Blocking probabilities w/o rerouting, with rerouting (equal and linear weight), and with wavelength conversion capability vs traffic load per node Source[1] 15 15

16 Performance Analysis (cont d) Processing Time Requirement: Compare the AG and MWPG Algorithms Implemented on SUN-SPARC system Randomly generated topolgy 50 nodes 60 bidirectional links 10 wavelengths per link Equal weight rerouting scheme Processing time = time spent for ( selecting a route + updating network information + termination of connection) MWPG is faster for moderate and high call arrival rates. For low call arrival rates both have same complexity, but MWPG takes more time updating lightpath retunability status information. AG MWPG Fig 4. Average processing time required (in ticks) per connection vs traffic loading per node for the random network with 50 nodes. Source[1] 16 16

17 Conclusion A time optimal for wavelength-routed WDM networks with parallel MTV-WR rerouting scheme was proposed. The algorithm requires only O(N 2 W) time units to minimize the weighted number of existing lightpaths to be rerouted. Simulations have proved that the MWPG algorithm improves blocking performance considerably compared to non rerouted networks. Simulations have also shown that this algorithm is faster than the AG in terms of processing connection requests at medium to high loads

18 References A time optimal wavelength for dynamic traffic in WDM networks by G Mohan and C Siva Ram Murthy, Journal of Lightwave Technology, Vol 17, No. 3, March 99 WDM Optical Networks: Concepts, Designs and Algorithms by G Mohan and C Siva Ram Murthy. Prentice Hall A wavelength in wide area all-optical networks, by K.C.Lee and V.O.K.Li, Journal of Lightwave Technology., Vol 14, June

19 Homework 1. List 3 advantages of the MWPG Algorithm over the AG Algorithm. 2. Explain why the AG algorithm requires lesser processing time for lower call arrival rates