1. CSC 778 Fall 2007 Routing & Wavelength Assignment Vinod Damle Hardik Thakker

2. CSC 778 Fall 2007 Agenda Introduction Problem Definition/Sub-division RCL Heuristic Dynamic RWA Conclusion & Questions

3. CSC 778 Fall 2007 RWA Lightpath (LP) – all optical WDM channel RWA – with a given set of connection requests, set up LPs by routing and assign a λ to each connection Connection Requests – Static & Dynamic Static – all requests known in advance, usually RWA is carried out offline - SLE Dynamic – LP is set up as each connection request arrives, and released after a finite time - DLE

4. CSC 778 Fall 2007 Links -> Fibers(1..n) -> λs (1..n) Wavelength continuity constraint may/may not exist Network Topology & Connections Link Fiber Wavelength A C B D c1 c2 c3 A->D C->D B->C AB CD c1A->D c2C->D c3B->C SLE DLE

5. CSC 778 Fall 2007 RWA RWA with λ conversion –Full capacity λ conversion: equivalent to circuit switching! (No WA, just routing) –However, full capacity λ conversion is expensive –Hence limited λ conversion is employed If select nodes have this capability – which nodes to place them? Share converters between output ports Limited range λ conversion

6. CSC 778 Fall 2007 RWA RWA dealt with separately as 2 sub-problems, Routing and Wavelength Assignment SLE – Generally treated as an ILP formulation –Objective: Minimize number of λs to set up given LPs or Maximize number of LPs for given λs Routing sub-problem –Fixed routing –Fixed-Alternate routing –Adaptive routing Shortest cost path routing

7. CSC 778 Fall 2007 RWA After LP route is determined, assign λ – Graph coloring –Given a set of LPs and their routes, assign λ so that no 2 LPs on the same fiber have the same λ In DLE, objective is to minimize blocking probability with a fixed physical topology (fibers, λs)

8. CSC 778 Fall 2007 Wavelength Assignment for Dynamic Traffic in Multi-Fiber WDM Networks Xijun Zhang Chunming Qiao

9. CSC 778 Fall 2007 RCL On-line wavelength assignment algorithm for dynamic traffic For a fixed physical topology, aims to minimize blocking probability Assumption –No wavelength converters –Route between any source destination pair is pre- selected –Network is at a particular state where set of connections has already been established and λs are already assigned

10. CSC 778 Fall 2007 Wavelength Path Capacity (WPC) We need a measure for Blocking Probability Link Capacity of a link L C (l, λ) – Number of fibers on which λ is available on link ‘l’ WPC of a path ‘p’ P C (p, λ) - link capacity of most congested link along the path (min of link capacities). LP can be established on a λ only if WPC > 0 Ex – 3 links (2 fibers each), 1 λ. A BC D WPC (p) = min ( 2, 1, 2) = 1

11. CSC 778 Fall 2007 Λ Assignment Strategies Objective – Establish LP on a particular λ such that blocking probability is minimized First fit – Assign to least λ index available Max Sum – Assign a λ which maximizes ‘residual WPC’ on all possible paths & wavelengths - Σ p Σ λ P C ’ (p, λ) Max Sum minimizes total WPC Loss –Minimize Σ p [P C (p, λ) – P C ’ (p, λ)] where P C and P C ’ are WPC before and after λ assignment

12. CSC 778 Fall 2007 RCL - Motivation 0654321 λ0λ0 λ1λ1 λ2λ2 λ3λ3 P2: 1->5 P3: 3->6 P4: 0->3 P1: 2->4 P1: (2, 4) P2: (1, 5)P3: (3, 6)P4: (0, 3) λ3λ3100 Λ2Λ2110 λ1λ1010 λ0λ0001 WPC of Paths P2: (1, 5)P3: (3, 6)P4: (0, 3) λ3λ3100 Λ2Λ2110 λ1λ1010 λ0λ0001 WPC Loss of PathsTotal Loss 1 2 1 1

13. CSC 778 Fall 2007 RCL Every entry in table must be weighted by some factor. Factor evaluates availability of an alternate λ for a particular path Define RCL (Relative Capacity Loss) - Ratio –R c (p, λ * ) = [P C (p, λ * ) – P C ’ (p, λ * )] ----------------------------------------------------------------------------------- Σ λ P C (p, λ) Ratio of WPC Loss of ‘p’ on λ * over the total WPC of ‘p’ on all wavelengths

14. CSC 778 Fall 2007 RCL Algorithm Algorithm aims to minimize effect of choosing a particular λ * on the paths which share common links Choose a λ * such that the sum of RCLs of all the neighboring paths (paths which have links in common with the current path request) is minimized –Choose λ * where Σ p € {Neighbors of p’} R C (p, λ * ) is minimized Non-Uniform Traffic: attach a weight to each R C and compute λ * P2: (1, 5)P3: (3, 6)P4: (0, 3) λ3λ3½0/20/1 Λ2Λ2½½ λ1λ10/2½0/1 λ0λ00/2 1/1 Total RCL 1/2 1 1

15. CSC 778 Fall 2007 RCL - Performance RWA with full λ conversion is considered optimal. Non Optimality Factor (NOF) defined as difference in blocking probability between say ‘RCL’, and the above To compare 2 different wavelength assignment algorithms – ‘A’ and ‘B’, define improvement ratio as {NOF(A) – NOF(B)}/NOF(A) MS vs RCL (Ref: Zhang & Qiao, Wavelength assignment for dynamic traffic in multi-fiber WDM networks)

16. CSC 778 Fall 2007 RCL - Drawbacks Longer paths have higher probability of getting blocked (Inherent to such schemes) Requires fixed routing – However, this could be countered with a scheme where RCL is applied to a set of pre-calculated routes between a source/destination pair

17. CSC 778 Fall 2007 Dynamic Routing & Wavelength Assignment by means of Genetic Algorithms

18. CSC 778 Fall 2007 Problem –Dynamic Routing and Wavelength Assignment (DRWA) of lightpaths in optical networks without wavelength converters Objective –To minimize the call blocking probability and reduce computation time Proposed Solution –Genetic algorithm to solve DRWA quickly and effectively an also provide fairness Introduction

19. CSC 778 Fall 2007 DRWA Algorithms Common Approach – Fixed Alternate Routing –Routing and Wavelength Assignment performed separately –Route chosen from pre-calculated set –Call blocked if no wavelength available along the pre- computed routes Advantages –Computation time of algorithm is low Disadvantages –Blocking Performance is not as good as the Adaptive routing algorithms

20. CSC 778 Fall 2007 DRWA Algorithms (..contd) AUR 1 – Adaptive Unconstrained Routing –Do not use a set of pre-computed routes –Dynamically search for shortest path using network information at that instant Advantages –Blocking performance better than constrained routing Disadvantages –Computationally more complex than constrained approach 1 Adaptive Wavelength Routing in All-Optical Networks; Ahmed Mokhtar and Murat Azizoglu

21. CSC 778 Fall 2007 Fairness Aim: All lightpath request should have low blocking probability independent of the location of end nodes Multi-hop connections are harder to establish than single-hop connections Network topology and traffic pattern result in congested links –Light Paths on congested links will be blocked Depending on the s-d pair –Individual blocking probability varies –High degree of unfairness

22. CSC 778 Fall 2007 Genetic Algorithm (GA) Search Algorithms based on mechanics of natural selection and natural genetics Works on individuals representing solution to the problem –E.g. finding best route from s-d, individuals in this case will be all routes from s-d Genetic Operators –Crossover - imitates the natural reproduction –Mutation – changes the genetic material –Reduction – selects the fittest individuals

23. CSC 778 Fall 2007 GRWA Run each time a lightpath is requested Coding of a route –(0 1 2 5) & (0 2 4 5) Evolution –Produces new generation which is hopefully fitter than the current generation

24. CSC 778 Fall 2007 GRWA (..contd) Step1: Generate initial population P of randomly generated routes Step2: Continue evolution until stopping criterion is met –Evolution over a number of iterations Crossover stage Mutation stage Reduction stage Step3: Return the best individual found

25. CSC 778 Fall 2007 Generation of Random Routes Find a route from s = 0 to d = 5 0 1 4 2 3 5

26. CSC 778 Fall 2007 Genetic Operators Crossover Operator –Applied to pair of routes that have one node on common

27. CSC 778 Fall 2007 Genetic Operators (..contd) Mutation Operator –New route is generated from a node selected randomly from a current route –Route from source to mutation node is untouched –Applied to all the individuals whose fitness value is below a threshold 1025 0 13 5 Parent route Child route Mutation Node

28. CSC 778 Fall 2007 Genetic Operators (..contd) Reduction Operator –Select P fittest individuals from both parents and children

29. CSC 778 Fall 2007 Fitness Function Determines goodness of individual Performs Wavelength Assignment Cost of light path –No. of links traversed (i.e. number of hops) –Infinite when no wavelengths are available Select the lowest indexed wavelength among the available wavelengths Fitness = (cost) -1

30. CSC 778 Fall 2007 Stopping Criterion G = No. of generations S = satisfactory cost value –Initially set to minimum number of hops between s-d –Value increased by 1 after each iteration Evolution stops in following conditions –Route with cost <= S is found –After G generations have evolved

31. CSC 778 Fall 2007 Fair - GRWA Adapt the values of ‘G’ and ‘P’ to the difficulty in establishing the connection G, P will be higher for difficult connection Specific values associated with each s-d pair Execute the genetic algorithm for (G s-d, P s-d ) to achieve equal blocking probability Combines advantages of fixed routing and adaptive routing –Uses pre-computed set of routes –If not available then uses GWRA

32. CSC 778 Fall 2007 Performance Evaluation Simulation –Arrival of light path requests independent Poisson process –Arrival Rate = Call holding time = –s-d pair selected randomly acc. uniform distribution

33. CSC 778 Fall 2007 Performance Evaluation (..contd) Probability of fulfilling the stopping criterion

34. CSC 778 Fall 2007 Performance Evaluation (..contd) Comparison of GRWA with AUR-E & Fair-GRWA

35. CSC 778 Fall 2007 Questions ?