1. 1 RECONFIGURATION IN WDM NETWORK WOOCHANG HWANG TAEKKYEUN LEE

2. 2 Overview I. Reconfiguration II. WDM Network III. Virtual Topology IV. Schemes V. Decision

3. 3 Reconfiguration Why?  Traffic fluctuate - A Virtual Topology optimized for a certain traffic pattern would lose its optimality with changes in the traffic pattern  Physical topology change - no more effective VT  Reconfiguration capability has been emphasized – new VT needed

4. 4 WDM NETWORK Rearrangeability ability to dynamically optimize the network - changing traffic pattern - network equipment failure  What makes the rearrangeability possible? - Logical connectivity Independence (VT) from physical topology

5. 5 WDM NETWORK Lightpath set up by configuring the optical switches and tranceivers - provide single-hop communication channels between the end nodes - eliminate the electronic processing at intermediate nodes  Virtual Topology A set of static light paths established to all- optical connectivity between nodes for a given traffic demand

6. 6 Reconfiguration Step  Overview  Get information about trafiic /PT Get optimal VT to adapt to new traffic pattern Should be the VT that minimize the disruption in the network (closeness to current VT) Decision to trigger reconfiguration or not to Transition from old VT to new VT

7. 7 Network Model (NSFNET)

8. 8 Scheme 1 – Problem spec PHYSICAL TOPOLOGY: G p = ( V,E p ) ; V = Set of network nodes E p = Set of links connecting the nodes D p (i) = Physical Degree of node i Wavelength channels carried by each fiber = W N*N traffic matrix, where N is the number of network nodes

9. 9 Scheme 1 –problem spec VIRTUAL TOPOLOGY: A virtual topology G v = (V,E v ) Two light paths that share a common link must use different wavelengths Sizes and configurations of the WRSs

10. 10 Scheme 1 –VT design I. VT Design It formulates the VT problem as an optimization problem. - Original optimization problem is NP- hard problem. - Linear formulation – using principles from multicommodity flow for physical routing of lightpaths and traffic flow on the VT, and using the following notations

11. 11 Scheme 1 -LF Linear Formulation s,d - source and destination of a packet i,j - originating and terminating nodes in a lightpath m,n – endpoints of a physical link that might occur in a lightpath

12. 12 Scheme 1 -LF 1. Given N = Number of node in the network W= Max number of wavelengths per fiber Pmn = number of fibers interconnecting nodes m and n. Pmn=0 for nodes which are not physically adjacent. denotes the total number of fiber links in the network. dmn = fiber length distance between m and n,expressed as a propagation delay D = shortest path delay matrix Dij denotes the delay(sum of propagation delay only) over the shortest path between i and j

13. 13 Scheme 1 -LF α = Lightpath length bound, 1<= α <  bounds the delay over a lightpath betwee two nodes I and j, with respect to the shortest path delay Dij between them. max permissible propagation delay α * Dij Ti = number of transmitters at node I Ri = number of receivers at node I  sd =traffic matrix, denotes the average rate of traffic flow from node s to d (in packets/sec)

14. 14 Scheme 1 -LF C = capacity of each channel  =max loading per channel, 0<  <1 restricts the queueing delay on a lightpath from getting unbounded by avoiding excessive link congestion -negligibly small compared to propagation delay for a large network, so we do not incorporate queuing delays explicitly

15. 15 Scheme 1 -LF 2. Variables Vij= Virtual topology,number of lightpaths from node i and j in the VT = Traffic routing, the traffic flowing from node s to node d and employing Vij as an intermediate virtual link. = physical topology route, number of lightpaths between nodes i and j being routed through fiber link mn.

16. 16 Scheme 1 -LF 3. Objectivity: Optimality criterion minimize the average packet hop distance.  sd is a constant for a given traffic.

17. 17 Scheme 1 -LF 4. Constraints Ensures that the number of lightpaths emerging from a node is constrained by the number of transmitters and receivers

18. 18 Scheme 1 -LF (5)=flow traffic is conserved at intermediate nodes (5)-(7) are multi commodity flow equations governing the routing lightpaths from source to destination

19. 19 Scheme 1 -LF (8) =ensure that the number of lightpaths flowing through a fiber link does not exceed W. It does not ensure the wavelength continuity. It assume that we have wavelength converter at each node.

20. 20 Scheme 1 -LF (10)-(12) = multicommodity-flow governing the flow of traffic through the virtual topology Traffic conservation on end points, and intermediate nodes.

21. 21 Scheme 1 -LF (13)= ensure that traffic can only flow through an existing lightpath (14)= specify the capacity constraint in the formulation

22. 22 Scheme 1 -LF

23. 23 Scheme 1 -LF (15)-(16)= May be incorporated to ensure bounded packet delays and to reduce the solution space of the problem (16) restricts the enumerated variables to be only among those in K alternate shortest paths from I to j, where K >= 1. - prevent a lightpath with an unnecessarily long route instead of a much shorter route.

24. 24 Scheme 1 -LF 5. Simplifying assumptions The number of variables and equation in the formulation are reduced - To make the problem more tractable, It reduce the number of constraints by pruning the search space. - tracking a limited number of alternate shortest paths, denoted K, between source and destination, such that the selected routes are within a constant factor (  >=1) of the shortest path. - all values of and are not enumerated - The amount of pruning required is a function of the size of the problem that can be solved in reason able time by the chosen LP solver.

25. 25 Scheme 1 -LF Wavelength-continuity constraints for a lightpath are intentionally ignored Queueing delays are also intentionally ignored, since propagation delay dominates The current formulation allows bifurcated routing of packet traffic. -Non-bifurcated routing significantly increased the running time of the optimization

26. 26 Scheme 1 –heuristic approach 6. Heuristic Approaches - become important when the problem formulation becomes large due to increase in the size of the network, and becomes difficult to solve by LP methods due to constraints.

27. 27 Scheme 1– Heuristic approach Maximizing single-hop traffic Attempts to establish lightpaths between source-destination pairs with the highest  sd values, subject to constraints on the number of transceivers at the two end nodes, and the availability of a wavelength in some path connecting the two end nodes.

28. 28 Scheme 1 –heuristic approach Procedure MaxSingleHop(void) While (not done) Find If ((free transmitter available at s’) AND (free receiver available at d’) AND (free wavelength available in any alternate path from s’ to d’)) begin Establish lightpath between s’ and d’ end endif endwhile

29. 29 Scheme 1 –heuristic approach  Maximizing Multihop Traffic Hsd = number of electronic hops needed to send a packet from source s to d. - start with PT - attempt to add a lightpath one by one - establish lightpaths in decreasing order of subject to constraints on the number of transceivers at the two end nodes, and the availability of a wavelength in some path connecting the two end nodes. - After each lightpath is established, Hsd values are recalculated, as traffic flows might have changed due to new lightpath, in order to minimize the average packet hop distance.

30. 30 Scheme 1 –heuristic approach Procedure MaxMultiHop(void) Initial Virtual Topology = Physical Topology while (not done) compute Hsd for all s,d find new  s’d’(Hs’d’-1) = Max (  sd(Hsd-1) ) if ((free transmitter available at s’) AND (free receiver available at d’) AND (free wavelength available in any alternate path from s’ to d’)) begin Establish lightpath between s’ and d’ end endif endwhile

31. 31 Scheme 1 -reconfiguration II. Reconfiguration -prefer for the new VT to largely similar to the current VT(closeness) - minimize the changes in the number of WRS configurations needed to adapt from existing VT to new VT.

32. 32 Scheme 1 -Recon. algorithm Algorithm

33. 33 Scheme 1 –recon. algorithm If we assume that Vij can only take on binary values, then (20) become linear. So, F’(2) may be solved directly using LP solver.

34. 34 Scheme 1 –simulation results

35. 35 Scheme 1 –simulation results

36. 36 Scheme 2 – problem spec Almost same as the scheme 1 except some parameters and objective function Also reconfiguration algorithm is little bit different.

37. 37 Scheme 2 -LF 1. Parameters N, M, Pmn, dmn, Dsd, , Ti, Ri, C (same parameters from the previous scheme1)  : :

38. 38 Scheme 2 -LF 2. Variables denotes the number of lightpaths between nodes I and j being routed through the fiber links between m and n.

39. 39 Scheme 2 -LF 3.Linear Formulation 1) Objective Function

40. 40 Scheme 2 -LF First term: Minimize the total number of lightapths set up in the network. Second term: minimize the average number of hops in the network encountered by a packet. (previous scheme’s objective) Third term: minimize the number of physical links used.

41. 41 Scheme 2 -LF 4. Constraints Resource constraints: Number of outgoing lightpaths <= number of transmitter at a node Number of incoming lightpaths <= number of receivers at a node

42. 42 Scheme 2 -LF

43. 43 Scheme 2 -LF

44. 44 Scheme 2 -LF

45. 45 Scheme 2 -LF

46. 46 Scheme 2 -LF Lightpath length bound Ensures that a lightpath between two nodes cannot be longer than  timesthe shortest distance between those two nodes.

47. 47 Scheme 2 –Recon. algorithm Reconfiguration

48. 48 Scheme 2 –Recon. algorithm

49. 49 Scheme 2 –simulation results

50. 50 Scheme 2 –simulation results

51. 51 Scheme 2 -simulation results

52. 52 Scheme 3 -overview Overview Traffic will be monitored systematically, central manager will collect data. Make decision to reconfigure signaling Reconfiguration process is seen as a continuous measurement adaptation system where small adjustments are made, instead of waiting for a noticeable drop in system efficiency and changing the topology entirely. Hitless transition method: transition between topologies was achieved by first establishing all new links without removing any link. The links of the first topology were removed only when the traffic was rerouted through the links of the new topology.

53. 53 Scheme 3 -approach Our approach: design the step adjustments in a hitless manner, so that a change can be either a lightpath addition or a deletion (after rerouting the traffic using this virtual link). Network traffic is measured periodically. Decide whether an adjustment is needed. (addition or deletion) This approach: only one lightpath change is allowed at the end of each observation period.

54. 54 Scheme 3 -MILP New parameters High watermark Low watermark At the end of an observation period, if the load of one or more lightpaths is higher than, a new lightpath is established to decrease that load. When the load is dropped below than, that link will be torn down if aiternate paths exist for diverting the traffic using that lightpath.

55. 55 Scheme 3 -MILP Problem formulation s,d = source and destination of a packet I,j = originating and terminating nodes of a lightpath

56. 56 Scheme 3 -MILP Given N= number of nodes = physical topology, number of fibers between node m and n. = average traffic rate measured during last observation. = where is a binary value denoting lightpath between nodes i and j, if there is no lightpath from i to j. 0 if there are k lightpaths from i to j.

57. 57 Scheme 3 -MILP W = number of wavelengths on each fiber C = Capacity of each wavelength channel Ti = number of transmitter Ri = number of receivers = highest and lowest lightpath loads measured during the observation period

58. 58 Scheme 3 -MILP Variables Physical routing binary variable if the lightpath from i to j is routed through the physical link (m,n) New virtual topology: is defined similar to. Note that V’ is at most one lightpath different from V. Traffic routing: The binary variable is 1 when the traffic flowing from node s to d employs as an intermediate lightpath, and 0 otherwise. Load of maximally-loaded lightpath in the network:

59. 59 Scheme 3 -MILP Objective Minimizes the load of the maximally loaded lightpath in the network. Allows us to balance the network load in the new VT, by addition/deletion of the best possible lightpath

60. 60 Scheme 3 -MILP Constraints On physical topology: (1) ensures that only one outgoing physical link of source nodes will be assigned to a lightpath. (2) ensures that only one incoming physical link of the destination node will assigned to a lightpath

61. 61 Scheme 3 -MILP (3) guarantees that the number of incoming and outgoing links reserved for a lightpath at any intermediate node will be equal. (4) number of wavelengths are limited to W on every physical link. (5) a physical link is assigned only if the lightpath exists.

62. 62 Scheme 3 -MILP On virtual topology connection Note that is unity when one or more lightpaths are heavy loaded. That will add a new lightpath to the VT. Is unity when one or more lightpath has a load below the low watermark, and in this case a lightpath will be deleted if (6)- total # of lightpaths in the new VT

63. 63 Scheme 3 -MILP (7) guarantees that the new VT is constituted by the same set of lightpath of the current VT except one lightpath being added or deleted. On VT traffic Variables:

64. 64 Scheme 3 -MILP (8) is a multicommodity-flow controling the routing of packet traffic on virtual link. (9) ensures that traffic can only flow through an existing lightpath (10) specifies the capacity constraint for any lightpath (11) provides that the load on any lightpath is smaller than or equal to the max load

65. 65 Scheme 3 -MILP limit the total number of lightpaths originating from and terminated at a node to the total number of transmitters and receivers

66. 66 Scheme 3 –heuristic appro. Heuristic adaptation algorithm Since frequent changes to the VT are not desirable, selection of traffic-observation period and decision of triggering a VT change should be made carefully It uses load-balancing ability of the current topology as an input to the triggering function of the adaptation algorithm. Having perfectly balanced loads on every link is practically npt possible, it aims to maintain quasi-balanced virtual links. is the load of the ith lightpath.

67. 67 Scheme 3 –heuristic appro. The objective of the this algorithm is to keep the load of every lightpath between. If the load of one or more lightpath is higher than, the lightpath having the maximum load will be considered, and a new lightpath will be added to decrease It choose to establish a lightpath between the end nodes of the multi- hop traffic with highest load. Doing so we expect to have a noticeable decrease in When the load of a virtual link decreases to a value below, either because of changes in the dynamic traffic or rerouting as a result of previous topology changes, the algorithm will tear down that link, unless it is not the only one link. it is possible that new congestion can be occur by deleting a lightpath, but this is a part of the adaptation process and indicates more lightpaths should be added.

68. 68 Scheme 3 –heuristic appro. The max link load is considered first, since highly loaded link would cause more problem than underutilized link. Lightpath deletion is performed only if that link is not critical; not on the unique path between i and j for which traffic rate All lightpath lower than are considered in increasing order of their loads, until an appropriate lightpath is found. Variation to its approach exist, such as deletion and addition in one step when the load of more than one lightpath is outside the region. Whenever a lightpath is added or deleted, the route for all packets traffic is re-calculated.

69. 69 Scheme 3 -heuristic algo.

70. 70 Scheme 3 –heuristic algo.

71. 71 Scheme 3 –heuristic algo.

72. 72 Scheme 3 –simulation results

73. 73 Scheme 3 –simulation results

74. 74 Scheme 3 –simulation results

75. 75 Scheme 3 –simulation results

76. 76 Scheme 3 –simulation results

77. 77 Scheme 3 –simulation rsults

78. 78 Scheme 3 –simulation results

79. 79 Scheme 3 -simulation results

80. 80 Scheme 4 - overview A specific node may monitor transmissions on the various channels, and apply statistical techniques to determine whether the overall conditions have changed in a way that significantly affects the optimality of the current wavelength assignment. VT design GLPT- generalized LPT problem (multiprocessor scheduling problem) - NP-hard Processor –> channels Tasks –> receivers Execution time –> bandwidth requirement  Markov decision process formulation & policy-iteration method

81. 81 Scheme 4 -VT VT design (1) Objective is to assign the receivers to the available channels such that the total bandwidth used in each channel is approximately the same among different channels. (2) the number of retunings required to take the network from assignment R to R’ is as small as possible. This problem is equal to the multiprocessor scheduling. (NP hard)

82. 82 Scheme 4 -VT The constrained Load Balancing Problem R: initial assignment T: traffic matrix R’: new assignment T’: new traffic matrix  Problem CLB Given an initial wavelength assignment R, a traffic matrix T’, and two positive integer K and L, is there a wavelength assignment R’ such that CLB problem is also NP-hard because it reduces to the multiprocessor scheduling problem which is NP-hard.

83. 83 Scheme 4 –heuristic appro. Heuristic based on CLB (GLPT) Approximation algorithm for the multiprocessor problem Processor= channels Tasks= receivers Execution time= bandwidth requirements  Modify LPT to take into account R, the previous wavelength assignment, by introducing a parameter ,  The new algorithm also orders the tasks in a list L in decreasing order of their bandwidth requirement.  When a channel i searches for a new receiver to assign it does not immediately take the first available receiver in the list.

84. 84 Scheme 4 –heuristic appro.  It considers the first  available receivers in the list.  If at least one of these receivers was assigned to the same channel i under the previous assignment R.  Then the channel starts assigning the receiver that has larger bandwidth requirement, even if it’s not the first one in the list.  If no such receiver exists, the processor executes the first available receiver, as in LPT.  Running time of GLPT=.  Higher , it is more likely that receivers will be assigned to the same channels as before  And the new wavelength assignment R’ will be closer to R; this may be achieved at the expense of load balancing.

85. 85 Scheme 4 –GLPT algo.

86. 86 Scheme 4 –GLPT algo.

87. 87 Scheme 4 -simulation results

88. 88 Scheme 4 –simulation results

89. 89 Scheme 4 -simulation results

90. 90 Scheme 4 –simulation results

91. 91 Scheme 4 - Formulation  Process Formulation DLB = degree of load balancing for a network with traffic matrix T operating under WLA R as right-hand side= the bandwidth requirement of the dominant channel second term in the right side= the lower bound, with respect to load balancing, for any WLA for traffic matrix T.

92. 92 Scheme 4 -Formulation  is a measure of how far away wavelength assignment R is from the lower bound.  =0, the load is perfectly balanced  > 0, channels are not equally balanced Higher  value means that inefficiency of the network

93. 93 Scheme 4 –MDP formulation Markov Decision Process Formulation Define the state of the network as a tuple (R,T) R= current WLA T= traffic matrix Assume that future traffic changes only depend on the current values of the elements of T, not the previous ones. So, the process (R,T) is a semi-Markov process Let M be the process embedded at instants when the traffic matrix changes. Then M is a discrete-time Markov process. Our formulation is in terms of the Markov process M. A network in state (R,T) will enter state (R’,T’) if the traffic matrix changes to T’.

94. 94 Scheme 4 -MDPF The decision is a function of the current state and is denoted by d[(R,T)]. Setting d[(R,T)] = implies that if the system is in state (R,T) and the traffic demands change, the network should be reconfigured into WLA. can R or R’ So new state can be (R’,T’) or (R,T’) The set of decisions for all network states defines a reconfiguration policy. To formulate the problem as a Markov decision process, we need to specify reward and cost function associated with each transition.

95. 95 Scheme 4 -MDPF Immediate expected reward:,  (.) is a nonincreasing function of Reconfiguration cost :, where  (.) is a nondecreasing function of the number of receivers that must be retuned. We assume that the rewards and costs are bounded The problem is how to reconfigure the network sequentially in time, so as to maximize the expected reward minus the cost over an infinite horizon.

96. 96 Scheme 4 -MDPF Z= set of admissible policies Reconfiguration problem can be formally stated as follows The point at which this policy becomes optimal is not easy to determine, as it depends on the transition probabilities of the underlying Markov chain. Consider an ergodic, discrete-space discrete-time Markov process with rewards and a set of alternatives per state that affect the probabilities and rewards governing the process.

97. 97 Scheme 4 -MDPF Policy-iteration algorithm can be used to obtain a policy that maximize the long-term reward in (3) for such a process. Initial, an arbitrary policy is specified from which all state transition rates are determined. The algorithm then enters its basic iteration cycle, which consists of two stages. The first stage is the value-determination operation, which evaluates the current policy. The second step: the policy-improvement routines uses a set of criteria to modify the decision at each state and obtain a new policy with higher reward than the original policy. This policy will be used as the starting point for the next iteration

98. 98 Scheme 4 -MDPF The cycle continues until the policies in two successive iterations are identical. At this point, algorithm has converged, and the final policy is guaranteed to be optimal with respect to maximizing the reward in (3). Difficulty in applying the policy-iteration algorithm to the Markov process M Potential number of states (R,T) is too large Alternative formulation

99. 99 Scheme 4 –alternative formulation Alternative Formulation Close examination of (3) Reward and cost functions depend only on not on actual values of traffic element or WLA involved.

100. 100 Scheme 4 –alter. formulation New process as Markov process M We make the simplifying assumption that the decision to reconfigure will also depend on the DLBs and the distance only. State: tuple,where  is the DLB achieved by the current WLA with respect to the current traffic matrix and D is the number of retunings required if the network were to reconfigure. It has Markovian property.  has real number value To apply policy-iteration algorithm, we need a discrete-state process So we quantize the  value with interval k. We have a new discrete-state process M’ with state

101. 101 Scheme 4 –new MP M’

102. 102 Scheme 4 –alter. formulation We note that GLPT algorithm guarantees that the DLB of the WLA obtained using the algorithm will never be more than 50% away from the degree of load balancing of the optimal WLA. Possible transition

103. 103 Scheme 4 –alter. formulation The new process M’ is a discrete-space discrete-time Markov process with rewards and two alternatives per state, and we can use the policy-iteration algorithm to obtain an optimal policy off-line and cache its decision If under the optimal policy, the decision associates with current state is to reconfigure, then the network must make a transition to the new WLA R’; otherwise, the network will continue operating under the current WLA R. We expect that as the number of interval K increases, the accuracy of the approximation will also increase, and the decision of the optimal policy obtained through the process will converge.

104. 104 Scheme 4 -transition Transition phase receivers should be retuned. Retuning strategy: when and how? While retuning: possible increasing delay or packet loss (penalty) Tradeoff between the length of the transition period and the portion of the network that becomes unavailable during this period. S, |S| = D(R,R’) Retuning strategy is defined as a partition of S into M, 1<=M<=|S|, subsets of receivers such that time is associated with subset represents a group of receivers that are simultaneously taken off-line for retuning.

105. 105 Scheme 4 -transition The retuning of group starts at time and lasts for a period of time equal to the receiver retuning latency L: maximum number of receivers in each group We note that a wide range of strategies can be obtained for the different values of L. By varying the L value, we hope to determine whether exists a tradeoff between the number of receivers that can be scheduled to retune at the same time and the associated packet losses during the transition phase.

106. 106 Scheme 4 –retuning strategy

107. 107 Scheme 4 –simulation results

108. 108 Scheme 4 –simulation results

109. 109 Scheme 4 –simulation results

110. 110 Scheme 4 –simulation results

111. 111 Scheme 4 -simulation results

112. 112 Scheme 4 –simulation results

113. 113 Scheme 4 –simulation results

114. 114 Scheme 4 –simulation results

115. 115 Scheme 4 –simulation results

116. 116 Scheme 4 –simulation results

117. 117 REFERENCES [1] I.Baldine and G.N.Rouskas, “Dynamic load balancing in broadcast WDM networks with tuning latencies”, in Proc. INFOCOM ’98, Mar. 1998, p78-95 [2] B. Mukherjee, Optical Communication Networks, McGraw-Hill, July 1997 [3] D. Banerjee and B. Mukherjee, “Wavelength-routed optical networks: Linear formulation, resource budgeting tradeoffs, and a reconfiguration study”, IEEE/ACM Transaction on Networking, vol. 8, no. 5, pp. 598-607, Oct. 2000 [4] B. ramamurthy and A. Ramakrishnan, “Virtual topology reconfiguration of wavelength routed optical WDM networks”, in Proceedings of IEEE GLOBECOM, 2000, pp. 1269-1275 [5] I.Baldine and G.N.Rouskas, “Traffic adaptive WDM networks: A study of reconfiguration issues”, IEEE Trans. Commun.Jan, 2001 [6] A. Gencata and B. Mukherjee, “Virtual-Topology adaptation for WDM Mesh network under dynamic traffic”, IEEE Trans. Commun. 2002