Optical Networks BM-UC Davis128 Wavelength Routing Switch (WRS)–Details of the UT Node
Optical Networks BM-UC Davis129 Optimization Problem Formulation On virtual topology connection matrix V ij On physical route variables p ij mn On virtual topology traffic variables sd ij On coloring of lightpaths c ij k Objective: Optimality criterion (a) Delay minimization: (b) Maximizing offered load (equivalent to minimizing maximum flow in a link): New optimality criterion (c) Minimize average hop distance
Optical Networks BM-UC Davis130 Solution Approach to Virtual Topology WDM WAN Design 1. Choice of optimal virtual topology Simulated annealing; optimization based on maximizing throughput, minimizing delay, maximizing single-hop traffic, etc. 2. Routing of lightpaths over the physical topology Alternate-path routing, multicommodity flow formulation, randomized routing 3. Wavelength assignment: Coloring of lightpaths to avoid wavelength clashes Graph-coloring algorithms, layered graph models 4. (Optimal) routing of packets over the virtual topology Shortest-path routing, flow-deviation algorithm, etc. 5. Iterate Check for convergence and go back to Step 1, if necessary.
Optical Networks BM-UC Davis131 Details of Virtual Topology Design Simulated Annealing Start with random virtual topology Perform node exchange operations on two random nodes Route packet traffic (optimally) using flow deviation Calculate maximum traffic scaleup for current configuration If maximum scaleup is higher then previous maximum, then accept current configuration; else accept current configuration with certain decreasing probability Repeat until problem solution stabilizes (frozen). Flow Deviation Perform shortest-path routing of the traffic Select path with large traffic congestion Route a fraction of this traffic to less-congested links Repeat above two steps iteratively, until solution is acceptable
Optical Networks BM-UC Davis132 NSFNET Traffic Matrix (11:45 PM to midnight, ET, Jan. 12, 1992)
Optical Networks BM-UC Davis134 Delay Components in a WDM Solution
Optical Networks BM-UC Davis135 Scaling of Bandwidth – The WDM Advantage No WDM (Physical Topology) WDM (with P transmitters/receivers per node) WDM Advantage Increasing P decreasing H v C = link speed (Mbps) H p = avg. hop distance (physical) N = number of nodes
Optical Networks BM-UC Davis136 Problems/Limitations of Solution 1 Nonlinear objective functions. Nonlinear constraints – on wavelength continuity. Resorted to heuristics Optimal virtual topology design (Simulated Annealing) Optimal packet routing on V.T. (Flow Deviation Algorithm) No routing and wavelength assignment (Shortest-path lightpath routing; no constraints on wavelengths).
Optical Networks BM-UC Davis137 Highlights/Contributions of Solution 2 Complete Virtual Topology Design Linear formulation Optimal solution Objective: Minimize average hop distance Assume: Wavelength conversion (Sparse conversion provides almost full conversion benefits). Resource Budgeting Tradeoffs Important/Expensive Resources: Transceivers and wavelengths Don’t under-utilize either of them! Hardware cost model. Optimal Reconfiguration Algorithm Minimize reconfiguration time.
Optical Networks BM-UC Davis138 Optional Constraints / Simplifying Assumptions Need scalability. Physical topology is a subset of the virtual topology. Bounded lightpath length Prevent long convoluted lightpaths from occuring. Prune the search space Consider K shortest paths (bounded K ).
Optical Networks BM-UC Davis139 Two Solutions from the LP (a) Two-wavelength solution (b) Five-wavelength solution
Optical Networks BM-UC Davis145 WDM Network Cost Model
Optical Networks BM-UC Davis146 Reconfiguration Algorithm Generate linear formulations F(1) and F(2) corresponding to traffic matrices sd 1 and sd 2. Derive solutions and S(1) and S(2), corresponding to F(1) and F(2) Modify F(2) to F’(2) by adding the new constraint: New objective function for F’(2) : or Although mod is nonlinear, above reconfiguration formulation is linear since the variables p’s and V’s are binary.
Optical Networks BM-UC Davis148 Summary of Virtual Topology Design Principles Use WDM to scale up an existing fiber-based WAN (Network’s information carrying capacity increased manifold) Employ packet-switched virtual topology … imbedded on a physical topology … as if we have a virtual Internet (which is reconfigurable under user control) … need optimum graph-imbedding algorithms Reuse electronic switch of existing WAN … as part of the WRS in the scaled-up WAN