Chapter 10 RWA 2019/5/9

Routing and Wavelength Assignment for Wavelength-Routed WDM Networks Combined routing and wavelength assignment problem Routing static: ILP formulation Incremental: connection requests arrive sequentially a lightpath is established for each connection and the lightpath remains in the network indenitely dynamic: on-line algorithms a lightpath is set up for each connection request as it arrives and the lightpath is released after some finite amount of time Wavelength assignment static: graph coloring approach dynamic: heuristics A new wavelength assignment heuristic First state the goal of this research is to write a tutorial for RWA. The new contribution is a wavelength assignment heuristic. Problem statement : static vs dynamic static: minimize the max flow on a link dynamic: minimize the blocking probability of future connections 2019/5/9

Static Lightpath Establishment (SLE) problem Static : The set of connections is known in advance Dynamic Lightpath Establishment (DLE) problem Incremental : Connection requests arrive sequentially, a lightpath is established for each connection, and a lightpath remains in the network indefinitely Dynamic : A lightpath is set up for each connection request as it arrives, and the lightpath is released after some finite amount of time 2019/5/9

RWA Problem statement Wavelength-continuity constraint The SLE problem can be formulated as a mixed integer programming. The work in proposed practical approximation algorithms to solve the SLE problem for large networks and graph –coloring problem. 2019/5/9

Combined Routing and Wavelength Assignment Problem Goal: minimize the max flow among all fiber links Assumption: wavelength-continuity constraint Coverage: Invariant- no lightpaths are assigned the same wavelength on the same fiber link multi-equation conservation of flows Last requirement: assume two connections between a source-destination pair take two different wavelengths - access station model 2019/5/9

Maximizing the number of established connection (fixed W) 2019/5/9

Routing - ILP Formulation without wavelength continuity constraint Assume at most one lightpath from any source to any destination. 2019/5/9

RWA with wavelength Conversion 2019/5/9

RWA with wavelength Conversion Sparse location of wavelength converters in the network Sharing of converters Limited-range wavelength conversion 2019/5/9

Routing - Algorithms For Dynamic Traffic Fixed routing (On/Off line) Fixed-alternate routing (On/Off line) Adaptive routing (On line) adaptive shortest path routing least congested path routing 2019/5/9

Fixed Routing Off-line calculation Shortest-path algorithm: Advantage: Dijkstra’s or Bellman-Ford algorithm Advantage: simple Disadvantage: high blocking probability and unable to handle fault situation 2019/5/9

Fixed-Alternate Routing Each node is required to maintain a routing table that contains an ordered list of a number of fixed routes to each destination node A primary route between s-d is defined as the first route An alternative route doesn’t share any links with the first route (link disjoint) Advantage Provide some degree of fault tolerance Reduce the blocking probability compared to fixed routing 2019/5/9

Adaptive Routing The route from a source node to a destination node is chosen dynamically, depending on the network state Ex: Shortest-cost-path routing Each unused link has the cost of 1 unit; used link ∞; wavelength converter link c units. Disadvantage: extensive updating routing tables Advantage: lower blocking probability than fixed and fixed-alternate routing Least-congestion-path routing (LCP) Advantage Lower connection blocking than fixed and fixed-alternate routing 2019/5/9

Consider fault-tolerant Protection Set up two link-disjoint lightpaths Primary lightpath transmit data Backup lightpath must be reserved Fast but need reserve resource Restoration The backup path is determined dynamically after the failure has occurred Slow but doesn't need reserve resource 2019/5/9

Wavelength Assignment 2019/5/9

Wavelength Assignment Heuristics Random First-Fit Least-Used/SPREAD Most-Used/PACK Min-Product Least Loaded MAX-SUM Relative Capacity Loss Wavelength Reservation Protecting Threshold Explain R, FF. will explain MS and RCL. wavelength reservation and protecting threshold are not independent algorithms and must be combined with other WA algorithm. will not explain LU, MU, MP and LL. 2019/5/9

Static Wavelength Assignment Two lightpaths share the same physical link are assigned different wavelengths Reduced to graph-coloring problem: 1.Construct a graph, such that each lightpath is represented by a node. There is one edge in between if two lightpaths share the same physical link. 2.Color the nodes such that no two adjacent nodes have the same colors. 2019/5/9

Static Wavelength-Assignment Minimizes the number of wavelengths used under the wavelength-continuity constraint reduced to the graph coloring problem Construct an auxiliary graph G(V,E) Color the nodes of the graph G Largest First Smallest Last 2019/5/9

Static Wavelength-Assignment (cont.) 2019/5/9

example 2019/5/9

Largest First 2019/5/9

Smallest Last 2019/5/9

First-Fit First available wavelength is chosen No global information needed Proffered in practice because of its small overhead and low complexity Perform well in terms of blocking probability and fairness The idea behind is to pack all of the in-use wavelengths towards lower end and continuous longer paths towards higher end 2019/5/9

FF example λ0 will be assigned λ0 will also be assigned MP and LL 2019/5/9

Least-Used (LU) Wavelength Assignment Least used in the network chosen first Balance load through all the wavelength Break the long wavelength path quickly Worse than Random: global information needed additional storage and computation cost not preferred in practice Disadvantage This scheme ends up breaking the long wavelength paths quickly Additional communication overhead 2019/5/9

LU example λ0 ,λ1 ,λ3 are each used two links λ2 is used only one link So LU will choose λ2 2019/5/9

Most-Used (MU) Assignment Select the most-used wavelength in the network Advantages: -outperforms FF, doing better job of packing connection into fewer wavelength -Conserving the spare capacity of less-used wavelength Disadvantages: -overhead, storage, computation cost are similar to those in LU 2019/5/9

MU example λ0 ,λ1 ,λ3 are each used two links λ2 is used only one link So MU will choose one of λ0 ,λ1 ,λ3 with equal probability 2019/5/9

Notations 2019/5/9

Min-Product (MP) Used in multi-fiber network The idea is to pack wavelength into fibers, minimizing the number of fibers in the network ∏ D lj l є π(p) for each wavelength j, 1≦j ≦W. Chose a set of wavelength j minimizing the above value Disadvantage: not better that multi-fiber version of FF -introduce additional computation costs - 2019/5/9

MP example λ1 : 2*3*1*3*5=90 λ2 : 3*2*4*1*2=48 λ3 : 1*2*1*2*1=4 1 2 3 4 5 λ1=2 λ2=3 λ3=1 λ1=3 λ2=2 λ3=2 λ1=1 λ2=4 λ3=1 λ1=3 λ2=1 λ3=2 λ1=5 λ2=2 λ3=1 λ1 : 2*3*1*3*5=90 λ2 : 3*2*4*1*2=48 λ3 : 1*2*1*2*1=4 So choose λ3 2019/5/9

Least-Loaded (LL) Assignment Multi-fiber network Select the wavelength that the largest residual capacity in the most-loaded link along route p. Advantage: outperforms MU and FF in terms of blocking probability LL selects the minimum indexed wavelength j in Sp that achieves 2019/5/9

LL example Set up lightpath from 0 to 2 1 2 3 4 5 Assume 7 fibers per link λ1=2(5) λ2=3(4) λ3=1(6) λ1=3(4) λ2=2(5) λ3=2(5) λ1=1(6) λ2=4(3) λ3=1(6) λ1=3(4) λ2=1(6) λ3=2(5) λ1=5(2) λ2=2(5) λ3=1(6) Set up lightpath from 0 to 2 Choose λ3 Max(min(residual capacity))=5 2019/5/9

MAX-SUM Assignment Applied to multi-fiber and single-fiber also Before lightpath establishment, the route is pre-selected; After lightpath establishment, it attempts to maximize the remaining path capacity 2019/5/9

MAX-SUM Assignment (continued) r(ψ, l, j) = Mj - D(ψ) lj r(ψ, l, j):link capacity, the number of fibers on which wavelength j is unused on link l r(ψ, p, j) = min r(ψ, l, j) l є π(p) r(ψ, p, j):the number of fibers on which wavelength j is available on the most-congested like along the path p 2019/5/9

MAX-SUM (MΣ) MΣconsiders all possible paths in the network and attempts to maximize the remaining path capacities after lightpath establishment 2019/5/9

MAX-SUM Assignment (continued) w R(ψ,p) = Σ min r(ψ, l, j) j=1 l є π(p) At last, chose the wavelength j that maximizes the quantity: Σ R(ψ’(j) ,p) pєP ψ’(j) be the next state of the network if j is assigned P is all the potential paths for the connection 2019/5/9

MΣexample 2019/5/9

Calculation of Max-Sum wavelengths P1:(2,4) 3 2 1 WPC: Wavelength-path Capacity 0 1 2 3 4 5 6 Show how to calculate the first row. Wavelength selected: 0, 1, or 3 2019/5/9

Relative Capacity Loss (RCL) Assignment Chose wavelength j to minimize the relative capacity loss: Σ (r(ψ, p, j) - r(ψ’(j), p, j))/ r(ψ, p, j) pєP Sometimes better than MAX-SUM -MAX-SUM could cause blocking Longer lightpaths have a higher block probability than shorter ones Some schemes to protect longer paths: Wavelength reservation (Rsv) and protesting threshold (Thr) 2019/5/9

Relative Capacity Loss (RCL) MΣ RCL 2019/5/9

RCL example 2019/5/9

Illustrative Example 1 2 3 4 5 6 wavelengths P1:(2,4) 3 2 1 0 Explain bus connections that are setup Note: control network not shown. All wavelengths shown are for data traffic 2019/5/9

Calculation of Relative Capacity Loss wavelengths P1:(2,4) 3 2 1 Wavelength selected: 1 or 3 0 1 2 3 4 5 6 Show how to calculate the first row. 2019/5/9

Random Wavelength Assignment Randomly chosen available wavelength Uniform probability No global information needed 2019/5/9

Connection management protocol: link-state Simulation Network 2 1 2 1 1 3 1 1 1 1 5 4 2 Connection management protocol: link-state 2019/5/9

Computational Complexity Wavelength reservation & Protecting threshold - constant Random & First-Fit - O(W) Min-Product & Least-Loaded - O(NW) Least-Used & Most-Used - O(LW) Max-Sum & Relative Capacity Loss - O(WN3) where W - # of wavelengths, N - # of nodes, L - # of links Don’t explain. Say MS and RCL are expensive. 2019/5/9

Distributed Relative Capacity Loss (DRCL) Speed up the wavelength-assignment procedure each node stores information on the capacity loss on each wavelength only table lookup small amount of calculation are required upon the arrival of a connection request Routing is implemented using the Bellman-Ford (each node exchange table with its neighboring nodes and updates its table) 2019/5/9

Distributed Relative Capacity Loss (DRCL) (cont.) DRCL considers all of the paths from the source node of the arriving connection request to every other node ,excluding the destination node of the arriving connection request DRCL choose the wavelength that minimize the sum of rcl(w,d) over all possible destination d 2019/5/9

DRCL example 2019/5/9

Distributed RCL Algorithm P1:(2,4) 3 2 1 0 1 2 3 4 5 6 * Wavelength selected: 3 Why DRCL? less info exchanged (only to neighbors) Fast computation - only table lookup adaptive routing (the performance of fixed routing is very limited) Calculate the first row. Drawback: no traffic information is considered. Might not work well with non-uniform traffic. RCL table at Node 2 2019/5/9

Characteristics of Distributed RCL Less state information is exchanged Faster computation of wavelength assignment upon a connection request Can be combined with adaptive routing 2019/5/9

Simulation Network 2 1 2 1 1 1 3 1 1 1 5 4 For uniform traffic 2 Average propagation delay between two nodes: 0.107 ms Average hop distance: 1.53 2019/5/9

Simulation Results of Distributed RCL Comparison of DRCL with adaptive routing and RCL with fixed routing No access station model. 2019/5/9

L: # of links, N: # of nodes, W: # of wavelengths Conclusion for RWA L: # of links, N: # of nodes, W: # of wavelengths 2019/5/9

2019/5/9

Future Research Survivable wavelength-routed WDM networks previous work: static traffic & single link failure [S. Ramamurthy 1998] higher layer protection -logical topology design with bundle cut in mind WDM layer protection - dynamic traffic 2019/5/9

Future Research (Cont’d) Managing multicast connections in wavelength-routed WDM networks KMB Bellman-Ford Chain 2019/5/9

Simulation Results 2019/5/9

Simulation Results (cont.) 2019/5/9

Simulation Results (cont.) 2019/5/9

Simulation Results (cont.) 2019/5/9