wavelength convertible network design using the simplified

Wavelength Convertible Network Design Using the Simplified-Interconnected-

Layered-Graph (SILG) ModelMark WurtzlerDepartment of Electrical Engineering and Computer ScienceUniversity of KansasEECS 864 Lecture

Problem Synopsis

The addition of wavelength converters to a WDM network can allow great performance improvement gains We seek the optimal reduction of lightpathsetup blocking probability with regard to the high cost of wavelength conversionSince cost prohibits conversion at every node, how do we allocate our limited # of converters?

A Basic WDM Convertible Network

http://home.att.net/~sbanerjee/papers/ChBa96.pdf

How does λ Conversion Help?

• Wavelength conversion opens up new lightpaths on

wavelengths that would otherwise be unused

• This can lower the blocking probability when trying to set

up a lightpathIn this figure, wavelength conversion at point A allows a third lightpath to be established, as opposed to two lightpaths in the non-convertible case on the left.

A


Structure of a Router w/ limited λconversion capability

The input ports are switched once to allow

inputs that require conversion to pass into

the wavelength converter bank.

Then, they are switched again to reroute the

proper wavelengths to the output ports.


How do we specify a WDM optical network to solve this problem?

R = { ri } is the set of wavelength routers in the networkC = { ci } is the set of wavelength converters at each wavelength routerA = { ai } is the set of access nodes in the networkL = { li } is the set of directed optical fiber links in the networkW = { wi } is the set of available wavelengths per link.

How do we specify a WDM optical network to solve this problem?

The number of wavelength converters ‘C’ at a node can range between 1 and (d*W), where ‘d’ is the number of incoming links at the nodeIf C=d*W, then the routing becomes similar to an electronic network – however the cost of conversion will likely not allow this solution

Network Topology


Solving the Routing Problem

Static SolutionIf we know all the routes needed in the system, the design can be performed by maximizing the flow function across all source and destinations. This flow is defined as:


In a similar way to how we defined the flow from a source to a destination, we define the flow on an edge eij as

Now, the static routing and wavelength (RAW) assignment can be optimized by maximizing flow


The corresponding integer linear program (ILP) can be solved, but is computationally unrealistic for large networks. Also, we desire a dynamic algorithm so that the network can adapt as new links are added.

Therefore, we must take a heuristic approach to a dynamic algorithm.

Introduction to the Simplified Interconnected-Layered-Graph (SILG) Model

A topology network N is defined in an ILG called G and a cost is given to each optical link c(l)B is defined as the lightpaths already set upThe graph is then simplified by deleting the wavelength converter nodes, access nodes, and the edges connecting these nodes.Directed edges (aka Interlayer Edges) are added corresponding to each wavelength router


We then create a counter β(i) at each router which starts at C (total # of converters) and is decremented as converters are usedA weight α is defined between inter-layer edges and c(l) is used on intra-layer edgesIf an edge is already occupied on a intra-layer link or all converters are in use on a inter-layer link, the weight is set to infinity

Dynamic Routing Algorithm for the SILG Model

1. Given: An optical network N(R, C, A, L, W)Transform N into a simplified interconnected–layered–graph G’(V’, E’).In G’ set the cost of intra–layer edges to c(l), and the cost of inter–layer edges to a positive constant .For each wavelength router i ε R, initialize an integer wavelength converter counter β(i) to |C|

2. Wait for a request.If it is a lightpath connection request from access Node s to access Node d, s, d ε A,Add Nodes s and d to G’Add directed edges from s to the router node to which it is connected for all the layers in G’Add directed edges to d from the router node to which it is connected for all the layers in G’Go to Step 3,otherwise // i.e., lightpath release request from access Node s to access Node dGo to Step 4.


Dynamic Routing Algorithm for the SILG Model

3. Find a shortest (i.e., cheapest) path p in G’ from Node s to Node d (e.g., by Dijkstra’salgorithm).If the cost of the path C p = infinity, block the request;Otherwise, accept the request and set up the lightpath along the shortest path.//Note that the shortest path will provide the wavelength(s) and the converter(s), if any, to be usedUpdate the cost of the intra–layer edges on path p to 8.Set converter counter (i) to (i)–1 if path p is routed via an inter–layer edge at Router iIf (β(i) = 0) then set the weight of all the inter–layer edges at Router i to infinity. Go to Step 2.4. Reset the weights of the intra–layer edges eij occupied by the lightpath to c(eij ).Set converter counter (i) to (i)+1 if path p was routed via an inter–layer edge at Router iIf (β(i) = 1) then set the weight of all the inter–layer edges at Router i to .Remove the access Nodes s and d, and the edges involving Nodes s and d from G’. Go to Step 2.


Example (Chen and Banerjee Simulations)

The authors, Chien Chen and Subrata Banerjee, performed simulations on ten random network topologiesOverview:

Six access Nodes/router, Cost/link=1Requests are Poisson arrivals# of ports/router=d Wavelengths/link=|W|

D=8, |W|=4 40 Node NetworkBlocking rate vs. Arrival Rate


D=8, |W|=4 40 Node NetworkNetwork Utilization vs. Arrival Rate


Weight of Interlayer Edges vs. Blocking Rate

Increasing the weight given to the converter edges causes longer lightpaths to be set up

This may actually increase blocking probability, but allow for longer lightpaths


Blocking Rate vs. Arrival Rate for Network: 20 Router and 40 Router Case


Computational Considerations

The Chien/Banerjee SILG algorithm results in an analysis with complexity proportional to |R|2|W|2

Previous designs were proportional to |R|4|W|2, so this heuristic provides a more efficient assignment of converters in a network

Homework Problems

1) How might the blocking rate be affected by increasing the intralayer edge weights in the SILG model?

2) Where does the bound on the computational complexity arise? (Hint: Think back to last week’s lecture on wavelength convertible networks)

Reference

The graphs and algorithms in this lecture weretaken from a Globecom submission:

Banerjee, Subrata and Chen, Chien. A new model for Optimal Routing in All-Optical Networks with Scalable Number of Wavelength Converters. Globecom ’95.http://home.att.net/~sbanerjee/papers/ChBa96.pdf

wavelength convertible network design using the simplified

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