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                 VISHAL ANAND
(Lab. for Advanced Network Design, Evaluation and Research)
               In collaboration with:
        Tushar Katarki and Chunming Qiao
           CSE Dept., SUNY at Buffalo

 Introduction
 Related work
 Maximum Profitability Problem
 Concluding remarks
 Questions and discussion

Vishal Anand
 Optical WDM networks - future backbone
  for wide area networks.
 Physical Topology - Optical wavelength
  routers connected by fiber links.
 Lightpath or connection - Path between
  two end nodes and a wavelength on that
 No wavelength conversion - Any lightpath
  uses the same wavelength on all the links
  its path spans.
Vishal Anand                                  3
The RWA(Routing & Wavelength
Assignment) Problem
 Given :
  – a network topology
  – a set of traffic demands (or connection
 Determine the routes and wavelengths to use
  so as to satisfy the demands.
 The RWA problem is usually solved to
  optimize some specified objective(s).
Vishal Anand                                  4
Previous and related work
 Example objectives
  – Minimize network-wide packet delay (e.g.
    number of hops).
  – Maximize throughput (e.g. number of
  – Maximize allowable capacity upgrade or
    scalability (for future traffic demands).
 Minimizing cost (network resources used)
  can also be an important objective.
 For a bandwidth broker (or carrier)
  maximizing profits is most important.
Vishal Anand                                    5
The Maximum Profitability Problem
 Given:
  – a set of connection requests, N.
  – a network topology.
  – earnings (revenue) Ei associated with each
    connection request, i.
  – cost of using any wavelength on a link l, Cl.
 Solve the RWA problem to maximize the
   profit, P = Total Earnings - Total Costs.
Vishal Anand                                        6
 Maximizing profit problem is a more
   general formulation.
    – If Ei=E, for each connection/lightpath i (i.e., all
      connections have equal earnings) OR if n=N
      (i.e., all the connection requests have to be
      satisfied) then the problem is same as the
      minimizing cost problem.
    – If Ei=E and if all connections/lightpaths have
      equal costs. Then the problem is the same as
      maximizing throughput problem.
 Hence a more direct study of the
   maximizing profit problem is necessary.
Vishal Anand                                                7
Network Model

 Network topology considered: 16 node
 Cost of using each wavelength on a link , is
  the same, but varies from link to link.
 No wavelength conversion capabilities at
  any of the nodes.
 Number of wavelengths on each link in the
  network is the same.
Vishal Anand
Heuristic based approach
 The RWA problem is known to be NP Hard
  and hence computationally intractable.
 Maximizing profit heuristic: MaxPro
    – Find a cheapest path for each connection request
      and compute the profit.
    – Sort the requests in the order of decreasing
      profit and store in a list.
    – Satisfy connection requests in decreasing order
      of profit (a greedy approach).
    – If a connection request is satisfied.
        • delete that connection from the sorted list.
Vishal Anand
    – If the cheapest path for a connection request is
      not available.
        • Re-compute a new cheapest path for only that
          connection request.
        • Compute the new profit for this connection request.
        • Insert this connection into the sorted list depending
          on the profit.

    – Repeat till no other connection request can be

Vishal Anand
Results and Comparison

 1) Results obtained from MaxPro compared
    – a minimizing cost heuristic
    – a random assignment heuristic
 2) Results of Maxpro compared with the
   optimal results from integer linear program.

Vishal Anand
Comparison of the heuristics

 MaxPro performs the best.
 Better than a minimizing cost heuristic.
Vishal Anand
Integer Linear Model
 Definitions:
    – W :Number of wavelengths on each link.
    – n, L :Number of nodes, links in the network.
    –      :Earnings obtained by satisfying a connection request between
      nodes  and .
    –    : Total number of alternate routes/paths available to reach node
       from node .
    –    : Cost of reaching node  from node  on route r.
    –    : = 1, if link j is used by the route r between nodes  and , 0
    –    : Number of connection requests between nodes  and .
    –    : = 1, indicates that the connection between node  and  is
      routed on route r using wavelength k.
Vishal Anand
 Objective function

 Subject to:

    – The total number of lightpaths established between a node pair
      should not exceed the number of requests between that node pair.

Vishal Anand

    – The total number of lightpaths established on any link should not
      exceed the number of wavelength on that link.

    – A wavelength on a link can support at most one lightpath.

    – The Integrality constraint.
Vishal Anand
Comparison of Maxpro with ILP

 MaxPro obtains on the average 90% of the
   results got from the ILP(optimal profit).
Vishal Anand
Summary and Future work
 Formulated a RWA problem with the
  objective of maximizing the profit.
 Proposed a maximizing profit heuristic.
 Compared results of a profit maximizing
  heuristic with a minimizing cost heuristic
  and ILP.
 Future work
    – Study the maximizing profit problem for the
      On-line traffic model.
    – Extend to cases where protection and
      restoration is required for the traffic.
Vishal Anand

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