LANDER
(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
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 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 path.
 No wavelength conversion - Any lightpath uses the same wavelength on all the links its path spans.
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 Given :
– a network topology
– a set of traffic demands (or connection requests).
 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).
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 Example objectives
– Minimize network-wide packet delay (e.g. number of hops).
–
Maximize throughput (e.g. number of lightpaths).
–
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.
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 Given:
– a set of connection requests, N.
– a network topology.
– earnings (revenue) E i connection request, i .
associated with each
– cost of using any wavelength on a link l , C l
.
 Solve the RWA problem to maximize the profit, P = Total Earnings - Total Costs .
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 Maximizing profit problem is a more general formulation.
–
If E i
=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 E i
=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.
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 Network topology considered: 16 node
NSFNET.
 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.
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 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.
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– 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 satisfied.
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 1) Results obtained from MaxPro compared with:
– a minimizing cost heuristic
– a random assignment heuristic
 2) Results of Maxpro compared with the optimal results from integer linear program.
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 MaxPro performs the best.
 Better than a minimizing cost heuristic.
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 Definitions:
– W :Number of wavelengths on each link.
– n, L :Number of nodes, links in the network .
–
E

:Earnings obtained by satisfying a connection request between nodes
 and

.
– R

: Total number of alternate routes/paths available to reach node
 from node

.
–
C r

: Cost of reaching node
 from node
 on route r.
– rj l

: = 1, if link j is used by the route r between nodes
 and

, 0 otherwise.
– d

: Number of connection requests between nodes
 and

.
– x rk
 rk : = 1, indicates that the connection between node
 and
 is routed on route r using wavelength k.
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 Objective function max n n



E

R  W  
 
1
 
1 r

1 k

1 x rk


R  r
 

1
C r
 k
W

1 x rk




 Subject to:
R  r
W 

1 k

1 x rk

 d

 
,

–
The total number of lightpaths established between a node pair should not exceed the number of requests between that node pair.
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And
R  n n 
 
1
 
1 r

1 l rj
 k
W 

1 x rk


W
 j

1 ,..., L
– The total number of lightpaths established on any link should not exceed the number of wavelength on that link.
n n R  
 
1
  
1 l rj
 x rk


1
 j

1 ,..., L ,
 k

1 ,..., W
– A wavelength on a link can support at most one lightpath.
x rk


 
– The Integrality constraint.
 
,

, r , k
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 MaxPro obtains on the average 90% of the results got from the ILP(optimal profit).
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 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.
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