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Distributed Virtual Circuit Switching Distributed Virtual Circuit Switching protocol with auction pricingprotocol with auction pricing

Loubna ECHABBI

Dominique BARTH

Laboratoire PRISM

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FrameworkFramework

Virtuel circuit switching networks.

Goal: Ressource allocation to satisfy some QoS.

How : connection establishment.

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Conflict : Congestion in a router

Definition: the demand is greater than the available resource.

Question : which criterions to choose accepted requests.

Maximize the number of accepted requests.

Minimize the remaining bandwidth.

for more fairness: Use auctions to charge accepted requests some congestion cost. These prices can be used to compute routing tables or in the service pricing.

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Auctions : local approach

At each router we have the following information:

A set of requests (budget, demand, destination..)

A set of outgoing links ( capacities )

A set of links obtained from the routing table which link each request to possible outgoing links. Two types of routing are studied :

Deterministic routing : 1 destination= 1 outgoing link.

Non deterministic routing : 1 destination= n outgoing links

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Auctions: first model Requests submit their offer .

The router chooses a combination of traffic that maximizes its profit.

The non accepted requests increase their offer (by one unit).

The stopping criteria : non accepted requests cannot increase their offer anymore. At each step the problem is NP-complete (even in the deterministic case: contains the knapsack problem).

Auctions final result is difficult to be characterized .

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Auctions : second model

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The main idea: each link fixes its cost.

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Second model : Deterministic case

Auctions on different links are independent

At each step the problem is polynomial.

The auction’s final result can be polynomialy obtained by sorting the requests in a decreasing order and accepting them in this order while keeping the capacity constraint held.

Note: When congestion occurs, the accepted requests are charged the first non accepted bid, else the cost is null.

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Second model: non deterministic case.

Definition: The set of stable links, at a given step, is the set of links such that all requests that can be routed at least on one element of this set, is indeed accepted on a link in that set.

Auction on different links are not independent.

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Second model: non deterministic case

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Second model: non deterministic case

Conjecture: the stable link maximization problem is NP-Complete.

Process: At each step, we maximize the number of stable links. At the end of each step, non stable links increase their offer and eliminate requests that cannot bargain .

Property: With any configuration that maximizes the set of stable links , stable links are the same.

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A heuristic idea

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Previous work and perspectives

Previous work:

Complexity study.

Implementation of the exact problem in Cplex.

Implementation of a simulator with the virtual circuit protocol layered on a grid network. Current work:

A comparison between the exact and the heuristic methods using the simulator.

Test of different auction strategies.