1. Workshop PRIXNET Distributed Virtual Circuit Switching protocol with auction pricing Loubna ECHABBI Dominique BARTH Laboratoire PRISM

2. Workshop PRIXNET Framework  Virtuel circuit switching networks.  Goal: Ressource allocation to satisfy some QoS.  How : connection establishment. O D 3 4 2 5 3

3. Workshop PRIXNET 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.

4. Workshop PRIXNET 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

5. Workshop PRIXNET 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.

6. Workshop PRIXNET Auctions : second model 2 4 4 3 3 1 2 3 * 1 4 3 3 1 * 3 * 1 3 4 1 4 4 3 3 1 2 3 1  The main idea: each link fixes its cost.

7. Workshop PRIXNET 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.

8. Workshop PRIXNET 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. 2 3 2 2 2 3 3 4

9. Workshop PRIXNET Second model: non deterministic case 4 3 3 1 2 1 2 1 3 1 2 1 3 4 3 3 1 2 1 2 1 3 1 2 1 3 2 3 2 2 3 4 3 3 1 2 * 2 4 3 3 1 2 * 2 2 3 1 3 1 2

10. Workshop PRIXNET 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.

11. Workshop PRIXNET A heuristic idea 63 2 3 1 1 1 5 4 3 2 1 2 5 * 2 0 * 4 3

12. Workshop PRIXNET 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.