Randomized Routing as a Regularized Solution to the Route Cost Minimization Problem
Abstract:
Often a link-state routing takes a form of the cost based scheme which admits an arriving request on the minimum cost route if this cost does not exceed the cost of the request, and rejects the request otherwise. Cost based strategies naturally arise as a result of optimization of the network performance or incorporating Quality of Service (QoS) requirements into the admission and routing processes. In the former case the implied cost of the resources represents expected future revenue losses due to insufficient resources for servicing future requests. In the latter case the cost of a route represents the expected level of QoS, e.g., bandwidth, delay, packet loss, etc., provided to the request carried on this route. In both cases due to the aggregation, statistical nature of the resource costs, delays in disseminating signaling information, non-steady or adversarial operational environment the cost of the resources may not be known exactly. Usually this uncertainty is modeled by assuming that resource costs are random variables with fixed probability distributions. We propose to explicitly recognize that the minimum cost route selection as an ill-posed problem and to view randomized routing as a regularized solution to this problem. We consider a specific case of regularization intended to guard against adversarial uncertainty, i.e., worst case scenario, with respect to the resource costs lying within known "confidence " intervals. Assuming that the network minimizes and the adversarial environment maximizes the losses resulted from non-optimal admission and routing decisions due to the uncertainty, we identify the optimal admission and routing decisions with the Nash equilibrium strategy in the corresponding game. We explicitly identify this strategy in a case of parallel, homogeneous structure.
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