QoS routing under adversarial binary uncertainty

A cost based admission control and routing scheme 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 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 revenue losses due to insufficient resources to service future requests. In the latter case, the cost of a route represents the expected level of QoS provided to the request. In both cases, due to aggregation, the statistical nature of the resource costs, propagation and queueing delays in disseminating signaling information, and a nonsteady or adversarial operational environment, the exact resource cost may be unknown. Usually, this uncertainty is modeled by assuming that resource costs are random variables with fixed probability distributions, which may or may not be known to the network. This paper explores a different approach intended to guard against adversarial uncertainty, i.e., worst case scenario, with respect to the resource costs lying within known "confidence" intervals. We assume that the network minimizes, and the adversarial environment maximizes, the loss or risk resulting from non-optimal admission and routing decisions due to the uncertainty. In a symmetric case, we explicitly identify the optimal network strategy by solving the corresponding game of the network against environment.