We study Bandwidth Reservation (BR) policies for the Bandwidth on Demand (BoD) problem in a class of multihop networks. We motivate an Erlang fixed-point BR heuristic for the general BoD problem by first establishing the optimality of BR on a class of multihop networks. The motivating problem is a wireline network comprising$k$links in tandem, each link of which is shared by two types of bandwidth demands, one type requiring one unit of bandwidth from every link, and the other type (being dedicated to the link) requiring one unit of bandwidth as well. First, for this$k$-hop tandem network, when each link has unit bandwidth, we demonstrate that a policy of BR form is optimal. We then study the BoD problem for a more general$k$-hop tandem network, in the “Kelly” limiting regime, where the arrival rates as well as the link bandwidths become large. For certain parameter regimes of the$k$-hop tandem network, we show that an admission control policy of BR form is asymptotically optimal. Motivated by these results, we propose an Erlang fixed-point based, link-by-link, heuristic algorithm for computing a BR policy for the BoD problem in a general network. We, finally, evaluate this proposal numerically.

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our main results are on the exponential rates of convergence of classification errors at equilibrium, which are analogous to the well-known Chernoff-Stein lemma and Chernoff information that describe the error exponents in the classical binary hypothesis testing problem, but with parameters derived from the adversarial model. The results are validated through numerical experiments.