Monotonicity properties for the stochastic knapsack

A stochastic system is considered in equilibrium with N servers, no waiting room, and K classes of customers. A class- k customer requires b_k servers and releases them simultaneously after a random period of time. This multiclass blocking system is motivated by loss networks that support a variety of traffic types (e.g. voice, video, facsimile). The effect of increasing the state-dependent arrival rates and the number of servers on the throughputs and blocking probabilities is considered. It is noted that the theory developed can be extended to the case where queueing is permitted in the knapsack