Admission control with incomplete information

We consider a multiple server loss model where customers arrive to a gatekeeper according to a Poisson process. Upon arrival of a new customer, the gatekeeper must decide whether to admit it or to block it. A blocked customer goes away, while an admitted customer starts service if any of the servers is free, or immediately departs if all are busy. A cost c is incurred when the gatekeeper blocks an arrival; a larger cost K is incurred if an admitted customer can not find a free server and therefore has to leave the system without being served. One key assumption is that the gatekeeper is informed when an admitted customer finds all servers busy, but is not informed when served customers depart.; We formulate the above problem as a stochastic dynamic programming model and consider two criteria: (a) the total expected discounted cost on an infinite time horizon, and (b) the long run average cost. In the case of a single server, we show that a threshold type policy which blocks for a certain amount of time after a new arrival is admitted is optimal if the service times are exponentially distributed; for general service distributions, we derive a sufficient condition which gives the structure of the optimal policy. However, when there are multiple servers, we cannot analytically determine the optimal policy, so we propose several heuristic policies. We analytically compute the best parameter for some heuristic policies and use simulation to estimate that of the others.; Finally we consider a game theory model consisting of many gatekeepers sharing a single server with exponential service distribution. Each gatekeeper acts as a selfish player trying to minimize his own long run average cost. We assume that each gatekeeper has his own Poisson arrivals and makes decisions that are not told to the others. We show that there exists a Nash equilibrium for this non-zero sum game, and also how a cooperative policy can be achieved by an agreement upon all gatekeepers, which then reduces the total long run average cost. Our models have various applications in the telecommunication networks.