Multi-Agent Customer Allocation in a Stochastic Service System

In many service systems, customers interact with an agent who directs customers to specific service facilities. Each agent, as a decision maker, seeks to allocate his/her customers to the service centers so as to optimize a measure of performance based on the customers' expected waiting time and the expected number of customers in service. In this paper, the problem of multiple agents, each optimizing his/her customer allocation decision in a stochastic service system, is analyzed as a noncooperative game. It is shown that an equilibrium point to such a game exists and sufficient conditions for which this equilibrium point is unique are also given. Finally, the relative efficiency of the multi-agent system is examined by comparing the customers' average waiting time in the multi-agent system to the one-agent case. It is shown that, in general, the multi-agent system is not as efficient as the one-agent one in terms of customer welfare.