Tolls and Welfare Optimization for Multiclass Traffic in Multiqueue Systems

We consider a queueing system with multiple heterogeneous servers serving a multiclass population. The classes are distinguished by time costs. All customers have i.i.d. service requirements. Arriving customers do not see the instantaneous queue occupancy. Arrivals are randomly routed to one of the servers and the routing probabilities are determined centrally to optimize the expected waiting cost. This is, in general, a difficult optimization problem and we obtain the structure of the routing matrix. Next we consider a system in which each queue charges an admission price. The arrivals are routed randomly to minimize an individual objective function that includes the expected waiting cost and the admission price. Once again, we obtain the structure of the equilibrium routing matrix for this case. Finally, we determine the admission prices to make the equilibrium routing probability matrix equal to a given optimal routing probability matrix.