Revenue maximization in service systems with heterogeneous customers

In this paper, we consider revenue maximization problems for service systems with heterogeneous customers. To extract meaningful insights, we consider a simplified two queue system where each server charges an admission price to its customers. The customers differ in their cost for unit delay and this customer heterogeneity is modeled as a random variable with distribution F. On arrival, the customers must choose a server that offers the lowest sum of admission price and the expected delay cost. Given the admission prices at the two servers and the explicit knowledge of the distribution F, we first characterize the Wardrop equilibrium routing for the heterogeneous customers. We then consider a monopoly system where both the servers belong to a single operator. For this system we characterize the revenue maximizing program for the monopoly operator and outline its properties. We then consider the duopoly problem where each server competes with the other server to maximize its revenue rate. For the special case when the servers have identical service capacity, we obtain the necessary condition for existence of symmetric Nash equilibrium prices. For the analysis of the monopoly and the duopoly problem, the heterogeneity distribution F is assumed to be explicitly known. However, for most practical scenarios, the functional form of F may not be known to the system operator and in such cases, the revenue maximizing prices cannot be determined. In the last part of the paper, we provide an elementary method to estimate the distribution F. This method relies on suitably varying the admission prices based on the properties of the Wardrop equilibrium. We also illustrate this method with some suitable numerical examples. (C) 2019 Elsevier B.V. All rights reserved.