Unfair Consequence of Fair Competition in Service Systems—An Agent-Based and Queueing Approach

Abstract

This paper considers the competition of service centers within a service system. Each service center is modeled as a multiple-server queue. Service centers compete with each other in a fair manner and adjust their service resources (number of servers) to accommodate the demand obtained from the competition. An agent-based approach is used to model the competition and adjustment processes. Our objective is to study the size distribution of service centers under a fair competition, i.e., to answer the question, will the size distribution be uniform, normal, or skewed? It turns out that a skewed distribution (e.g., power law distribution) is obtained. Two data sets of hospital sizes are analyzed and are found to have a skewed distribution. An analytical argument is provided to explain how a fair competition could give rise to a skewed (i.e., unfair) size distribution.