Essays on strategic queueing

Abstract

This thesis includes three essays exploring some economic implications of queueing. A preliminary chapter introducing useful results from the literature which help contextualize the original research in the thesis is presented first. This introductory chapter starts by surveying queueing results from probability theory and operations research. Then it covers a few seminal papers on strategic queueing, mostly but not exclusively from the economics literature. These cover issues of individual and social welfare in the context of First Come First Served (FCFS) and Equitable Processor Sharing (EPS) queues, with one or multiple servers, as well as a discussion of strategic interactions surrounding queue cutting. Then an overview of some important papers on the impact of queueing on competitive behaviour, mostly Industrial Organization economists, is presented. The first original chapter presents a model for the endogenous determination of the number of queues in an M/M/2 system. Customers arriving at a system where two customers are being served play a game, choosing between two parallel queues or one single queue. Subgame perfect equilibria are obtained, varying with customer characteristics and game specifications. With risk neutrality and when jockeying is not permitted, a single queue is an equilibrium, as is two queues. With risk neutrality and jockeying allowed, there is a unique two queue equilibrium. With risk aversion and no jockeying, there is a unique single queue equilibrium, and with risk aversion and jockeying, the equilibrium depends on the magnitude of risk aversion. The second chapter analyses the individual decisions taken by consumers when deciding whether to join an M/M/1 queue where a subset of customers who interact repeatedly can both cut the queue and be overtaken once they join, by-passing occasional users. This is shown to be an equilibrium in repeated games for sufficiently patient customers. The expected sojourn time for customers under this discipline is described as a solution of a system of difference equations, and this is then used to obtain a threshold joining strategy for arrivals, which is independent of the number of regular customers in the queue, as regulars form a sub-queue under the LCFS discipline. Numerical methods are then employed to contrast sojourn times and thresholds with the equilibrium for a strict First Come First Served queueing discipline, and with the socially optimal joining rule. Finally, the third chapter describes a duopoly market for healthcare where one of the two providers is publicly owned and charges a price of zero, while the other sets a price so as to maximize its profit. Both providers are subject to congestion in the form of an M/M/1 queue, and they serve patient-customers with randomly distributed unit costs of time. Consumer demand (as market share) for both providers is obtained and described with its full complement of comparative statics. The private provider’s pricing decision is explored, and equilibrium existence is proven. Social welfare functions are described and the welfare maximizing condition obtained. Numerical simulations with uniform and Kumaraswamy distributions are performed for several parameter values, showcasing the pricing provider’s decision and its relationship with social welfare.