Congestion and Strategic Behavior in Queueing Systems

University Of Nevada Las Vegas, Las Vegas NV

Investigators

Abstract

Queueing theory is a body of mathematical theory that attempts to find solutions to a large class of problems where the arrival pattern of customers is assumed to be exogenously determined. This is the case, for example, when motorists pull into gas stations along the highway to refuel their cars. In a radical departure from this approach, the focus of the present research is on queueing problems when the arrival pattern of customers is assumed to be endogenously determined, with each customer determining if and exactly when to join a queue. This is the case, for example when drivers decide at what time to bring their cars for emission inspection. If communication is not possible, endogenously determined arrivals give rise to problems of tacit coordination. We are interested in studying these problems from three perspectives-theoretical, experimental, and empirical. From a theoretical perspective we formulate the problem as one of interactive decision making, solve it using solution concepts of game theory, and study its equilibrium behavior. Experimentally, we investigate the emergence of tacit coordination, or any other patterns of behavior, in progressively more realistic queueing problems. One proposed experiment controls the level of congestion by manipulating the fixed service time. Another relaxes the assumption that service time is fixed and models it as random variable drawn from a commonly known distribution. A third experiment allows customers to form queues before service commences. In yet another experiment, the investigation is extended to multi-server queueing systems with parallel waiting lines. Empirically, we propose to collect data on arrival time, waiting time, and service time in actual emission control stations. Congestion and waiting in lines have become pernicious problems of modern society. Yet we know almost nothing about the strategic thinking that governs the behavior of customers who wish to minimize their waiting time in line by choosing the "right" arrival time. Nor do we know much about the dynamics that result in improvement in coordination over time. Decisions regarding the amount of service capacity to provide must frequently be made in governmental offices, supermarkets, banks, medical clinics, gas stations, etc. From the perspective of the agency, providing too much service involves excessive cost, whereas providing too little service may cause the waiting line to become excessively long. Excessive waiting time carries with it heavy social costs, and at times costs of lost customers. Therefore, the ultimate goal of the server is to achieve an economic balance between the cost of service and the costs associated with waiting for that service. Our proposed research is aimed at determining the factors that affect congestion, and the conditions that may help or hinder tacit coordination when customers make strategic decisions about joining queues.