Title:

Equilibrium arrival times to a congested queue

Abstract:

Suppose customers need to choose when to arrive to a congested queue with some desired service at the end, provided by a single server that operates only during a certain time interval. Naturally, customers want to avoid congestion and the costs associated with it. However, the choices made by individual customers have consequences on the entire system.

Modelling such a situation requires tools from both Queueing Theory and Game Theory. I will briefly talk about the overlap between the above two disciplines. I will then present a model where the customers incur not only congestion (waiting) costs but also penalties for their index of arrival. Arriving before other customers is desirable when the value of service decreases with every admitted customer. This may be the case for example when arriving at a concert or a bus with unmarked seats or going to lunch in a busy cafeteria.

I will present the game theoretic analysis of such a queueing system. Specifically, the probability distribution of the arrival process which constitutes a symmetric Nash equilibrium is characterized as a system of functional differential equations and an algorithm for its computation is derived.