Title: Queueing Games Speaker: Moshe Haviv Affiliation: Department of Statistics The Hebrew University of Jerusalem Abstract: The whereabouts of customers in a queueing system interact. If more customers join the queue, one's waiting time may increase, up to a level that one may prefer not to join at all. This logic applies of course to the other customers, but if all stay out one may better join. So who are those to join and who are those not to join? Also, if too many packets are routed along one path, then an individual packet might be better assigned to some other path. But who will select this path, the individual himself or a central planner? Their objectives may not coincide: a self optimizer customer ignore the externalities that may results from any of his decisions and which effect others. For another decision problem, suppose acquiring the information which line or path is shorter, comes with some cost. Clearly, one has an incentive to pay for this information. Yet, one's incentive goes down with the fraction of those who acquire the information as the more informed customers are, the more they will tend to make the two lines even anyhow. The talk will deal with these and similar decision models. Many decision problems in queues can be modeled as non-cooperative games. In such games, players (or in our case, customers, service providers or routers) have to take actions. While selecting their actions they are not fully informed on the actions taken by others. In fact, in many situations, decision making is down simultaneously. Of course, each player wants to optimize his gains (utility) but one's optimal action is a function of what others are doing. Here comes the solution concept of {\it Nash equilibrium}. It replaces the concept of {\it optimal solution} which is used when a single decision maker is involved. Most of the talk will be devoted to customers as decision makers who take actions as time progresses. Examples for that are to join or not to join the queue, which line to join, to pay or not to pay a premium in order to get higher priority level, or to renege or not from a queue when waiting costs start to be too high. Their decisions will be compared with those of a central planer who tries to maximize a social objective. The talk is based on a 2003 book co-authored with Refael Hassin bearing the same title {\it To Queue or not to Queue: Equilibrium Behavior in Queueing Systems}, and published by Kluwer's International Series.