Social Cost of Deviation: New and Old Results onOptimal Customer Behavior in Queues

We revisit some of the classic optimization problems in single- and multi-server queueing systems. We look at these problems as strategic games, using the concept of social cost of deviation (SCoD), which is the extra cost associated with a customer who deviates from the socially prescribed strategy. In particular, we show that a necessary condition for a symmetric profile to be socially optimal is that any deviation from it, if done by a single customer, is suboptimal; that is, the corresponding SCoD is nonnegative. We exemplify this by characterizing the socially optimal strategies for unobservable and observable “to queue or not to queue” problems and for multi-server selection problems. We then use the SCoD concept to derive the symmetric socially optimal strategy in a two-person game of strategic timing of arrival. Furthermore, we show that this strategy is also the symmetric Nash equilibrium strategy if the service regime is of random order with preemption.