Double-ended queues with impatience

The effect of “impatient” behaviour is studied primarily in the context of “double-ended” queues where each demands service from the other, typically taxis and passengers. Related models, single queue, and double, with a variety of mechanisms are considered. “Impatience” is to be understood in a wider context than simply becoming tired of waiting: it can arise because the customer, for some reason, runs out of time (inventory and organ transplantation), or because an alternative service becomes available (communication applications). The emphasis in this paper is theoretical but a brief numerical assessment of operational consequences is given.