Prior assessments for prediction in queues

Queuing theory models systems which provide services to customers whose arrival times and service requirements are random. The main quantities of interest in a queuing system are not usually the parameters governing the queue but observable quantities such as the number of customers in the queue or the time that a customer spends in the system. The Bayesian approach is thus ideally suited to handle the inferential aims for a queuing situation. In this paper the prediction of several quantities in an M/M/1 queue in equilibrium is addressed. Special care is devoted to the selection of an appropriate family of prior distributions and a brand-new family is introduced to generalize the natural conjugate distribution: the Gauss hypergeometric family of distributions. The results are illustrated with a real life example.