QUEUES WITH ADVANCED RESERVATIONS: AN INFINITE-SERVER PROXY FOR THE BOOKINGS DIARY

Abstract

Queues with advanced reservations are endemic in the real world. In such a queue, the 'arrival' process is an incoming stream of customer 'booking requests', rather than actual customers requiring immediate service. We consider a model with a Poisson booking request process with rate λ. Associated with each request is a pair of independent random variables (Ri, Si) constituting a request for service over a period Si, starting at a time Ri into the future. Our interest is in the probability that a customer will be rejected due to capacity constraints. We present a simulation of a finite-capacity queue in which we record the proportion of rejected customers, and then move to an analysis of a q..