Queues with Scheduled Arrivals: A Correction, Simplification and Extension

Abstract

Summary Customers are scheduled to arrive at a queue during equal time intervals but they may be late; the lateness distribution is perfectly general. Bulk arrivals with an exponential service time distribution, single arrivals with staged services and single arrivals with a general service time distribution are considered when customers must arrive in the interval for which they were scheduled or not at all. Results given by the author in a previous paper, for single arrivals who may come in a later interval than the one for which they were scheduled and have an exponential service time distribution, are corrected. It is concluded that when customers are scheduled then the equilibrium distribution of queue length is a truncated sum of weighted geometric distributions, irrespective of the number of arrivals per interval, the lateness distribution, the service time distribution and the number of servers.