New results in the theory of repeated orders queueing systems

Abstract

The repeated orders queueing system (ROO) permits no waiting or queue in the normal sense. Instead customers who find the service (or device, to use an engineering term) busy make reapplications at random intervals and in random order until their needs are met. Thus a second demand stream supplements the basic first arrival stream. Familiar examples are provided in a telephone communication setting, in particular in the context of a multiaccess computing system. Cohen [3] and Aleksandrov [1] made the first contributions to the theory of ROO. This paper complements their work with a steady-state analysis of system time (waiting time including service of a new arrival), of service idle time, and of system busy period.