A Multiserver Poisson Queue with a General Startup Time Under N-Policy

Abstract

This paper deals with the steady state behaviour of an M⁄M⁄c queueing system with a general startup time under N-policy, where the system is turned off as soon as the system becomes empty and turned on again when the queue size becomes ‘ N’. The service of the first customer in each busy period is always preceded by a random startup time (during which no proper work is done) to gearup the system. We place our emphasis on understanding the operational characteristic of the queueing system and derive the probability generating functions of the queue size distribution and joint distribution of the number of arrivals and startup time. Also, we provide appropriate interpretation of the queue size distribution and other performance measures. Finally, we verify some results of M⁄M⁄1 queueing system with general startup time under N-policy.

Analysis of a Multiserver Queue with Setup Times

“…In contrast, we have been able to find only one paper by Borthakur and Choudhury [7] concerning a multiserver queue with setup times. In [7] the authors consider a system where all the servers are simultaneously turned off as soon as the system becomes empty. The servers remain inactive until N ≥ c customers are accumulated.…”

“…Then a start up period begins in order to make the system operative. Our paper also deals with a multiserver queue with setup times but the operating rules governing our model differ substantially of those considered in [7].…”

Equilibrium customer strategies in a single server Markovian queue with setup times

“…In such models once a server is reactivated, a generally random time is required for setup before it can begin serving customers. Bischof, Choudhury, He and Jewkes [4,8,9,16] and the references therein consider various single server systems with setup times, while Borthakur, Choudhury, Artalejo et al [3,5] deal with some multiserver models. In particular, the performance evaluation for an M/M/1 queue with server setups has been carried in [1, p. 51-54], and its multiserver counterpart in [3].…”