Calculation of delay characteristics for multiserver queues with constant service times

Abstract

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.Editor: Artalejo

An All Geometric Discrete-Time Multiserver Queueing System

“…Discrete-time multiserver queueing systems have received considerable attention in the past in several settings [5,6,7,8,13]. Specifically, [13] handles a multiserver queueing system with priorities.…”

“…Specifically, [13] handles a multiserver queueing system with priorities. Multiserver queueing systems with batch arrivals are considered in [5,6] for geometric, respectively deterministic service times, while [7,8] deal with multiserver systems with general independent arrivals and geometric and constant service times. These papers all have in common that the number of servers present in the system is constant.…”

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