Transient Analysis of Single Server Queueing System with Glue Periods

Abstract

In this work, we investigate a single server queueing system with glue periods. The arrival stream is governed by a Poisson process, while service times and glue periods are assumed to be exponentially distributed. The glue period is triggered just before the arrival of the customer at the station. During the glue period, customers arriving at the station stick to the station’s queue and will be served during the service period of the station. The glue period is when customers can also make a reservation at a station for service in the subsequent service period of that station. We derive the probability distribution at random points and at departure points and other performance indices such as the average number of customers and the average waiting time in the queue and the system by applying the Laplace Transform technique. The time-dependent performance measures of the system are examined. The related steady-state investigation and key performance measures of the system are likewise exhibited. Finally, we validate our analytical results by some numerical examples and study the impact of parameters on the system’s performance characteristics.