We consider the busy period in the GI/M/1 queue with multiple exponential vacations. We derive the transform of the joint distribution of the length of a busy period, the number of customers served during the busy period, and the residual interarrival time at the instant the busy period ends.

Consider an M/M/1 queueing system with server vacations where the server is turned oo as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding co...

This paper studies a large class of M/C/l queues with vacations. By means of a probabilistic interpretation we obtain a functional equation which gives a unified approach to derive time-dependent results for the workload distribution. We also discuss application of our result to a number vacation models.

We derive the waiting time distribution in a GI/M/1 queueing system with dependence between the service time of each customer and the subsequent interarrival times. In addition, the server takes exponentially distributed vacations when there are no customers left to serve in the queue.

this paper studies an m/g/1 repairable queueing system with multiple vacations and n-policy, in which the service station is subject to occasional random breakdowns. when the service station breaks down, it is repaired by a repair facility. moreover, the repair facility may fail during the repair period of the service station. the failed repair facility resumes repair after completion of its re...

While vacation processes are considered to be ordinary behavior for servers, the study of queueing networks with server vacations is limited, interesting, and challenging. In this paper, we provide a unified and effective method of functional analysis for the study of a supermarket model with server multiple vacations. Firstly, we analyze a supermarket model of N identical servers with server m...

In this paper we present a detailed analysis of queueing models with vacations and impatient customers, where the source of impatience is the absence of the server. Instead of the standard assumption that customers perform independent abandonments, we consider situations where customers abandon the system simultaneously. This is, for example, the case in remote systems where customers may decid...