Showing papers by "Kailash C. Madan published in 2010"
TL;DR: A single server queue with general service time distribution, random system breakdowns and Bernoulli schedule server vacations where after a service completion, the server may decide to leave the system with probability p, or to continue serving customers with probability 1−p is analysed.
Abstract: We analyse a single server queue with general service time distribution, random system breakdowns and Bernoulli schedule server vacations where after a service completion, the server may decide to leave the system with probability p, or to continue serving customers with probability 1−p. It is assumed that the customers arrive to the system in batches of variable size, but served one by one. If the system breaks down, it enters a repair process immediately. It is assumed that the repair time has general distribution, while the vacation time has exponential distribution. The purpose is to find the steady-state results in explicit and closed form in terms of the probability-generating functions for the number of customers in the queue, the average number of customers and the average waiting time in the queue. Some special cases of interest are discussed and a numerical illustration is provided.
14 citations
TL;DR: In this paper, a single server queue with a second optional service, Bernoulli schedule server vacations, and random system breakdowns was analyzed, where customers arrive to the system in batches of variable size, but served one by one.
Abstract: A single server queue with a second optional service, Bernoulli schedule server vacations, and random system breakdowns was analyzed. It is assumed that customers arrive to the system in batches of variable size, but served one by one. As soon as the first service of a customer is completed, then with probability k he may opt for the second service. After a customer is served, the server may decide to leave the system with probability p, or to continue serving customers with probability 1 - p. If the system breaks down, it enters a repair process immediately. The repair time and the vacation time both are assumed to have general distributions. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers, and the average waiting time in the queue. Some special cases of interest are presented and a numerical illustration is provided.
6 citations