Showing papers by "Kailash C. Madan published in 2003"

An M/G/1 queue with second optional service with general service time distribution

Abstract: We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate A (> 0), all demand the first 'essential' service, whereas only some of them demand the second 'optional' service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B 1 (v) and that of the second optional service with general (arbitrary) distribution with distribution function B 2 (v). The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly.

Steady state analysis of two MX/Ma, b/1 queue models with random breakdowns

Abstract: We study two models of a single server bulk queueing system M X /M a,b /1 in which the service facility suffers time homogeneous random breakdowns from time to time. In model A, the repair times are assumed to be exponential and in model B, the repair times are assumed to be detrministic. We obtain the probability generating functions of the queue size and the system size, the average queue size, the average system size and the average waiting time in the queue and the system. Some particular cases of interest are discussed and some known results are derived as special cases. A numerical example is also provided.

On two parallel servers with random breakdowns

Abstract: We study a queueing system with two parallel servers subject to random breakdowns. The arrivals are assumed to be Poisson, one by one, and the service times of the two channels are identical exponential. Either channel can fail any time, independently of the other and either channel may fail not only while it is working but it may even fail also when it is idle. The system possesses two independent repair facilities, one for each channel. The failure times as well as the repair times of the service channels are identical exponential. We obtain time-dependent results in terms of the system size distribution as well as the probabilities for various states of the servers. Corresponding steady state results are derived and a particular case is discussed.

Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

Abstract: We examine an M/D/2 queue with Bernoulli schedules and a single vacation policy. We have assumed Poisson arrivals waiting in a single queue and two parallel servers who provide identical deterministic service to customers on first -come, first-served basis. We consider two models; in one we assume that after completion of a service both servers can take a vacation while in the other we assume that only one may take a vacation. The vacation periods in both models are assumed to be exponential. We obtain steady state probability generating functions of system size for various states of the servers.