Showing papers by "Kailash C. Madan published in 2015"

On a M[x]/(G1,G2)/1 queue with third-stage optional service and deterministic server vacations

Abstract: We study a single server queueing system with Poisson arrivals in batches of variable size, assuming that customers in a batch are pre-ordered for the purpose of service. The server provides two stages of general heterogeneous service to all customers one by one on the basis of first come, first severed rule. A customer whose two stages of service are complete, may decide to take the third stage optional service with a certain probability or may just leave the system without taking the third stage service. Every time when a customer’s required number of services (two or three as the case may be) is complete, the server has the option to take a vacation with a certain probability or continue staying in the system to serve the other customers. We further assume that whenever the server takes a vacation, it is a vacation of fixed length‘d’. We find steady state probability generating function of number of customers in an explicit form, the steady state probabilities of various states of the system, the average queue size, the average system size, and the average waiting time in the queue as well as the average waiting time in the system.

A single server bulk input queue with random failures and two phase repairs with delay

Abstract: We study a batch arrival single server queueing system, where the server (service channel) provides one by one general service to customers. It is assumed that the service channel goes through random failures from time to time. As the result of a breakdown, the service of a customer in service is suspended, the service channel waits for the repairs to start and this waiting time termed as ‘delay time’ is assumed to be general. Further, the repair process involves two phases of repairs with different general repair time distributions. We derive the queue size distribution as well as mean number of customers in the system at a random epoch under the steady state conditions. In addition, we discuss some particular cases and derive some known results known earlier. KEYWORDS: batch arrivals, single server queue, random time-homogeneous failures, delay time, two-phase repairs, queue size distribution, mean number of customers in the system. RESUMEN Estudiamos el arribo de paquetes a un servidor de colas simple, donde el servidor (canal de servicio) provee de un servicio general a los clientes del tipo uno-a-uno. Se asume que el canal de servicio transita por fallos aleatorios de ocasion en ocasion como resultado de las interrupciones. Como resultado de las interrupciones, el servicio al cliente se suspende, el canal de servicio se pone en espera de la reparacion y el tiempo de espera, llamado tiempo de atraso, se asume como general. Ademas, el proceso de reparacion contiene dos fases de reparacion con diferentes distribuciones de los tiempos de reparacion. Derivamos la distribucion del tamano de la cola asi como el numero medio de clientes en el sistema en un periodo aleatorio bajo condiciones de fijas de estado. Adicionalmente , discutimos algunos casos particulares y derivamos algunos resultados conocidos previamente.