Showing papers by "Kailash C. Madan published in 2014"

A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns

Abstract: We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results.

A batch arrival queue with second optional service and reneging during vacation periods

Abstract: We study a two phase queuing system model where arrivals come to the system in batches of variable size following a compound Poisson process. We consider that service is provided in two phases, the first service is essential and second service is optional. Service becomes unavailable when the server goes for vacation and customers may decide to renege. We treat reneging in this paper when service is unavailable as the server is on vacation. We obtain steady state results in terms of probability generating function. Some special cases are discussed and a numerical illustration is provided. KEY WORDS: Second optional service, Reneging, Server vacation, Steady state queue size distribution MSC: 90B22 RESUMEN Estudiamos un sistema bifasico de colas donde los arribos llegan al sistema en lotes de tamano variable que siguen un proceso compuesto de Poisson. Consideramos que el servicio esta provisto de dos fases, en el primero el servicio es esencial y el segundo el servicio es opcional. El servicio no esta disponible si este sale de vacaciones y los clientes pueden optar por retirarse. Tratamos en este trabajo el retiro cuando el servicio no esta disponible por estar de vacaciones el servidor. Obtenemos un servicio estable en terminos de la funcion generatriz de probabilidad. Algunos casos especiales son discutidos y se brinda una ilustracion numerica

On a single server queue with arrivals in batches of variable size, general service in three fluctuating modes, balking, random breakdowns and a stand-by server during breakdown periods

Abstract: We study a single server queuing system with arrivals in batches of variable size and general service in three fluctuating modes with different mean service rates. It is assumed that just after completion of the previous service or just after completion of repairs or just after arrival of a fresh batch of customers at a time when the system is in an idle state, the service to next customer may start in mode j with probability p j where j 1,2,3 j p . The system is assumed to be subject to random failures with the general repair time distribution. The system is equipped with a stand-by server which operates only during the breakdown periods of the system. We further assume that an arriving batch may balk and leave the system as soon as it arrives or may join the system. The balking rates have been assumed to be different during the working periods or the breakdown periods of the main server. Steady state results for the queue size distribution at a random epoch have been obtained explicitly. Probabilities of the idle state as well as the utilization factor of the system have been found explicitly. Many particular cases of interest are discussed. KEYWORDS: batch arrivals, balking, general service in three fluctuating modes, random breakdowns, repair times, steady state MSC: 90B22 RESUMEN Estudiamos un sistema de colas con un solo servidor con arribos en paquetes de tamano variable y serviciaje general en tres modos fluctuantes con diferentes tasas media de serviciaje. Se asume que justo despues de completar el servicio previo o justamente despues de completar la reparacion o justo despues de llegar un grupo nuevo de clientes en un momento en el que el sistema esta en estado disponible, el servicio del proximo cliente puede comenzar en el modo j con probabilidad j p donde j 1,2,3 Se asume que el sistema esta sujeto a roturas aleatorias con una distribucion general del tiempo de reparacion. El sistema esta equipado con un servidor en espera que opera solamente durante los periodos de parada del sistema. Asumimos ademas que un paquete puede que arribe y deje el sistema tan pronto como llega o uede unirse al sistema. Las tasas de abandono se han sido asumidas diferentes durante los periodos de trabajo o de interrupcion del servidor central. Se han obtenido resultados explicitos sobre el estado estable de la distribucion del tamano de las colas en una epoca aleatoria. Las probabilidades del estado libre asi como el factor de utilizacion del sistema han sido hallados explicitamente Muchos casos particulares de interes son discutidos.