monita baruah - Academia.edu (original) (raw)
Papers by monita baruah
American Journal of Operations Research, 2013
We study a two stage queuing model where the server provides two stages of service one by one in ... more We study a two stage queuing model where the server provides two stages of service one by one in succession. We consider reneging to occur when the server is unavailable during the system breakdown or vacation periods. We concentrate on deriving the steady state solutions by using supplementary variable technique and calculate the mean queue length and mean waiting time. Further some special cases are also discussed and numerical examples are presented.
Applied Mathematical Sciences, 2013
The present paper aims at studying a queuing model with two stage heterogeneous service where cus... more The present paper aims at studying a queuing model with two stage heterogeneous service where customer arrival is in batches and has a single server providing service in two stages, one after the other in succession. A service is said to be completed when both services are done. Also the server is assumed to go for vacation after completion of the two stages of service with probability p or may continue serving the next customer with probability (1-p). In addition, we have included balking which reflects customer's impatient ...
The purpose of this research is to investigate and analyse some batch arrival queueing systems wi... more The purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without se...
We study a two phase queuing system model where arrivals come to the system in batches of variabl... more 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 bifásico de colas donde los arribos llegan al sistema en lotes de tamaño 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. E...
Applied mathematical sciences, 2013
The present paper aims at studying a queuing model with two stage heterogeneous service where cus... more The present paper aims at studying a queuing model with two stage heterogeneous service where customer arrival is in batches and has a single server providing service in two stages, one after the other in succession. A service is said to be completed when both services are done. Also the server is assumed to go for vacation after completion of the two stages of service with probability p or may continue serving the next customer with probability (1-p). In addition, we have included balking which reflects customer’s impatient behavior where an arriving batch decides not to join the queue for some reasons. We also added optional re-service where a customer may require re-service for any of the services or depart from the system once service is completed. We derive the steady state queue size distribution and discuss some special cases.
Journal of Probability and Statistics
We study the behavior of a batch arrival queuing system equipped with a single server providing g... more 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.
Journal of Mathematics Research, 2012
American Journal of Operations Research, 2013
We study a two stage queuing model where the server provides two stages of service one by one in ... more We study a two stage queuing model where the server provides two stages of service one by one in succession. We consider reneging to occur when the server is unavailable during the system breakdown or vacation periods. We concentrate on deriving the steady state solutions by using supplementary variable technique and calculate the mean queue length and mean waiting time. Further some special cases are also discussed and numerical examples are presented.
Applied Mathematical Sciences, 2013
The present paper aims at studying a queuing model with two stage heterogeneous service where cus... more The present paper aims at studying a queuing model with two stage heterogeneous service where customer arrival is in batches and has a single server providing service in two stages, one after the other in succession. A service is said to be completed when both services are done. Also the server is assumed to go for vacation after completion of the two stages of service with probability p or may continue serving the next customer with probability (1-p). In addition, we have included balking which reflects customer's impatient ...
The purpose of this research is to investigate and analyse some batch arrival queueing systems wi... more The purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without se...
We study a two phase queuing system model where arrivals come to the system in batches of variabl... more 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 bifásico de colas donde los arribos llegan al sistema en lotes de tamaño 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. E...
Applied mathematical sciences, 2013
The present paper aims at studying a queuing model with two stage heterogeneous service where cus... more The present paper aims at studying a queuing model with two stage heterogeneous service where customer arrival is in batches and has a single server providing service in two stages, one after the other in succession. A service is said to be completed when both services are done. Also the server is assumed to go for vacation after completion of the two stages of service with probability p or may continue serving the next customer with probability (1-p). In addition, we have included balking which reflects customer’s impatient behavior where an arriving batch decides not to join the queue for some reasons. We also added optional re-service where a customer may require re-service for any of the services or depart from the system once service is completed. We derive the steady state queue size distribution and discuss some special cases.
Journal of Probability and Statistics
We study the behavior of a batch arrival queuing system equipped with a single server providing g... more 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.
Journal of Mathematics Research, 2012