Mitali Deka

Bio: Mitali Deka is an academic researcher from Fairleigh Dickinson University. The author has contributed to research in topics: Queue management system & M/G/1 queue. The author has an hindex of 4, co-authored 7 publications receiving 89 citations.

A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy

Abstract: This paper deals with an MX/G/1 unreliable queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion, the server takes sequence of vacations until a batch of new customer arrive. Further concept of the delay time is also introduced. We assume that customers arrive to the system according to a Poisson process with rate . While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. After completion of both phases of service, the server either goes for a vacation with probability p(0 ≤ p ≤ 1) or may continue to serve the next unit, if any, with probability q(= 1 – p). Otherwise; it remains in the system until a customer arrives. For this model, we derive queue size distributions at various epochs, busy period distribution, waiting time distribution under the steady-state condition. Next, we derive reliability functi...

An Unreliable Server Retrial Queue with Two Phases of Service and General Retrial Times Under Bernoulli Vacation Schedule

Abstract: This paper deals with the steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with the FCFS (first come, first served) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or serves the next unit, if any, with probability (1 – p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property. We also provide a reliabili...

A Batch Arrival Unreliable Server Bernoulli Vacation Queue with Two Phases of Service and Delayed Repair

Abstract: This paper deals with batch arrival unreliable queue with two phases of service and vacation under Bernoulli vacation schedule, which consist of a breakdown period and a delay period. For this model, we first derive the joint distribution of state of the server and queue size, which is one of the chief objectives of this paper. Secondly, we derive the pgf of the stationary queue size distribution at a departure epoch. Next, we derive the Laplace Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measures and reliability indices of this model

A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

Abstract: This paper deals with the steady state behaviour of an Mx/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with first come, first served (FCFS) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or may serve the next unit, if any, with probability (1 - p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property.

A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy

Abstract: In this paper, we consider a single server feedback retrial queueing system with multiple working vacations and vacation interruption. An arriving customer may balk the system at some particular times. As soon as orbit becomes empty at regular service completion instant, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. After completion of regular service, the unsatisfied customer may rejoin into the orbit to get another service as feedback customer. The normal busy server may get to breakdown and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.

A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy

Abstract: This paper deals with an MX/G/1 unreliable queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion, the server takes sequence of vacations until a batch of new customer arrive. Further concept of the delay time is also introduced. We assume that customers arrive to the system according to a Poisson process with rate . While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. After completion of both phases of service, the server either goes for a vacation with probability p(0 ≤ p ≤ 1) or may continue to serve the next unit, if any, with probability q(= 1 – p). Otherwise; it remains in the system until a customer arrives. For this model, we derive queue size distributions at various epochs, busy period distribution, waiting time distribution under the steady-state condition. Next, we derive reliability functi...

Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers

Abstract: In this investigation, a single server M/M/1/N feedback queueing system with vacation, balking, reneging and retention of reneged customers is analyzed. By considering the mathematical modeling, we derive the steady state probabilities of the number of customers in the system. We obtain important measures of effectiveness of the model by using the stationary distribution, and develop a cost model of the queueing system. Further, a numerical study and a cost profit analysis are carried out.

Analysis of a single server batch arrival unreliable queue with balking and general retrial time

Abstract: This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and reserved time Here we assume that customers arrive according to compound Poisson processes Any arri