Optimization of Balking and Reneging Queue with Vacation Interruption underN-Policy

Abstract

This paper analyzes a finite buffer multiple working vacations queue with balking, reneging, and vacation interruption underpolicy. In the working vacation, a customer is served at a lower rate and at the instants of a service completion; if there are at least customers in the queue, the vacation is interrupted and the server switches to regular busy period otherwise continues the vacation. Using Markov process and recursive technique, we derive the stationary system length distributions at arbitrary epoch. Various performance measures and some special models of the system are presented. Cost analysis is carried out using particle swarm optimization and quadratic fit search method. Finally, some numerical results showing the effect of model parameters on key performance measures of the system are presented.

Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers

“…As it has been discussed in Laxmi et al [25], given a 3-point pattern, we can fit a quadratic function by using corresponding functional values that has a unique minimum, x q , for the given objective function Γ(x). The unique optimum x q of the quadratic function agreeing with Γ(x) at 3-point operation (x l , x m , x u ) is given by…”

Transient performance analysis of a single server queuing model with retention of reneging customers

“…He derives the transient solution of the model. Vijaya Laxmi et al [22] study a finite buffer multiple vacation queue with balking, reneging and vacation interruption under N-policy. They further carry out the cost analysis of the model using swarm optimization and quadratic fit research methods.…”

Study of customers' impatience in aGI/M/1/Nqueue with working vacations

“…Vijaya Laxmi, Goswami, and Jyothsna (2013a) have analysed M/ M/1/N queues with balking, reneging and working vacations. These authors have also discussed a finite buffer single server queueing system with balking, reneging, and vacation interruption under N-policy and multiple working vacations (Vijaya Laxmi, Goswami, & Jyothsna, 2013b). A renewal input finite buffer single server queueing system with multiple working vacations and balking has been studied by Vijaya Laxmi and Jyothsna (2013).…”

“…These authors have also discussed a finite buffer single server queueing system with balking, reneging, and vacation interruption under N-policy and multiple working vacations (Vijaya Laxmi, Goswami, & Jyothsna, 2013b). A renewal input finite buffer single server queueing system with multiple working vacations and balking has been studied by Vijaya Laxmi and Jyothsna (2013). However, to the best of our knowledge, there is no literature that considers balking and reneging simultaneously in a renewal input queueing system with working vacations.…”