Kanithi Jyothsna

Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed.

Impatient customer queue with Bernoulli schedule vacation interruption

Abstract This paper deals with an infinite buffer M/M/1 queue with working vacations and Bernoulli schedule vacation interruption wherein the customers balk with a probability. Whenever the system becomes empty, the server takes a working vacation during which service is provided with a lower rate and if there are customers at a service completion instant, vacation is interrupted and the server resumes a normal working period with probability q or continues the vacation with probability 1 − q . The service times during working vacation and vacation times are assumed to be exponentially distributed. During a working vacation customers may renege due to impatience. The closed form expressions of the steady-state probabilities and the performance measures of the model are obtained using generating functions. Various numerical results are presented to show the effect of the model parameters on the system performance measures.

Analysis of Discrete-Time Single Server Queue with Balking and Multiple Working Vacations

Abstract This paper analyzes a discrete-time single server queueing system with balking and multiple working vacations. The arriving customers balk (that is, do not join the queue) with a probability. The inter-arrival times of customers are assumed to be independent and geometrically distributed. The server works at a different rate rather than completely stopping service during vacations. The service times during a service period, service times during a vacation period and vacation times are assumed to be geometrically distributed. We obtain the closed form expressions for the steady-state probabilities at arbitrary and outside observer’s observation epochs. Computational experiences with a variety of numerical results are discussed in the form of tables and graphs. Moreover, some queueing models discussed in the literature are derived as special cases of our model.

Balking and Reneging Multiple Working Vacations Queue with Heterogeneous Servers

This paper presents the analysis of a renewal input multiple working vacations queue with balking, reneging and heterogeneous servers. Whenever the system becomes empty the second server leaves for a working vacation whereas the first server remains idle in the system. During a working vacation the second server provides service at a slower rate rather than completely stopping service. The steady-state probabilities of the model are obtained using supplementary variable and recursive techniques. Various performance measures of the model such as expected system length, expected balking rate, etc., have been discussed. Finally, some numerical results have been presented to show the effect of model parameters on the system performance measures.

Performance analysis of variant working vacation queue with balking and reneging

This paper studies the effect of balking and reneging in a single server queue under variant working vacation policy. Arriving customers balk (do not join the queue) with a probability and renege (leave the queue after joining) according to exponential distribution. Under the variant vacation policy the server leaves for a working vacation as soon as the system becomes empty. The server takes at most J working vacations until he finds at least one customer in the queue on return from a working vacation. If customers are not found in the queue by the end of Jth vacation, the server remains idle in the system. The system length probabilities are derived using matrix form solution. Some performance measures of the model and cost analysis through quadratic fit search method have been discussed. Finally, the sensitivity analysis is carried out through some numerical experiments.

Optimization of Balking and Reneging Queue with VacationInterruption under -Policy

This paper analyzes a finite buffer multiple working vacations queue with balking, reneging, and vacation interruption under -policy. 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.

An inventory model with negative customers and service interruptions

In this paper, we consider a single server queueing system with inventory wherein customers arrive according to Poisson process. A customer turns out to be an ordinary customer or a negative customer. An ordinary customer, on arrival, joins the queue and a negative customer, on the other hand, does not join the queue but takes away one waiting customer, if any. The inventory is served at an exponential rate to the waiting customers and it is replenished according to (s; S) policy with positive lead time. Due to breakdowns the service process is subjected to interruptions, which follows an exponential distribution and the broken down server is repaired at an exponential rate. Matrix geometric solution is obtained for the steady state probability distribution of the inventory model. Finally, cost analysis is carried out.

Discrete-time renewal input queue with balking and multiple working vacations

This paper analyzes a discrete-time finite buffer GI/Geo/1 queue with multiple working vacations wherein the customers may balk due to impatience. The service times during working vacation and vacation times are assumed to be geometrically distributed. Embedded Markov chain and supplementary variable techniques have been adopted to obtain the steady-state system length distributions at pre-arrival and arbitrary epochs, respectively. Various performance measures of the model and waiting-time distribution are also presented. A variety of numerical results showing the effect of model parameters on key performance measures are demonstrated.

Analysis of a working vacations queue with impatient customers operating under a triadic policy

The objective of this paper is to analyze a finite buffer M/M/2 working vacations queue with balking and reneging wherein the servers operate under a triadic (0,Q,N,M) policy. As soon as the system becomes empty, both the servers leave for working vacations with only one of the two servers being active during the vacation. The service times during the working vacation and the vacation times are assumed to be exponentially distributed. Various performance measures are discussed and cost analysis is carried out using the quadratic fit search method. Finally, using some numerical results we present the parameter effect on the performance measures of the model.

Optimization of Service Rate in a Discrete-Time Impatient Customer Queue Using Particle Swarm Optimization

This paper investigates a discrete-time balking, reneging queue with Bernoulli-schedule vacation interruption. Particle swarm optimization which is a biologically inspired optimization technique mimicking the behavior of birds flocking or fish schooling is implemented to determine the optimum service rate that minimizes the total expected cost function per unit time. A potential application of the considered queueing problem in an inbound email contact center is also presented.