P. Vijaya Laxmi

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.

Perishable inventory system with service interruptions, retrial demands and negative customers

In this paper, we consider a continuous review perishable inventory system wherein demands arrive according to the Poisson process, each demanding exactly one unit of inventory item and the life time of each item is assumed to be exponential. The operating policy is (s, S) policy, i.e., whenever the inventory level drops to s, an order for Q(=S - s) items is placed. The ordered items are received after a random time which is distributed as exponential. The service may be interrupted according to the Poisson process in which case it restarts after an exponentially distributed time. The demands that occur during the server breakdown period or stock-out period may turn out to be ordinary or a negative demand and then they enter into the orbit of infinite size. These orbiting demands send out a signal to compete for their demand which is distributed as exponential. The matrix analytic method is used for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results.

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 a Renewal Input Bulk Service Queue with Accessible and Non-Accessible Batches

Abstract In this paper, we consider a single-server infinite-(finite-) buffer bulk-service queues. The interarrival and service times are respectively, arbitrarily and exponentially distributed. The customers are served by a single server in accessible or non-accessible batches of maximum size ‘b’ with a minimum threshold value ‘a’. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state queue length distributions at prearrival and arbitrary epochs. Finally, some numerical results have been presented.

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.

Analysis of state dependent N-policy queue with working vacations

In this paper, we study a finite buffer renewal input N-policy queue with state dependent services and working vacations. The amount of service demanded by a customer is conditioned by the queue length at the moment service is begun for that customer. We provide a recursive algorithm using the supplementary variable technique to compute the stationary queue length distribution of the system. Some queueing models discussed in the literature are derived as special cases. Finally, using some numerical results, we present the parameter effect on various performance measures.

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.