(R1971) Analysis of Feedback Queueing Model with Differentiated Vacations under Classical Retrial Policy

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical interpretation of the results obtained. Finally, the cost is optimized using the parabolic method

Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate.

In present paper we have introduced the concept of differentiated vacations in a retrial queueing model with state dependent arrival rates of customers. The arrival rate of customers is different in various states of the server. The vacation types are differentiated by means of their durations as well as the previous state of the server. In type I vacation, server goes just after providing service to at least one customer whereas in type II, it comes after remaining free for some time. In steady state, we have obtained the system size probabilities and other system performance measures. Finally, sensitivity and cost analysis of the proposed model is also performed. The probability generating function technique, parabolic method and MATLAB is used for the purpose

Study of feedback retrial queueing system with working vacation, setup time, and perfect repair

This manuscript analyses a retrial queueing system with working vacation, interruption, feedback, and setup time with the perfect repair. In the proposed model, the server takes vacation whenever the system gets empty but it still serves the customers at a relatively lower speed. The concept of power saving is included in the model. To save the power the server is turned off immediately on being empty at vacation completion instant. The customer who arrives when the system is turned off activates the server and he has to wait for his turn till the server is turned on. The unreliable server may sometimes fail to activate during setup. It is then sent for repair and repaired server immediately starts serving the waiting customers. Using probability generating function, explicit expressions for system size and different states of server for the model are obtained and results are analyzed graphically using MATLAB software

Non-Markovian Queueing System, Mx/G/1 with Server Breakdown and Repair Times

This paper deals with the steady state behavior of an MX/G/1 queue with breakdown. It assumed that customers arrive to the system in batches of variable size, but serve one by one. The main new assumption in this paper is that the repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average waiting time in the queue

(R1881) Impatient Customers in Queueing System with Optional Vacation Policies and Power Saving Mode

In this manuscript, a queueing system with two optional vacation policies, power-saving mode under reneging and retention of reneged customers in both vacations is analyzed. If the server is free, it chooses either of the vacations, classical vacation or working vacation. During vacations, the customers may get impatient due to delays and may leave the system, but they are retained in the system with some convincing mechanisms. On vacation completion, if the system is empty, the server is turned off to facilitate better utilization of the resources. Some of the operating system characteristics are derived using the probability generating functions technique. The numerical results are graphically represented by using MATLAB software

Batch arrival bulk service queue with unreliable server, second optional service, two different vacations and restricted admissibility policy

This paper is concerned with batch arrival queue with an additional second optional service to a batch of customers with dissimilar service rate where the idea of restricted admissibility of arriving batch of customers is also introduced. The server may take two different vacations (i) Emergency vacation-during service the server may go for vacation to an emergency call and after completion of the vacation, the server continues the remaining service to a batch of customers. (ii) Bernoulli vacation-after completion of first essential or second optional service, the server may take a vacation or may remain in the system to serve the next unit, if any. While the server is functioning with first essential or second optional service, it may break off for a short period of time. As a result of breakdown, a batch of customers, either in first essential or second optional service is interrupted. The service channel will be sent to repair process immediately. The repair process presumed to be general distribution. Here, we assumed that the customers just being served before server breakdown wait for the server to complete its remaining service after the completion of the repair process. We derived the queue size distribution at a random epoch and at a departure epoch under the steady state condition. Moreover, various system performance measures, the mean queue size and the average waiting time in the queue have been obtained explicitly. Some particular cases and special cases are determined. A numerical result is also introduced

Optimum cost analysis of batch service retrial queuing system with server failure, threshold and multiple vacations

The aim of this paper is to analyze the queuing model entitled to cost optimization in bulk arrival and a batch service retrial queuing system with threshold, server failure, non-disruptive service, and multiple vacations. When bulk arrival of customers find the server is busy, then all customers will join in the orbit. On the other hand, if the server is free, then batch service will be provided according to the general bulk service rule. Batch size varies from a minimum of one and a maximum of ‘b’ number of customers. Customers in the orbit seek service one by one through constant retrial policy whenever the server is in idle state. The server may encounter failure during service. If the server fails, then ‘renewal of service station’ will be considered with probability . If there is no server failure with probability in the service completion or after the renewal process and if the orbit is empty, the server then leaves for multiple vacations. The server stays on vacation until the orbit size reaches the value N. For this proposed queuing model, a probability generating function of the orbit size will be obtained by using the supplementary variable technique and various performance measures will be presented with suitable numerical illustrations. A real time application is also discussed for this system. Additionally, a cost effective model is developed for this queuing model

Analysis of an M[X]/G/1 Feedback Retrial Queue with Two Phase Service, Bernoulli Vacation, Delaying Repair and Orbit Search

In this paper, we considered a batch arrival feedback retrial queue with two phase of service under Bernoulli vacation schedule and orbit search. At the arrival epoch of a batch, if the server is busy, under repair or on vacation then the whole batch joins the orbit. Where as if the server is free, then one of the arriving customers starts his service immediately and the rest join the orbit. At the completion epoch of each service, the server either goes for a vacation or may wait for serving the next customer. 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 repair process does not start immediately after a breakdown and there is a delay time for repair to start. After vacation completion, the server searches for the customers in the orbit (i.e. customer in the orbit, if any taken for service immediately) or remains idle. The probability generating function of the number of customers in the system and orbit are found using the supplementary variable technique. The mean numbers of customers in the system/orbit and special cases are analyzed. The effects of various parameters on the performance measure are illustrated numerically. Keywords: Feedback, retrial queue, Bernoulli vacation, delaying repair, orbit searc

Mathematical Analysis of Queue with Phase Service: An Overview

We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent

(R1975) MAP/PH(1), PH(2)/2 Queue with Multiple Vacation, Optional Service, Consultations and Interruptions

Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s waiting time distribution has been examined in more detail during the busy times. The system’s key parameters are assessed, and a few graphs and numerical representations are constructed