A Retrieval Queueing Model With Feedback

A multi-server retrial queuing model with feedback is considered in this paper.Input flow of calls is modeled using a Markovian Arrival Process (M AP) and the service time is assumed to follow an exponential distribution. An arriving call enters into service should there be a free server. Otherwise, in accordance to Bernoulli trials, the call will enter into an infinite orbit (referred to as a retrial orbit) to retry along with other calls to get into service or will leave the system forever. After obtaining a service each call, independent of the others, will either enter into a finite orbit (referred to as a feedback orbit) for another service or leave the system forever. The decision to enter into the feedback orbit or not is done according to another Bernoulli trial. Calls from these two buffers will compete with the main source of calls based on signals received from two independent Poisson processes.The rates of these processes depend on the phase of the M AP. The steady-state analysis of the model is carried out and illustrative numerical examples including economical aspects are presented

Transient behavior of M[x]/G/1 Retrial Queueing Model with Non Persistent Customers, Random break down, Delaying Repair and Bernoulli Vacation

In this paper we consider a single server batch arrival non-Markovian retrial queueing model with non persistent customers. In accordance with Poisson process, customers arrive in batches with arrival rate  and are served one by one with first come first served basis. The server is being considered as unreliable that it may encounter break down at any time. In order to resume its service the server has to be sent for repair, but the repair does not start immediately so that there is a waiting time before the repair process. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p. More details can be found in the full paper. Key words: Batch size, break down, delay time, transient solution, steady solution,  reliability indices

(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

Bulk queueing system with starting failure and single vacation

To analyze an M^([X])/G(a,b)/1 queue with starting failure, repair and single vacation. This type of queueing model has a wide range of applications in production/manufacturing systems. Important performance measures and stability conditions are obtained. Further, we discuss some particular cases. Finally, numerical results of the proposed model have been derived

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

A Discrete-Time G

This paper is concerned with a discrete-time Geo/G/1 retrial queueing model with J vacations and two types of breakdowns. If the orbit is empty, the server takes at most J vacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system

Non Markovian Queue with Two Types service Optional Re-service and General Vacation Distribution

We consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with probability 1 -θ: The re-service periods and vacation periods are assumed to be general. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived and thus we deduce the steady state results. We obtain the average queue size and average waiting time. Some system performance measures and numerical illustrations are discussed

Approximate Analysis of an Unreliable M/M/2 Retrial Queue

This thesis considers the performance evaluation of an M/M/2 retrial queue for which both servers are subject to active and idle breakdowns. Customers may abandon service requests if they are blocked from service upon arrival, or if their service is interrupted by a server failure. Customers choosing to remain in the system enter a retrial orbit for a random amount of time before attempting to re-access an available server. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure. Interfailure times, repair times and times between retrials are exponentially distributed, and all processes are assumed to be mutually independent. Modeling the number of customers in the orbit and status of the servers as a continuous-time Markov chain, we employ a phase-merging algorithm to approximately analyze the limiting behavior. Subsequently, we derive approximate expressions for several congestion and delay measures. Using a benchmark simulation model, we assess the accuracy of the approximations and show that, when the algorithm assumptions are met, the approximation procedure yields favorable results. However, as the rate of abandonment for blocked arrivals decreases, the performance declines while the results are insensitive to the rate of abandonment of customers preempted by a server failure

Asymptotical analysis of queueing system MMPP|M|N with feedback

Рассматривается система массового обслуживания с N обслуживающими приборами с обратной связью и орбитой. Считается, что ограничений на количество заявок, поступающих на орбиту, нет. Входящий поток является марковски модулированным пуассоновским (MMPP). Методом асимптотического анализа находятся распределения вероятностей числа занятых приборов в системе и числа заявок на орбите