Standard and retrial queueing systems: a comparative analysis

We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.)leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, ossess unique distinguished features. We also mention some open problems.We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.)leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, ossess unique distinguished features. We also mention some open problems

Insensitive Bounds for the Stationary Distribution of a Single Server Retrial Queue with Server Subject to Active Breakdowns

The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results

Asymptotic analysis of highly reliable retrial queueing systems

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 2000.Thesis (Master's) -- Bilkent University, 2000.Includes bibliographical references leaves 66-71The thesis is concerned with the asymptotic analysis of the time of first loss of a customer and the flow of lost customers in some types of Markov retrial queueing systems with flnite buffer. A retrial queueing system is characterized by the following feature: an arriving customer finding all of the servers busy must leave the service area and join a special buffer. After this it may re-apply for service after some random time. If the buffer is full the customer is lost. The analysis of the time of first loss of a customer is based on the method of so-called S — sets and the results about the asymptotic behavior of the first exit time from the fixed subset of states of semi-Markov process of a special structure (so-called monotone structure). Single server retrial queueing systems [M IM IlIm with retrials) as well as multiple server retrial queueing systems {M IM fsfm with retrials) are analyzed in cases of fast service and both fast service and fast retrials. Exponential approximation for the time of first loss and Poisson approximation for the flow of lost customers are proved for all of the considered cases.Kurtuluş, MüminM.S

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

Performance Modeling of Finite-Source Cognitive Radio Networks

This paper deals with performance modeling aspects of radio frequency licensing. The utilization of mobile cellular networks can be increased by the idea of the cognitive radio. Licensed users (Primary Users - PUs) and normál users (Secondary Users - SUs) are considered. The main idea is, that the SUs are able to access to the available non-licensed radio frequencies. A finite-source retrial queueing model with two non independent frequency bands (considered as service units) is proposed for the performance evaluation of the system. A service unit with a priority queue and another service unit with an orbit are assigned to the PUs and SUs, respectively. The users are classified into two classes: the PUs have got a licensed frequency, while the SUs have got a frequency band, too but it suffers from the overloading. We assume that during the service of the non-overloaded band the PUs have preemptive priority over SUs. The involved inter-event times are supposed to be independent and exponentially distributed random variables. The novelty of this work lies in the fact that we consider the effect of retrial phenomenon of SUs in performance modeling of radio frequency licensing by using a finite-source queueing model which takes the unreliability of radio transmission into account for the first time. In the literature, most work studied the performance of cognitive radio networks under a mixed spectrum environment of licensed and unlicensed bands where the blocked SUs and the preempted SUs are forced to leave the system forever when there are no idle channels in the system. But in practical situation, the blocked SUs and the preempted SUs may do not leave the system forever and try to continue their services after random amount of time. By the help of an appropriate continuous time Markov chain using MOSEL (MOdeling Specification and Evaluation Language) tool several numerical examples are provided showing the effects of different input parameters on the main performance measures of the cognitive radio networks. Our primary focus is to determine an optimal number of SUs, where at the secondary band the gained utilization, that is when switching to the cognitive radio, has a maximum value

Unreliable Retrial Queues in a Random Environment

This dissertation investigates stability conditions and approximate steady-state performance measures for unreliable, single-server retrial queues operating in a randomly evolving environment. In such systems, arriving customers that find the server busy or failed join a retrial queue from which they attempt to regain access to the server at random intervals. Such models are useful for the performance evaluation of communications and computer networks which are characterized by time-varying arrival, service and failure rates. To model this time-varying behavior, we study systems whose parameters are modulated by a finite Markov process. Two distinct cases are analyzed. The first considers systems with Markov-modulated arrival, service, retrial, failure and repair rates assuming all interevent and service times are exponentially distributed. The joint process of the orbit size, environment state, and server status is shown to be a tri-layered, level-dependent quasi-birth-and-death (LDQBD) process, and we provide a necessary and sufficient condition for the positive recurrence of LDQBDs using classical techniques. Moreover, we apply efficient numerical algorithms, designed to exploit the matrix-geometric structure of the model, to compute the approximate steady-state orbit size distribution and mean congestion and delay measures. The second case assumes that customers bring generally distributed service requirements while all other processes are identical to the first case. We show that the joint process of orbit size, environment state and server status is a level-dependent, M/G/1-type stochastic process. By employing regenerative theory, and exploiting the M/G/1-type structure, we derive a necessary and sufficient condition for stability of the system. Finally, for the exponential model, we illustrate how the main results may be used to simultaneously select mean time customers spend in orbit, subject to bound and stability constraints