Showing papers on "Retrial queue published in 2006"

A bibliographical guide to the analysis of retrial queues through matrix analytic techniques

Abstract: This paper provides a bibliographical guide to researchers who are interested in the analysis of retrial queues through matrix analytic methods. It includes an author index and a subject index of research papers written in English and published in journals or collective publications, as well as some papers accepted for a forthcoming publication.

A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs

Abstract: In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov chain of M/G/1 type to provide the stationary performance measures of the system, for example, the stationary availability, failure frequency and queue length. Furthermore, we use the RG-factorization of a level-dependent Markov renewal process of M/G/1 type to express the Laplace transform of the distribution of a first passage time such as the reliability function and the busy period.

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

Abstract: This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

A Discrete-Time Geo/G/1 retrial queue with the server subject to starting failures

Abstract: This paper studies a discrete-time Geo/G/1 retrial queue where the server is subject to starting failures. We analyse the Markov chain underlying the regarded queueing system and present some performance measures of the system in steady-state. Then, we give two stochastic decomposition laws and find a measure of the proximity between the system size distributions of our model and the corresponding model without retrials. We also develop a procedure for calculating the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle, busy or down. Besides, we prove that the M/G/1 retrial queue with starting failures can be approximated by its discrete-time counterpart. Finally, some numerical examples show the influence of the parameters on several performance characteristics.

Tail asymptotics for the queue length in an M/G/1 retrial queue

Abstract: In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue.

A Discrete-Time Retrial Queue with Unreliable Server and General Server Lifetime

Abstract: Proceedings of the Seminar on Stability Problems for Stochastic Models, Pamplona, Spain, 2003, Part II.

Waiting‐time probabilities in the M/G/1 retrial queue

Abstract: This paper deals with the difficult problem of calculating the waiting-time probabilities in the M/G/1 queue with retrials. The waiting-time distribution is approximated by a gamma distribution by matching the first two moments. Numerical results indicate that this approximation performs satisfactory for practical purposes.

Mean value analysis of single server retrial queues

Abstract: Mean value analysis is an elegant tool for determining mean performance measures in queueing models. In this paper we show how mean value analysis can be applied to retrial queues. First, we illustrate the technique for the standard M/G/1 retrial queue with exponential retrial times. After that we show how the relations can be adapted to obtain mean performance measures in more advanced M/G/1-type retrial queues.

Geo/G/1 retrial queue with 2nd optional service

Abstract: We consider a discrete-time Geo/G/1 retrial queue in which all the arriving customers demand a first essential service whereas only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and derive a stochastic decomposition law. We also develop a recursive procedure for computing the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle and busy with an essential or optional service. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

On the single-server retrial queue

Abstract: In this work, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Using the decomposition property of M/G/1 retrial queues with breakdowns that holds under exponential assumption for retrial times as an approximation in the non-exponential case, we consider an approximate solution for the steady-state queue size distribution.

Multiserver queue with addressed retrials

Abstract: This paper presents a multiserver retrial queueing system with servers kept apart, thereby rendering it impossible for one to know the status (idle/busy) of the others. Customers proceeding to one channel will have to go to orbit if the server in it is busy and retry after some time to some channel, not necessarily the one already tried. Each orbital customer, independently of others, chooses the server randomly according to some specified probability distribution. Further this distribution is identical for all customers. We assume that the same ‘orbit’ is used by all retrial customers, between repeated attempts, to access the servers. We derive the system state probability distribution under Poisson arrival process of external customers, exponentially distributed service times and linear retrial rates to access the servers. Several system state characteristics are obtained and numerical illustrations provided.

An M/G/1 retrial queue with second multi-optional service, feedback and unreliable server

Abstract: An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.

On bulk-service MAP/PHL,N/1/N G-Queues with repeated attempts

Abstract: We consider a retrial queue with a finite buffer of size N, with arrivals of ordinary units and of negative units (which cancel one ordinary unit), both assumed to be Markovian arrival processes The service requirements are of phase type In addition, a PHL,N bulk service discipline is assumed This means that the units are served in groups of size at least L, where 1≤ L≤ N If at the completion of a service fewer than L units are present at the buffer, the server switches off and waits until the buffer length reaches the threshold L Then it switches on and initiates service for such a group of units On the contrary, if at the completion of a service L or more units are present at the buffer, all units enter service as a group Units arriving when the buffer is full are not lost, but they join a group of unsatisfied units called “orbit” Our interest is in the continuous-time Markov chain describing the state of the queue at arbitrary times, which constitutes a level dependent quasi-birth-and-death process We start by analyzing a simplified version of our queueing model, which is amenable to numerical calculation and is based on spatially homogeneous quasi-birth-and-death processes This leads to modified matrix-geometric formulas that reveal the basic qualitative properties of our algorithmic approach for computing performance measures

Algorithmic analysis of theMAP/PH/1 retrial queue

Abstract: In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.

An m/g/1 retrial queue with second multi-optional service, feedback and unreliable server

Abstract: 有二阶段的服务和反馈的一个 M/G/1 再审队列在这篇论文被学习，在服务者在服务期间服从于开始的失败和故障的地方。Primarycustomers 根据泊松进程得到系统在里面，并且如果服务器在到达之上是可得到的，他们将立即收到服务。否则，他们将进入一条再审轨道并且根据 first-come-first-served (FCFS ) 在轨道被排队纪律。Customersare 允许在特别时间畏缩不前并且背信。所有顾客要求第一种“必要”的服务，而仅仅他们的一些要求第二种“多可选”的服务。再审时间，服务时间和服务者的修理时间都是任意地分布式的，这被假定。为系统稳定性的 Thenecessary 和足够的状况被导出。用一个增补可变方法，一些排队和系统的可靠性措施的不变的解决方案被获得。

A maximum entropy approach for the busy period of the M/G/1 retrial queue

Abstract: This paper concerns the busy period of a single server queueing model with exponentially distributed repeated attempts. Several authors have analyzed the structure of the busy period in terms of the Laplace transform but, the information about the density function is limited to first and second order moments. We use the maximum entropy principle to find the least biased density function subject to several mean value constraints. We perform results for three different service time distributions: 3-stage Erlang, hyperexponential and exponential. Also a numerical comparative analysis between the exact Laplace transform and the corresponding maximum entropy density is presented.

Monotonicity properties in various retrial queues and their applications

Abstract: We consider several multi-server retrial queueing models with exponential retrial times that arise in the literature of retrial queues. The effect of retrial rates on the behavior of the queue length process is investigated via sample path approach. We show that the number of customers in orbit and in the system as a whole are monotonically changed if the retrial rates in one system are bounded by the rates in second one. The monotonicity results are applied to show the convergence of generalized truncated systems that have been widely used for approximating the stationary queue length distribution in retrial queues.

Estimators of the retrial rate in m/g/1 retrial queues

Abstract: In this article we analyze the M/G/1 retrial queue from a statistical viewpoint. Assuming that retrials are exponentially distributed we focus on the estimation of the retrial parameter for constant and non-constant retrial policies, including the non-ergodic case. We consider different estimators and compare their asymptotic variances. We test numerically the accuracy of the proposed estimators.

An m2/g2/1 retrial queue with priority customers, 2 nd optional service and linear retrial policy

Abstract: We analyze an M2/G2/1 retrial queuing system with two types of customers and linear retrial policy. If any arriving customer finds the server idle, then it begins his service immediately. Blocked customers from the first flow are queued in order to be served; whereas blocked customers from the second flow leave the service area, but after some random amount of time they repeat an attempt to get service. After essential service completion, a customer either may abandon the system forever or may immediately ask for a second service. The essential and optional service times are arbitrarily and exponentially distributed respectively. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime.

Stochastic analysis of controlled retrial queues with heterogeneous servers and constant retrial rate 1

Abstract: In this paper we analyse a controlled retrial queue with two exponential heterogeneous servers in which the time between two successive repeated attempts is independent of the number of customers applying for the service. The customers upon arrival are queued in the orbit or enters service area according to the control policy. This system is analysed as controlled quasi-birth-and-death (QBD) process. It is showed that the optimal control policy is of threshold and monotone type. We propose the value iteration algorithm for the calculation of optimal threshold levels and perform the steady-state analysis using matrix-geometric approach. The main performance characteristics are calculated for the system under optimal threshold policy (OTP) and compared with the same characteristics for the model under scheduling threshold policy (STP) and other heuristic policies, e.g. the usage of the Fastest Free Server (FFS) or Random Server Selection (RSS).