Showing papers on "Retrial queue published in 2009"
TL;DR: A general retrial queue with balking and Bernoulli feedback, where the server operates a modified vacation policy, which has potential applications in e-mail system and WWW server is studied.
77 citations
TL;DR: The Markov chain underlying the queueing system and its ergodicity condition is analyzed and the generating functions of the number of customers in the orbit and in the system are obtained along with the marginal distributions of the orbit size when the server is idle, busy or down.
73 citations
TL;DR: In this article, the authors considered an M / M / s queue with balking, reneging and retrials, where the customers who balked at entering the system or reneged on waiting line can join the virtual pool of customers, called orbit and repeat its request after random amount of time.
46 citations
TL;DR: In this article, a batch arrival retrial queue with general retrial times, where the server is subject to starting failures and provides two phases of heterogeneous service to all customers under Bernoulli vacation schedules, is investigated.
45 citations
TL;DR: A batch arrival retrial queue with general retrial times under a modified vacation policy with potential applications in packet-switched networks is considered and some important system characteristics are derived.
41 citations
TL;DR: This paper deals with a multiserver feedback retrial queueing system with finite waiting position and constant retrial rate, analyzed as a quasi-birth-and-death process, and the necessary and sufficient condition for stability of the system is investigated.
39 citations
TL;DR: The primary aim of this analysis is to show the effect of balking, impatience, and buffer size on the steady-state performance measures.
36 citations
TL;DR: This paper deals with the steady state behaviour of an M^X/G/1 retrial queue with an additional second phase of optional service and unreliable server where breakdowns occur randomly at any instant while serving the customers.
30 citations
TL;DR: In this paper, the authors derived analytical solutions for M/M/3/3 and M/m/4/4 retrial queues without technical assumptions under some technical assumptions.
Abstract: This paper studies M/M/$c$/$c$ retrial queues, where $c$ servers are
all identical. In the retrial queues, an arriving customer is served
immediately if it finds an idle server upon arrival, otherwise the
customer tries to enter the system after an exponentially distributed
time independently of other customers. As is well known, it is a
challenging problem to obtain an analytical solution for the stationary
joint distribution of the numbers of retrial customers and busy
servers in the M/M/$c$/$c$ retrial queue especially for $c \ge
3$. Under some technical assumptions, a few analytical solutions have
been presented for $c \ge 3$. This paper derives analytical solutions
for M/M/3/3 and M/M/4/4 retrial queues without such technical
assumptions. Through many numerical examples, we show that the derived
analytical solutions can be computed by a numerically stable
algorithm.
30 citations
TL;DR: The Markov chain underlying the considered queueing system and some performance measures of the system in steady-state are presented and bounds for the distance between the system size distribution of the model and the corresponding model without retrials are given.
30 citations
TL;DR: This paper considers an M/G/1 retrial queue with vacations and derives several stochastic comparison properties in the sense of strong Stochastic ordering and convex ordering and provides simple insensitive bounds for the stationary queue length distribution.
TL;DR: An unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable for streaming multimedia applications is studied.
Abstract: As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.
01 Jan 2009
TL;DR: An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated and the authors obtain the steady-state solutions for both queueing and reliability measures of interest.
Abstract: Received: 24 November 2005 / Revised: 1 April 2008c 2009 Springer Science + Business Media, LLCAbstract An M/G/1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time,two-phase service and server breakdown is investigated in this paper. Customers are allowed to balkand renege at particular times. Assume that the customers who find the server busy are queued inthe orbit in accordance with an FCFS discipline. All customers demand the first “essential” service,whereas only some of them demand the second “optional” service, and the second service is multi-optional. During the service, the server is subject to breakdown and repair. Assume that the retrialtime, the service time, and the repair time of the server are all arbitrarily distributed. By using thesupplementary variables method, the authors obtain the steady-state solutions for both queueing andreliability measures of interest.Key words Balking, breakdowns, retrial queue, two-phase service.
TL;DR: In this article, an M/G/1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated.
Abstract: An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest.
TL;DR: In this paper, a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals is considered.
Abstract: This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.
Journal Article•
TL;DR: In this paper, the steady state behavior of an M/G/1 queueing system with an additional second phase of service and generalized retrial times under constant retrial policy was investigated.
Abstract: This paper deals with steady state behaviour of an M/G/1 queueing system with an additional second phase of service and generalized retrial times under constant retrial policy. We derive the joint distribution of server state and number of customer in the orbit, additional queue size distribution due to retrial times, system size distribution. Further, we derive some system performance measures .This model generalizes both the classical M/G/1 queue with general retrial time and M/G/1 queue with classical waiting line and a second phase of service.
TL;DR: Using matrix-geometric approach, various interesting and important system performance measures are obtained and extensive numerical illustrations are presented to indicate the quantifying nature of the approach to obtain solutions to this queueing system.
Abstract: In this paper, a steady-state Markovian multi-server retrial queueing system with Bernoulli vacation scheduling service is studied. Using matrix-geometric approach, various interesting and important system performance measures are obtained. Further, the probability descriptors like ideal retrial and vain retrial are provided. Finally, extensive numerical illustrations are presented to indicate the quantifying nature of the approach to obtain solutions to this queueing system.
TL;DR: In this paper, the authors consider queuing systems where customers are not allowed to queue; instead of that they make repeated attempts, or retrials, in order to enter service after some time.
TL;DR: It appears that it is the mean batch size (and not the batch size distribution) that has the main effect on the system performance, and geometric retrial times are shown to have an overall better performance compared with two other distributions.
Abstract: We consider a discrete-time Geo^[^X^]/G/1 retrial queue with general retrial times. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for different performance measures. The present model is proved to have a stochastic decomposition law. Hence, a measure of the proximity between the distributions of the system size in the present model and the corresponding one without retrials is derived. A set of numerical results is presented with a focus on the effect of batch arrivals and general retrial times on the system performance. It appears that it is the mean batch size (and not the batch size distribution) that has the main effect on the system performance. Moreover, increasing the mean batch size is shown to have a noticeable effect on the size of the stability region. Finally, geometric retrial times are shown to have an overall better performance compared with two other distributions.
01 Jan 2009
TL;DR: In this paper, the steady state behaviour of an M/G/1 retrial queue with nonpersistent customers and two phases of heterogeneous service and different vacation policies is studied.
Abstract: This paper studies the steady state behaviour of an M/G/1 retrial queue with non-persistent customers and two phases of heterogeneous service and different vacation policies. If the primary call, on arrival finds the server busy, it becomes impatient and leaves the system with probability (1- α ) and with probabilityα , it enters into an orbit. The server provides preliminary first essential service (FES) and followed by second essential service (SES) to primary arriving calls or calls from the retrial group. On completion of SES the server may go for i th (i=1,2,3,…,M) type of vacation with
TL;DR: A single server retrial queue with Bernoulli vacations and a priority queue is studied, and it is shown that the general stochastic decomposition law for M/G/1 vacation models holds for this system too.
Abstract: We study a single server retrial queue with Bernoulli vacations and a priority queue. A customer who finds the server busy upon arrival, either joins the priority queue with probability α, or leaves the service area and enters a retrial group (orbit) with probability α-bar (= 1 − α). Using the supplementary variable technique, we find the joint probability generating function of the number of customers in the priority queue and of the number of customers in the retrial group in a closed form. Also, we find explicit expressions for the mean queue length and the mean waiting time for both queues, and derive steady-state performance measures for the system. We show that the general stochastic decomposition law for M/G/1 vacation models holds for our system too. Some special cases and numerical results are also discussed.
TL;DR: The M^X/G/1 retrial queue with vacations is considered in an energetic interpretation in the sense that the service of a customer requires not only a random time, but also a random amount of energy with arbitrarily probability distribution.
TL;DR: This work considers a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment and shows that the tail of the queue size distribution is asymptotically geometric.
Abstract: We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.
Posted Content•
TL;DR: In this article, the authors considered a single server retrial queue with the server subject to interruptions and classical retrial policy for the access from the orbit to the server, and analyzed the equilibrium distribution of the system and obtained the generating functions of the limiting distribution.
Abstract: We consider a single server retrial queue with the server subject to interruptions and classical retrial policy for the access from the orbit to the server. We analyze the equilibrium distribution of the system and obtain the generating functions of the limiting distribution.
04 Dec 2009
TL;DR: A steady-state analysis is performed of the corresponding continuous-time Markov chain of the M/M/1 queue with constant retrial rate and non-reliable removable server to minimize the longrun average losses given cost structure.
Abstract: The paper is concerned with the optimal control with respect to N-policy of the M/M/1 queue with constant retrial rate and non-reliable removable server. According to the N-policy, the server can start service only when the number of customers in the system reaches level N (N ≥ 1). We perform a steady-state analysis of the corresponding continuous-time Markov chain and calculate optimal threshold level to minimize the longrun average losses given cost structure.
Journal Article•
TL;DR: In this paper, the authors considered a retrial queue with impatient customers, where the repair is not immediate and it starts after a random amount of time and the customer in service can either remain in service position or leave and return.
Abstract: Bulk arrival retrial queue with impatient customers is considered. The server is subject to breakdown and repair. The repair is not immediate and it starts after a random amount of time. While the server is being repaired, the customer in service can either remain in service position or leave and return. If the server is blocked upon the arrival of a batch, then the customers may leave the system without service or enter the orbit to retry for service after a random time. Upon retrial, the customer enters the service if the server is idle; otherwise goes back to the retrial orbit or renege the system. The condition for the system to be stable, analytical results for the queue length distribution and some performance measures are derived. Numerical results are presented.
29 Jul 2009
TL;DR: In this article, the authors considered a state-dependent M/M/c/c + r retrial queue with Bernoulli abandonment and derived analytical solutions for the stationary joint distribution of the queue length in the system and that in the orbit, assuming that the capacity of the system is less than or equal to 4.
Abstract: This paper considers a state-dependent M/M/c/c + r retrial queue with Bernoulli abandonment, where the number of servers is equal to c, the capacity of the buffer is equal to r and that of the virtual waiting room for retrial customers is infinite. We call the virtual waiting room by orbit hereafter. We assume that the arrival and service rates depend on the number of customers in the system (the servers and buffer). Such retrial queues cover conventional M/M/c/c retrial queues without abandonment, as special cases. By a continued fraction approach, we derive analytical solutions for the stationary joint distribution of the queue length in the system and that in the orbit, assuming that the capacity of the system is less than or equal to 4. We also show that our analytical solutions can be numerically computed with any accuracy.
26 Dec 2009
TL;DR: The necessary and sufficient condition for the system stability is obtained and the queue indices of server are derived with the supplementary variable method.
Abstract: This paper considers an M/G/1 retrial queue system with single vacation and server breakdowns. The necessary and sufficient condition for the system stability is obtained. The queue indices of server are also derived with the supplementary variable method. Besides, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.
13 Dec 2009
TL;DR: The Markov chain underlying the considered queueing system and some performance measures of the system in steady-state are presented and a focus on the effect of feedback and balking on the system performance is presented.
Abstract: We consider a discrete-time Geo/G/1 queue with general retrial times, balking customers, feedback, and starting failures of the server. We analyze the Markov chain underlying the considered queueing system and present some performance measures of the system in steady-state. Numerical results are presented with a focus on the effect of feedback and balking on the system performance.
TL;DR: In this article, the stability conditions and the system state probabilities are investigated both in a transient and in a steady state for a queueing system with Poisson arrivals and arbitrarily distributed service times, vacation times, and start-up and close-down times.
Abstract: We consider a queueing system with Poisson arrivals and arbitrarily distributed service times, vacation times, and start-up and close-down times. The model accepts two types of customers—the ordinary and the retrial customers—and the server takes a single vacation each time he becomes free. For such a model the stability conditions and the system state probabilities are investigated both in a transient and in the steady state. Numerical results are finally obtained and used to observe system performance for various values of the parameters.