Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
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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 considers a c-server queuing model in which customers arrive according to a batch Markovian arrival process (BMAP) and the steady state analysis of the model is performed by exploiting the structure of the coefficient matrices.
Abstract: In this paper, we consider a c-server queuing model in which customers arrive according to a batch Markovian arrival process (BMAP). These customers are served in groups of varying sizes ranging from a predetermined value L through a maximum size, K. The service times are exponentially distributed. Any customer not entering into service immediately orbit in an infinite space. These orbiting customers compete for service by sending out signals that are exponentially distributed with parameter t. Under a full access policy freed servers offer services to orbiting customers in groups of varying sizes. This multi-server retrial queue under the full access policy is a QBD process and the steady state analysis of the model is performed by exploiting the structure of the coefficient matrices. Some interesting numerical examples are discussed.
41 citations
TL;DR: A stochastic decomposition law is derived from the Markov chain underlying the considered queueing system and the concept of generalized service time is introduced and a recursive procedure is developed to obtain the steady-state distributions of the orbit and system size.
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.
40 citations
TL;DR: A stability analysis of a multiserver retrial GI/G/m queue with renewal input of primary customers, interarrival time τ with rate $\lambda=1/\mathsf{E}\tau$ , service time S, and exponential retrial times of customers blocked in the orbit is considered.
Abstract: We consider a multiserver retrial GI/G/m queue with renewal input of primary customers, interarrival time ? with rate $\lambda=1/\mathsf{E}\tau$ , service time S, and exponential retrial times of customers blocked in the orbit. In the model, an arriving primary customer enters the system and gets a service immediately if there is an empty server, otherwise (if all m servers are busy) he joins the orbit and attempts to enter the system after an exponentially distributed time. Exploiting the regenerative structure of the (non-Markovian) stochastic process representing the total number of customers in the system (in service and in orbit), we determine stability conditions of the system and some of its variations. More precisely, we consider a discrete-time process embedded at the input instants and prove that if $\rho=:\lambda\mathsf{E}S and $\mathsf{P}(\tau>S)>0$ , then the regeneration period is aperiodic with a finite mean. Consequently, this queue has a stationary distribution under the same conditions as a standard multiserver queue GI/G/m with infinite buffer. To establish this result, we apply a renewal technique and a characterization of the limiting behavior of the forward renewal time in the (renewal) process of regenerations. The key step in the proof is to show that the service discipline is asymptotically work-conserving as the orbit size increases. Included are extensions of this stability analysis to continuous-time processes, a retrial system with impatient customers, a system with a general retrial rate, and a system with finite buffer for waiting primary customers. We also consider the regenerative structure of a multi-dimensional Markov process describing the system.
40 citations
TL;DR: It is proved that the M/G/1 retrial queue with starting failures can be approximated by its discrete-time counterpart and two stochastic decomposition laws are given.
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.
40 citations