Showing papers on "Retrial queue published in 1995"
TL;DR: Using the method of supplementary variables, formulas are derived for the limiting probability distribution of the single-server retrial queueing system and some major performance measures including system throughput and mean delay.
71 citations
TL;DR: It is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/, and the approximation approaches the exact when the length of the interval tends to zero, and recursive formulas for the steady-state probabilities are developed.
Abstract: In this paper, we study the steady-state queue size distribution of the discrete-timeGeo/G/1 retrial queue. We derive analytic formulas for the probability generating function of the number of customers in the system in steady-state. It is shown that the stochastic decomposition law holds for theGeo/G/1 retrial queue. Recursive formulas for the steady-state probabilities are developed. Computations based on these recursive formulas are numerically stable because the recursions involve only nonnegative terms. Since the regularGeo/G/1 queue is a special case of theGeo/G/1 retrial queue, the recursive formulas can also be used to compute the steady-state queue size distribution of the regularGeo/G/1 queue. Furthermore, it is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/1 retrial queue by dividing the time into small intervals of equal length and the approximation approaches the exact when the length of the interval tends to zero. This relationship allows us to apply the recursive formulas derived in this paper to compute the approximate steady-state queue size distribution of the continuous-timeM/G/1 retrial queue and the regularM/G/1 queue.
68 citations
TL;DR: This paper finds the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and shows that the results are consistent with the known results for a classical retrial queueing system.
Abstract: We consider anM/G/1 priority retrial queueing system with two types of calls which models a telephone switching system and a cellular mobile communication system. In the case that arriving calls are blocked due to the server being busy, type I calls are queued in a priority queue of finite capacityK whereas type II calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form. When λ1=0, it is shown that our results are consistent with the known results for a classical retrial queueing system.
65 citations
TL;DR: This work considers a queueing system where a customer who finds all channels busy must decide either to join the queue or to retry after an exponentially distributed time, and approximates the performance by using the RTA approximation introduced by Wolff and Greenberg.
35 citations
TL;DR: In this paper, a matrix analytical approach is applied to retrial queues with phase type service time distributions and a matrix product form is obtained for the joint stationary distribution of queue length and service phase and a stability condition is derived.
Abstract: A matrix analytical approach is applied to retrial queues with phase type service time distributions. A matrix product form is obtained for the joint stationary distribution of queue length and service phase and a stability condition is derived. A numerical method is derived for obtaining the distribution of the number of retrials per customer and the distribution and moments of the waiting time in orbit. We also consider two extensions: The M/M/1 retrial queue with geometric loss and state dependent M/PH/1 retrial queues.
24 citations
TL;DR: A retrial queue accepting two types of customers with correlated batch arrivals and preemptive resume priorities is studied and the virtual waiting time of an arbitrary ordinary customer in a steady state is analysed.
Abstract: A retrial queue accepting two types of customers with correlated batch arrivals and preemptive resume priorities is studied. The service times are arbitrarily distributed with a different distribution for each type of customer and the server takes a single vacation each time he becomes free. For such a model the state probabilities are obtained both in a transient and in a steady state. Finally, the virtual waiting time of an arbitrary ordinary customer in a steady state is analysed.
24 citations
TL;DR: A new Markovian description of retrial queues is introduced in connection with this problem and a simple asymptotic formula is derived for the variance of the estimator when the interval of observation is long.
Abstract: We consider estimation of the rate of retrials for anM/M/1 repeated orders queueing system with the help of integral estimators. The main problem is connected with the statistical accuracy of the estimator, i.e. with its variance. We derive a simple asymptotic formula for this variance when the interval of observation is long. In connection with this problem we introduce a new Markovian description of retrial queues.
11 citations