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: In this paper, the effect of retrial times on the behavior of a single server retrial queue is investigated and the authors derive monotonicity properties of several system performance measures of interest.
Abstract: A single server retrial queue is a queueing system consisting of a primary queue with finite capacity, an orbit and a server. Customers can arrive at the primary queue either from outside the system or from the orbit. If the primary queue is full, an arriving customer joins the orbit and conducts a retrial later. Otherwise, he enters the primary queue, waits for service and then leaves the system after service completion. We investigate the effect of retrial times on the behavior of the system. In particular, we assume that the retrial time distributions are phase type and introduce a new relation, which we call K-dominance (short for Kalmykov), on these distributions. Longer retrial times with respect to this K-dominance are shown to result in a more congested system in the stochastic sense. From these results, we derive monotonicity properties of several system performance measures of interest.
20 citations
TL;DR: This paper considers an unreliable single server retrial queue accepting two types of customers, with negative arrivals, preemptive resume priorities and vacations, and proves that the model satisfies the stochastic decomposition property.
Abstract: In this paper we consider an unreliable single server retrial queue accepting two types of customers, with negative arrivals, preemptive resume priorities and vacations. A distinguishing feature of the model is that the rates of the Poisson arrival process depends on the server state. For this model we investigate the stability conditions and the joint queue length distribution in steady state. We also prove that our model satisfies the stochastic decomposition property. Transient, as well as steady state solutions for reliability measures are obtained. Finally, numerical results demonstrate the typical features of the model under consideration.
20 citations
TL;DR: In this paper, mean value analysis is applied to retrial queues and adapted to obtain mean performance measures in more advanced M/G/1-type retrial queuing models.
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.
20 citations
TL;DR: In this paper, a single server retrial queueing system with working vacations is considered, where the regular busy server is subjected to breakdown due to the arrival of negative customers, and the server goes for a working vacation when the orbit becomes empty at the time of service completion for a positive customer.
20 citations
TL;DR: The dependencies of the basic performance measures of the system on the capacity of the pool and the threshold are obtained and numerical results are presented.
Abstract: A single-server retrial queue with a MAP flow, PH service times and a pool of finite capacity for accumulation of the customers and their group service is considered. Service to the next group is not provided until the number of customers in the pool will reach a certain predefined threshold value. The service time of a group depends on its size and it is less than the sum of the individual service times. The dependencies of the basic performance measures of the system on the capacity of the pool and the threshold are obtained. Numerical results are presented.
20 citations