Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: An infinite-capacity M/M/c retrial queue with second optional service (SOS) channel is considered and the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time are determined.
Abstract: We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a free server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a free server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.
9 citations
TL;DR: A Fuzzy Based Threshold Policy (FBTP) is proposed to control the server, substitute for conventional threshold policies and numerical experiments are provided to show that the proposed method is superior to crisp threshold policies.
Abstract: In this paper we deal with a single server retrial queue with vacations. The server serves the customers until the system becomes empty, then it takes a vacation. The system consists of two types of costs. The blocking cost is considered whenever a customer is blocked either because of the server is busy or off. There is also a cost each time the server is turned on. The problem is to find an effective policy for turning on the dormant server. We propose a Fuzzy Based Threshold Policy (FBTP) to control the server, substitute for conventional threshold policies. The FBTP is based on four input parameters, an inference stage and it is tuned up using a stochastic List Based Threshold Accepting (LBTA) algorithm. Simulation models are developed to validate the fuzzy controller. Numerical experiments are provided to show that the proposed method is superior to crisp threshold policies.
9 citations
TL;DR: A priority queueing-inventory problem with two types of customers that represents an accurate enough model of many real-world systems, including wireless sensor networks and system of cognitive radio with energy harvesting and healthcare systems is studied.
Abstract: In this paper, we study a priority queueing-inventory problem with two types of customers. Arrival of customers follows Marked Markovian arrival process and service times have phase-type distribution with parameters depending on the type of customer in service. For service of each type of customer, a certain number of additional items are needed. High priority customers do not have waiting space and so leave the system when on their arrival a priority 1 customer is in service or the number of available additional items is less than the required threshold. Preemptive priority is assumed. Type 2 customers, encountering a busy server or idle with the number of available additional items less than a threshold, go to an orbit of infinite capacity to retry for service. The customers in orbit are non-persistent: if on retrial the server is found to be busy/idle with the number of additional items less than the threshold, this customer abandons the system with certain probability. Such a system represents an accurate enough model of many real-world systems, including wireless sensor networks and system of cognitive radio with energy harvesting and healthcare systems. The probability distribution of the system states is computed, using which several of the characteristics are derived. A detailed numerical study of the system, including the analysis of the influence of the threshold, is performed.
9 citations
TL;DR: This paper uses the maximum entropy principle to find the least biased density function subject to several mean value constraints and performs results for three different service time distributions: 3-stage Erlang, hyperexponential and exponential.
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.
9 citations
18 Nov 2015
TL;DR: In this paper, the retrial queueing system of MMPP|M|1 type is studied by means of the second order asymptotic analysis method under heavy load condition.
Abstract: In the paper, the retrial queueing system of MMPP|M|1 type is studied by means of the second order asymptotic analysis method under heavy load condition. During the investigation, the theorem about the form of the asymptotic characteristic function of the number of calls in the orbit is formulated and proved. The asymptotic distribution is compared with the exact one obtained by means of numerical algorithm. The conclusion about method application area is made.
9 citations