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 steady-state behavior of an MX/G/1 retrial queue with the Bernoulli vacation schedule and unreliable server under linear retrial policy is investigated.
Abstract: This article deals with the steady-state behavior of an MX/G/1 retrial queue with the Bernoulli vacation schedule and unreliable server, under linear retrial policy. Breakdowns can occur randomly at any instant while the server is providing service to the customers. Further, the concept of Bernoulli admission mechanism is introduced. This model generalizes both the classical MX/G/1 retrial queue with unreliable server as well as the MX/G/1 retrial queue with the Bernoulli vacation model. The authors carry out an extensive analysis of this model. Namely, the embedded Markov chain, the stationary distribution of the number of units in the orbit, and the state of the server are studied. Some important performance measures and reliability indices of this model are obtained. Finally, numerical illustrations are provided and sensitivity analyses on some of the system parameters are conducted.
01 Jan 2018
TL;DR: The supplementary variable technique is used to obtain the steady-state probability generating functions for the system/orbit and some important system performance measures.
Abstract: This article discusses the concepts of preemptive priority retrial queue with two-phase service, feedback, and Bernoulli vacation for an unreliable server, which consists of breakdown period. The queue involves two types of customers, known as priority and ordinary customers. The server provides first essential service and second essential service to the arriving customers or customers from the orbit. The server takes Bernoulli vacation, when an orbit becomes empty. The supplementary variable technique is used to obtain the steady-state probability generating functions for the system/orbit and some important system performance measures.
05 Jun 2010
TL;DR: The Markov chain underlying the considered queuing system and its ergodicity condition is studied, explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained.
Abstract: We considered an unreliable Geo/Geo/1 retrial queue with infinite-capacity orbit and normal queue. In this model it is assume that if the server subjected to starting failures and breakdown during services of a customer, the customer leaves the server, joins a retrial group and repeatedly attempts to access the server in random intervals to get service. We study the Markov chain underlying the considered queuing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.
TL;DR: In this paper , the authors present the usage of retrial queues with cloud computing systems in which the operating unit (the server) and the storing unit (buffer) are independently considered.
Abstract: This study presents the usage of retrial queues with cloud computing systems in which the operating unit (the server) and the storing unit (buffer) are independently considered. In fact, the tasks cannot occupy the server to the system. Instead, they are stored in the buffer and sent back to the server after a random time. Upon a service completion, the server does not always get to work while waiting for a new task or a task from the buffer. After the idle time, the server instantly starts searching for a task from the buffer. The analysis model proposed in this study refers to a retrial queue system searching for tasks from theorbit with limited size under a multi-server context, and the model is modelized into the 3-dimension Markov chain. The solution is based on building an algorithm under the analytical methodology of the quasi birthdeath (QBD) process that utilizes the Q-matrix to calculate the probability of states toward the proposed model.
TL;DR: In this paper , a Markov model of birth-death process is developed using the Chapman-Kolmogorov governing equations for server retrial queueing systems with vacation times and discouraged customers.
Abstract: The proposed model deals with the study of two server retrial queueing system with vacation times and discouraged customers. The servers under consideration are functioning with variant speeds to provide service. The customers will directly enter into the service channel if any one of the server is found free upon arrival. Otherwise, the customer will move to the orbit to occupy the server later. At the service completion epoch, the server turns to vacation state if no more customers were found in the waiting area. During this vacation or working period, the customers may leave the system forever due to their longer waiting time. This Markov model of birth-death process is developed using the Chapman-Kolmogorov governing equations. By using the recursive approach, we obtain the stationary distributions for the arriving customers. Few performance indices were identified to depict the behavior of the formulated model.