A discrete-time queue with preferred customers and partial buffer sharing
type: Item
instance of: scholarly article
title: A discrete-time queue with preferred customers and partial buffer sharing
zbMATH Open document ID: 1394.90210
DOI: 10.1155/2015/173938
author: Shizhong Zhou
author: Li-Wei Liu
author: Jianjun Li
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: We analyze a discrete-time Geo/Geo/1 queueing system with preferred customers and partial buffer sharing. In this model, customers arrive according to geometrical arrival processes with probability \(\lambda\). If an arriving customer finds the server idle, he begins instantly his services. Otherwise, if the server is busy at the arrival epoch, the arrival either interrupts the customer being served to commence his own service with probability \(\theta\) (the customer is called the preferred customer) or joins the waiting line at the back of the queue with probability \(\widetilde{\theta}\) (the customer is called the normal customer) if permitted. The interrupted customer joins the waiting line at the head of the queue. If the total number of customers in the system is equal to or more than threshold \(N\), the normal customer will be ignored to enter into the system. But this restriction is not suitable for the preferred customers; that is, this system never loses preferred customers. A necessary and sufficient condition for the system to be stable is investigated and the stationary distribution of the queue length of the system is also obtained. Further, we develop a novel method to solve the probability generating function of the busy period of the system. The distribution of sojourn time of a customer in the server and the other indexes are acquired as well.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 6925655
Wikidata QID: Q59117471
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/173938
OpenAlex ID: W1551090310
cites work: Discrete-Time Queuing Theory
cites work: Queueing Theory
cites work: Queueing networks with discrete time scale. Explicit expressions for the steady state behaviour of discrete time stochastic networks
cites work: Performance analysis of finite buffer discrete-time queue with bulk service
cites work: Discrete time geo\(/G/1\) queue with multiple adaptive vacations
cites work: A preemptive discrete-time priority buffer system with partial buffer sharing
cites work: Discrete time \(GI/Geom/1\) queueing system with priority
cites work: Performance analysis of a \(GI-Geo-1\) buffer with a preemptive resume priority scheduling discipline
cites work: A recursive method for Bernoulli arrival queues and its application to partial buffer sharing in ATM
cites work: A discrete-time queueing system with optional LCFS discipline
cites work: A discrete-time Geo/G/1 retrial queue with preferred and impatient customers
cites work: Performance comparison of some discrete service time systems
description: scientific article; zbMATH DE number 6925655