Multiserver queue with guard channel for priority and retrial customers
type: Item
instance of: scholarly article
title: Multiserver queue with guard channel for priority and retrial customers
zbMATH Open document ID: 1398.60093
DOI: 10.1155/2016/7168359
author: Kazuki Kajiwara
author: Tuan Phung-Duc
published in: International Journal of Stochastic Analysis
publication date: 2018-10-08T00:00:00Z
review text: Summary: This paper considers a retrial queueing model where a group of guard channels is reserved for priority and retrial customers. Priority and normal customers arrive at the system according to two distinct Poisson processes. Priority customers are accepted if there is an idle channel upon arrival while normal customers are accepted if and only if the number of idle channels is larger than the number of guard channels. Blocked customers (priority or normal) join a virtual orbit and repeat their attempts in a later time. Customers from the orbit (retrial customers) are accepted if there is an idle channel available upon arrival. We formulate the queueing system using a level dependent quasi-birth-and-death (QBD) process. We obtain a Taylor series expansion for the nonzero elements of the rate matrices of the level dependent QBD process. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we develop an efficient numerical algorithm to calculate the joint stationary distribution.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 6948429
zbMATH Keywords: retrial queueing model
zbMATH Keywords: quasi-birth-and-death process
zbMATH Keywords: guard channels
MaRDI profile type: Publication
Wikidata QID: Q59125093
full work available at URL: https://doi.org/10.1155/2016/7168359
OpenAlex ID: W2292251339
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description: scientific article; zbMATH DE number 6948429