Analysis of a MAP/PH/1 queue with discretionary priority based on service stages
Ning Zhao1; Zhaotong Lian2; Kan Wu3
2015-08
Source PublicationAsia-Pacific Journal of Operational Research
ABS Journal Level1
ISSN0217-5959
Volume32Issue:6Pages:1-22
Other Abstract

In this paper, we study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queuing system can be modeled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions. We present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modeled into a QBD process where the block elements of the generator matrix have finite dimensions. The sojourn time distributions of both high and low priority customers are obtained. Some managerial insights are given after comparing the discretionary priority rule with the preemptive and nonpreemptive disciplines numerically.

KeywordDiscretionary Matrix-geometric Method Priority Queuing System Sojourn Time
DOIhttp://doi.org/10.1142/S0217595915500426
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaOperations Research & Management Science
WOS SubjectOperations Research & Management Science
WOS IDWOS:000368112500002
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
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Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF ACCOUNTING AND INFORMATION MANAGEMENT
Corresponding AuthorKan Wu
Affiliation1.Faculty of Science,Kunming University of Science and Technology,,Kunming,China
2.Faculty of Business Administration,University of Macau,,Macao
3.School of Mechanical and Aerospace Engineering,Nanyang Technological University,,Singapore
Recommended Citation
GB/T 7714
Ning Zhao,Zhaotong Lian,Kan Wu. Analysis of a MAP/PH/1 queue with discretionary priority based on service stages[J]. Asia-Pacific Journal of Operational Research,2015,32(6):1-22.
APA Ning Zhao,Zhaotong Lian,&Kan Wu.(2015).Analysis of a MAP/PH/1 queue with discretionary priority based on service stages.Asia-Pacific Journal of Operational Research,32(6),1-22.
MLA Ning Zhao,et al."Analysis of a MAP/PH/1 queue with discretionary priority based on service stages".Asia-Pacific Journal of Operational Research 32.6(2015):1-22.
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