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M A P + M A P M 2 N ∞ Queueing System with Absolute Priority and Reservation of Servers
Joint Authors
Sun, Bin
Dudin, Sergey A.
Lee, Moon Ho
Dudin, Alexander N.
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-11-27
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We consider a multiserver queueing system with an infinite buffer and two types of customers.
The flow of customers is described by two Markovian arrival processes (MAPs).
Type 1 customers have absolute priority over type 2 customers.
If the arriving type 1 customer encounters all servers busy, but some of them provide service to type 2 customers, service of one type 2 customer is terminated and type 1 customer occupies the released server.
To avoid too frequent termination of service of type 2 customers, we suggest reservation of some number of servers for type 1 customers.
Type 2 customers, who do not succeed to get a server upon arrival or are knocked out from a server, join the buffer or leave the system forever.
During a waiting period in the buffer, type 2 customers can be impatient and may leave the system forever.
The ergodicity condition of the system is derived in an analytically tractable form.
The stationary distribution of the system states and the main performance measures are calculated.
The Laplace-Stieltjes transform of the waiting time distribution of an arbitrary type 2 customer is derived.
Numerical examples are presented.
The problem of the optimal channel reservation is numerically solved.
American Psychological Association (APA)
Sun, Bin& Lee, Moon Ho& Dudin, Alexander N.& Dudin, Sergey A.. 2014. M A P + M A P M 2 N ∞ Queueing System with Absolute Priority and Reservation of Servers. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-1046484
Modern Language Association (MLA)
Sun, Bin…[et al.]. M A P + M A P M 2 N ∞ Queueing System with Absolute Priority and Reservation of Servers. Mathematical Problems in Engineering No. 2014 (2014), pp.1-15.
https://search.emarefa.net/detail/BIM-1046484
American Medical Association (AMA)
Sun, Bin& Lee, Moon Ho& Dudin, Alexander N.& Dudin, Sergey A.. M A P + M A P M 2 N ∞ Queueing System with Absolute Priority and Reservation of Servers. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-1046484
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1046484