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OPSEARCH : Volume 52, Issue 3, September 2015

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OPSEARCH : Volume 52, Issue 1, March 2015

A batch arrival multi phase queueing system with random feedback in service and single vacation policy

Content Provider	Springer Nature Link
Author	Zadeh, A. Badamchi
Copyright Year	2015
Abstract	We study a batch arrival Poisson input, k phases heterogeneous services with randomly feedback in services. The first phase of service is essential for all customers, but with probability γ $_{1}$ a tagged customer chose second phase, with probability α $_{1}$ feedback to tail of original queue or with probability β $_{1}$ = 1 − γ $_{1}$ − α $_{1}$ leave the system. Also, after completion of the second phase, with probability γ $_{2}$ the customer leads to the third service, or with probability α $_{2}$ feedback to tail of original queue, or leaves the system with probability β $_{2}$ = 1 − γ $_{2}$ − α $_{2}$. Like that, in kth phase feedback with probability α $_{ k }$ or leaves the system with probability 1 − α $_{ k }$. After completion of each phases, the server either goes for a vacation with probability 𝜃(0 ≤ 𝜃 ≤ 1), or may continue to serve the next unit with probability 1 − 𝜃, if any. Otherwise, it remains in the system until a customer arrives, which is single vacation policy. We assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. In this paper we derive the steady- state equations, PGF’s of the system, and measures of sysytem.
Starting Page	617
Ending Page	630
Page Count	14
File Format	PDF
ISSN	00303887
Journal	OPSEARCH
Volume Number	52
Issue Number	4
e-ISSN	09750320
Language	English
Publisher	Springer India
Publisher Date	2015-03-22
Publisher Place	New Delhi
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	M/G/1 queue Multi phases of heterogeneous service Feedback Admissibility restricted Single vacation Mean queue size Mean response time Operation Research/Decision Theory Management Mathematics
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research Management Information Systems Information Systems Computer Science Applications

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