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A Note on the Waiting-Time Distribution in an Infinite-Buffer GI[X]C-MSP1 Queueing System
Joint Authors
Banik, A. D.
Chaudhry, Mohan L.
Kim, James J.
Source
Journal of Probability and Statistics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-02
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
This paper deals with a batch arrival infinite-buffer single server queue.
The interbatch arrival times are generally distributed and arrivals are occurring in batches of random size.
The service process is correlated and its structure is presented through a continuous-time Markovian service process (C-MSP).
We obtain the probability density function (p.d.f.) of actual waiting time for the first and an arbitrary customer of an arrival batch.
The proposed analysis is based on the roots of the characteristic equations involved in the Laplace-Stieltjes transform (LST) of waiting times in the system for the first, an arbitrary, and the last customer of an arrival batch.
The corresponding mean sojourn times in the system may be obtained using these probability density functions or the above LSTs.
Numerical results for some variants of the interbatch arrival distribution (Pareto and phase-type) have been presented to show the influence of model parameters on the waiting-time distribution.
Finally, a simple computational procedure (through solving a set of simultaneous linear equations) is proposed to obtain the “R” matrix of the corresponding GI/M/1-type Markov chain embedded at a prearrival epoch of a batch.
American Psychological Association (APA)
Banik, A. D.& Chaudhry, Mohan L.& Kim, James J.. 2018. A Note on the Waiting-Time Distribution in an Infinite-Buffer GI[X]C-MSP1 Queueing System. Journal of Probability and Statistics،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1197696
Modern Language Association (MLA)
Banik, A. D.…[et al.]. A Note on the Waiting-Time Distribution in an Infinite-Buffer GI[X]C-MSP1 Queueing System. Journal of Probability and Statistics No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1197696
American Medical Association (AMA)
Banik, A. D.& Chaudhry, Mohan L.& Kim, James J.. A Note on the Waiting-Time Distribution in an Infinite-Buffer GI[X]C-MSP1 Queueing System. Journal of Probability and Statistics. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1197696
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197696