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Transient solution of a finite‐capacity M/G a,b /1 queueing system
Author(s) -
Jacob M. J.,
Krishnamoorthy A.,
Madhusoodanan T. P.
Publication year - 1988
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198806)35:3<437::aid-nav3220350312>3.0.co;2-w
Subject(s) - queueing system , poisson distribution , queue , queueing theory , computer science , bulk queue , transient (computer programming) , renewal theory , random variable , distribution (mathematics) , layered queueing network , mathematical optimization , real time computing , mathematics , computer network , statistics , operating system , mathematical analysis
In this article we consider a single‐server, bulk‐service queueing system in which the waiting room is of finite capacity. Arrival process is Poisson and all the arrivals taking place when the waiting room is full are lost. The service times are generally distributed independent random variables and the distribution is depending on the batch size being served. Using renewal theory, we derive the time‐dependent solution for the system‐size probabilities at arbitrary time points. Also we give expressions for the distribution of virtual waiting time in the queue at any time t .