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Multi‐server Batch‐service Systems
Author(s) -
Adan I. J. B. F.,
Resing J. A C.
Publication year - 2000
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00137
Subject(s) - erlang (programming language) , computer science , poisson distribution , queueing system , server , queueing theory , batch processing , expression (computer science) , service (business) , process (computing) , mathematical optimization , markov process , markovian arrival process , erlang distribution , poisson process , compound poisson process , bulk queue , batch production , closed form expression , real time computing , exponential distribution , mathematics , computer network , operating system , statistics , theoretical computer science , operations management , engineering , functional programming , economy , mathematical analysis , economics , programming language
In this paper we analyse a multi‐server batch‐service queueing model. Customers arrive one by one according to a Poisson process. They are served in batches under the following threshold policy: when a server becomes available a new batch of waiting customers is taken into service as soon as their number reaches a threshold a . The maximum allowable batch size is equal to b . Two classes of batch service time distributions are considered: Coxian‐2 and Erlang‐ r distributions. In both cases the queueing model can be described by a Markov process. For this process it is shown that the equilibrium probabilities for states with all servers busy can be expressed as a finite sum of geometric terms. This form is used to derive a closed form expression for the waiting time distribution.