Open AccessThe truncated Hyper-Poisson queues: Hk/Ma,b/C/N with balking, reneging and general bulk service rule
Author(s) -
Ahmed Shawky,
Mahdy S. El-Paoumy
Publication year - 2008
Publication title -
yugoslav journal of operations research/yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 2334-6043
pISSN - 0354-0243
DOI - 10.2298/yjor0801023s
Subject(s) - poisson distribution , queue , fifo (computing and electronics) , mathematics , combinatorics , burke's theorem , service (business) , discrete mathematics , state (computer science) , computer science , mathematical optimization , statistics , queue management system , algorithm , computer network , fork–join queue , business , computer hardware , marketing
The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained.