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The M / M /1 queue with gated random order of service
Author(s) -
Resing Jacques,
Rietman Ronald
Publication year - 2004
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 - 10.1046/j.0039-0402.2003.00112.x
Subject(s) - bulk queue , service (business) , queue , computer science , joint probability distribution , mathematics , computer network , operations research , statistics , business , marketing
We analyse an M / M /1 queueing model with gated random order of service discipline. In this service discipline there is a waiting room, in which arriving customers are collected, and a service queue. Each time the service queue becomes empty, all customers in the waiting room are instantaneously put in random order in the service queue. We find the joint stationary distribution of the number of customers in the waiting room and the service queue. Furthermore, we obtain the bivariate Laplace–Stieltjes transform of the joint distribution of the sojourn times of a customer in the waiting room and the service queue.