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Workload distribution of discrete‐time parallel queues with two servers
Author(s) -
Wang P. Patrick
Publication year - 2000
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(200008)47:5<440::aid-nav5>3.0.co;2-w
Subject(s) - queue , workload , fork–join queue , computer science , server , constant (computer programming) , service (business) , mathematical optimization , real time computing , queue management system , mathematics , computer network , operating system , economy , economics , programming language
We study discrete‐time, parallel queues with two identical servers. Customers arrive randomly at the system and join the queue with the shortest workload that is defined as the total service time required for the server to complete all the customers in the queue. The arrivals are assumed to follow a geometric distribution and the service times are assumed to have a general distribution. It is a no‐jockeying queue. The two‐dimensional state space is truncated into a banded array. The resulting modified queue is studied using the method of probability generating function (pgf) The workload distribution in steady state is obtained in form of pgf. A special case where the service time is a deterministic constant is further investigated. Numerical examples are illustrated. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 440–454, 2000