Jackson's theorem (queueing theory): Difference between revisions

Revision as of 17:57, 20 October 2011

Revision as of 17:57, 20 October 2011

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Jackson was inspired by the work of [[Burke's theorem|Burke]] and Reich,<ref>{{cite journal|title=Waiting Times When Queues are in Tandem|journal=[[Annals of Mathematical Statistics]]|volume=28|number=3|month=September|year=1957|first=Edgar|last=Reich|doi=10.1214/aoms/1177706889|jstor=2237237}}</ref> though Walrand notes "product form results … [are] a much less immediate result of the output theorem than Jackson himself appeared to believe in his fundamental paper".<ref>{{cite journal|title=A Probabilistic Look at Networks of Quasi-Reversible Queues|journal=[[IEEE Transactions on Information Theory]]|volume=29|number=6|month=November|year=1983|first=Jean|last=Walrand|doi=10.1109/TIT.1983.1056762}}</ref>

An earlier [[product form solution]] was found by R. R. P. Jackson for tandem queues (a finite chain of queues where each customer must visit each queue in order) and cyclic networks (a loop of queues where each customer must visit each queue in order).<ref>{{cite journal|title=Book review: Queueing networks and product forms: a systems approach|first=R. R. P.|last=Jackson|doi=10.1093/imaman/6.4.382|year=1995|volume=56|number=4|pages=382–384|journal=IMA Journal of Management Mathematics}}</ref>

==Definition of a Jackson network==