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

Revision as of 12:29, 15 July 2011

Revision as of 17:02, 15 September 2011

Line 1:

In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]] '''Jackson's theorem''' is a theorem by [[James R. Jackson]].<ref>''{{cite journal|title=Jobshop-like Queueing Systems'' [[|first=James R. |last=Jackson]] in |journal=Management Science, Vol. |volume=10, No. |number=1 (|month=Oct., |year=1963), pp. |pages=131-142|doi=10.1287/mnsc.1040.0268|jstor=30046149}}</ref> It was the first significant development in the theory of [[queueing theory|networks of queues]], and generalising and applying the ideas of the theorem to search for similar [[product form solution]]s in other networks has been the subject of much research,<ref>''Networks of Queues'' [[F. P. Kelly]] in Advances in Applied Probability, Vol. 8, No. 2 (Jun., 1976), pp. 416-432</ref> including ideas used in the development of the Internet.<ref>''Comments on "Jobshop-Like Queueing Systems": The Background'' [[James R. Jackson]] in Management Science, Vol. 50, No. 12, Ten Most Influential Titles of Management Sciences First Fifty Years (Dec., 2004), p. 1803</ref> The paper was printed in the journal [[Management Science]]’s ‘Ten Most Influential Titles of Management Sciences First Fifty Years.’<ref>''Jobshop-like Queueing Systems'' [[James R. Jackson]] in Management Science, Vol. 50, No. 12, Ten Most Influential Titles of Management Sciences First Fifty Years</ref>

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>

==Definition of a Jackson network==