Content deleted Content added
Gareth Jones (talk | contribs) m more tidying references |
Gareth Jones (talk | contribs) m formatting references, linking to journal management science |
||
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 name="jackson">{{cite journal|title=Jobshop-like Queueing Systems|first=James R.|last=Jackson|journal=[[Management Science: A Journal of the Institute for Operations Research and the Management Sciences|Management Science]]|volume=10|number=1|month=Oct.|year=1963|pages=131-142|doi=10.1287/mnsc.1040.0268|jstor=2627213}}</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>{{cite journal|title=Networks of Queues|authorlink=F. P. Kelly|first=F. P.|last=Kelly|journal=Advances in Applied Probability|volume=8|number=2|month=Jun.|year=1976|pages=416-432|jstor=1425912}}</ref> including ideas used in the development of the Internet.<ref>{{cite journal|title=Comments on "Jobshop-Like Queueing Systems": The Background|first=James R.|last=Jackson|journal=|[[Management Science: A Journal of the Institute for Operations Research and the Management Sciences|Management Science]]|volume=50|number=12|month=December|year=2004|pages=1796-1802|jstor=30046150}}</ref> The paper was re-printed in the journal [[Management Science: A Journal of the Institute for Operations Research and the Management Sciences|Management Science]]’s ‘Ten Most Influential Titles of Management Sciences First Fifty Years.’<ref>{{cite journal|title=Jobshop-Like Queueing Systems|first=James R.|last=Jackson|journal=|[[Management Science: A Journal of the Institute for Operations Research and the Management Sciences|Management Science]]|volume=50|number=12|month=December|year=2004|pages=1796-1802|jstor=30046149}}</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>
Line 22:
==Generalized Jackson network==
A '''generalized Jackson network''' allows [[renewal process|renewal arrival processes]] that need not be Poisson processes, and independent, identically distributed non-exponential service times. In general, this network does not have a [[product form solution|product form stationary distribution]], so approximations are sought.<ref>
==See also==
| |||