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Models for queue length in clocked queueing networks
Author(s) -
Percus Ora E.,
Percus J. K.
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430205
Subject(s) - queue , queueing theory , series (stratigraphy) , markov chain , mathematics , burke's theorem , bulk queue , fork–join queue , computer science , markov process , process (computing) , algorithm , queue management system , computer network , statistics , biology , paleontology , operating system
We analyze a discrete‐time network of queues. The unit element of the network is the 2 × 2 buffered switch, which we regard as a system of two queues working in parallel. We show how to transform transition probability information from the output of one switch, or network stage, to the input of the next one. This is used to carry out a Markov time series input model to predict mean queue length at every stage of the system. Another model considered is a renewal process time series model, which we use to find the mean queue length of the second stage of the network. Numerical simulations fall within the narrow band spanned by the two models.