Queueing Networks: A Survey of Their Random Processes

In this paper we review three topics in queueing network theory: queue length processes, sojourn times, and flow processes. In the discussion of the queue length processes we present results for the continuous-time process and several embedded processes. Then we compare continuous-time processes wit...

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Bibliographic Details
Published inSIAM review Vol. 27; no. 3; pp. 335 - 403
Main Authors Disney, Ralph L., Konig, Dieter
Format Journal Article
LanguageEnglish
Published Philadelphia, PA The Society for Industrial and Applied Mathematics 01.09.1985
Society for Industrial and Applied Mathematics
Subjects
Applied sciences
Computer systems
Customer services
Equations
Exact sciences and technology
Feedback
LIFO
Markov analysis
Markov chains
Markov processes
Network servers
Operational research and scientific management
Operational research. Management science
Poisson process
Queueing networks
Queueing theory
Queuing theory. Traffic theory
Random variables
Servers
Service centers
Stochastic processes
Queue
Queue length
Network
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Summary:In this paper we review three topics in queueing network theory: queue length processes, sojourn times, and flow processes. In the discussion of the queue length processes we present results for the continuous-time process and several embedded processes. Then we compare continuous-time processes with embedded processes. In considerable generality we present results for mean sojourn times and discuss the distributions of sojourn times. In the discussion of flow processes we present results for various queueing systems. Our bibliography of over 300 references, while not exhaustive, does cover the major papers for the topics considered.
ISSN:0036-1445
1095-7200
DOI:10.1137/1027109