Abstract
This paper exposes the stochastic structure of traffic processes in a class of finite state queueing systems which are modeled in continuous time as Markov processes. The theory is presented for theM/E k /φ/L class under a wide range of queue disciplines. Particular traffic processes of interest include the arrival, input, output, departure and overflow processes. Several examples are given which demonstrate that the theory unifies many earlier works, as well as providing some new results. Several extensions to the model are discussed.
Similar content being viewed by others
References
E. Çinlar and R.L. Disney, Streams of overflows from a finite queue. Oper. Res. 15 (1967) 131–134.
R.L. Disney and P.C. Kiessler,Traffic Processes in Queueing Networks: A Markov Renewal Approach (Johns Hopkins Univ. Press, Baltimore, 1987).
F.P. Kelly,Reversibility and Stochastic Networks (J. Wiley, Chichester, 1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Barnes, J.A., Disney, R.L. Traffic processes in a class of finite Markovian queues. Queueing Syst 6, 311–326 (1990). https://doi.org/10.1007/BF02411480
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02411480