Abstract
We consider a matched queueing network PH/M/c→oPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.
Similar content being viewed by others
References
B.Q. Chen, Ergodicity for the queueing model of a single-berth seaport, J. Eng. Math. 5 (1988) 1–7 (in Chinese).
G.H. Hsu, Q.M. He and X.S. Liu, The stationary behavior of the matched queueing system, Acta Math. Appl. Sinica 13 (1990) 39–48.
G.H. Hsu, Q.M. He and X.S. Liu, The matched queueing system with a double input, Acta Math. Appl. Sinica, Eng. Ser. 10 (1993) No. 1.
M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models (Johns Hopkins University Press, Baltimore and London, 1981).
X.Y. Yang and B.Q. Chen, An application of stochastic simulation to the design of the coal loading and unloading system in a seaport, Theory and Practice of Syst. Eng. 3 (1984) 41–47 (in Chinese).
Author information
Authors and Affiliations
Additional information
The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.
Rights and permissions
About this article
Cite this article
Hsu, G.H., Jensen, U. The matched queueing network PH/M/c→oPH/PH/1. Queueing Syst 13, 315–333 (1993). https://doi.org/10.1007/BF01149259
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01149259