Asymptotic behavior of the expansion method for open finite queueing networks
The paper presents an approximation technique for the modeling of finite capacity queueing networks. In the first part, the `expansion method', already discussed in earlier papers, is described. The basic idea behind it is the introduction of `holding nodes' representing the additional waiting times incurred by customers due to blocking. In limiting the analysis to exponential service times and an external Poisson arrival process, an exhaustive set of recursive equations is derived based on mean value computation and well-known approximations [see \textit{J. Labetoulle} and \textit{G. Pujolle}, IEEE Trans. Software Eng. SE-6, No.4 (1980)]. In part two, the value of the expansion method with regard to meeting an upper bound throughput criterion [\textit{P. C. Bell}, Oper. Res. Lett. 1, 230-235 (1982; Zbl 0499.90039)] even for quite `unbalanced' service rates is demonstrated.
scientific article; zbMATH DE number 4082683