• The Journal of Korean Institute of Communications and Information Sciences
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• v.12 no.6
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• pp.545-553
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• 1987

An approximation algorithm has been obtained to analyze the network of single server tandem queues with a finite length. In the queueing network with a finite queue length, the blocking which is mutually dependent, occure due to the limitation of the queue length. Thus, it is difficults to analyze such a queueing network. In this paper each queue has been regarded as the independent M/M/1/K system to analyze the queueing network with the blocking, which is based on the assumption that an arrival rate to the present station is increased by the blocking of the following stations. The performance measures, such as state probability, average queue length and tha waiting time, can be easily obtained using the proposed algorithm. In order to justify this approximation algorithm, comparison of the results of this algorithm with those of state transition simultaneous equations has been made an verified with computer simulation.

• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.4
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• pp.1-10
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• 2004

In this paper we study bounds for characteristics of stationary waiting times in (max, +)-linear systems with a Poisson arrival process. which are prevalent in manufacturing systems, kanban systems, cyclic and acyclic fork-and-join type systems, finite or infinite capacity tandem queues with various kinds of blocking, transportation systems, and telecommunication networks, and so on. Recently, some results on series expansion for characteristics, such as higher moments, Laplace transform, and tail probability, of transient and stationary waiting times in a class of (max, +)-linear systems via Taylor series expansions have been studied. In order to overcome the computational complexity in those results, we consider bounds for characteristics of stationary waiting times using valuable stochastic ordering results. Some numerical examples are also provided.