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An Application of the Conservation Law to Analyzing Single Server Queueing Systems with Two Independent Input Streams
Shuichi SUMITA
Publication
IEICE TRANSACTIONS (19761990)
Vol.E69
No.5
pp.628637 Publication Date: 1986/05/25 Online ISSN:
DOI: Print ISSN: 00000000 Type of Manuscript: PAPER Category: Communication Networks Keyword:
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Summary:
This paper presents a new approach, based on the conservation law, for analyzing the following single server queueing system with two classes of customers. The arrival process of one class customers is a Poisson process, while that of the other is represented by a renewal process and therefore need not be a Poisson process. Both classes of customers have exponential service time distributions. These queueing models with two input streams are often encountered in communication systems. Utilizing the conservation law, it is shown that for various types of workconserving queueing disciplines, the mean time in the system for each class of customers can be expressed in teams of the total workload in the system. When the total workload is known, these formulas can be used to obtain numerical solutions for the mean time in the system. The most important result in this approach is that the mean time in the system for each class of customers can be easily computed even when the service rates of both classes of customers are different. This is demonstrated by computing the mean time in the system using the derived formulas. The approximation formulas for the total workload are also presented based on the diffusion approximations, because it is difficult to obtain exact solutions for the total workload except for some special cases. Comparisons of exact and approximate results show that these approximation formulas provide good approximate values.

