Abstract
We address the approximate analysis of open networks of PH¦PH¦1 and PH¦PH¦1¦K queues. We start from the analysis of open queueing networks (QNs) as proposed by Whitt, where large QNs are decomposed into individual GI¦G¦1 queues, characterized by the first and second moment of the service and interarrival time distribution. We extend this approach in two ways.
First of all, we use PH¦PH¦1 queues, instead of GI¦G¦1 queues, so that the individual queues can be solved exactly, using matrix-geometric techniques. Secondly, we allow for the inclusion of finite-buffer queues. In doing so, the proposed decomposition becomes an iterative process.
We present the mathematical background of the approach as well as a tool implementation (Qnaut). It turns out that our approach not only yields accurate results (within a few percents from simulation results) but also is very fast in obtaining them (in comparison with simulation).
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Haverkort, B.R. (1995). Approximate analysis of networks of PH¦PH|1¦K queues: Theory & tool support. In: Beilner, H., Bause, F. (eds) Quantitative Evaluation of Computing and Communication Systems. TOOLS 1995. Lecture Notes in Computer Science, vol 977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024319
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DOI: https://doi.org/10.1007/BFb0024319
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