Throughput bounds for closed queueing networks |
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Authors: | Jiri Kriz |
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Affiliation: | Computer Science Group, Department KLR-PC, Brown Boveri Research Center, CH-5405 Baden-Dättwil, Switzerland |
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Abstract: | Analytical lower and upper bounds for the throughput of closed queueing networks with single and delay (infinite) servers are studied in this paper. The numerical evaluation of these bounds requires a small number of significant operations which is independent of the population N. This is in contrast to the exact computation of the throughput which requires at least O(N) operations as N tends to infinity. The bounds are given by simple closed-form analytical expressions and may be more suitable for various performance studies than the algorithmical form of the exact solution.In this paper, the previously known balanced-job bounds are generalized to networks containing delay servers (terminals) and a hierarchy of bounds is obtained for single and multiple class networks. For the single class network, further new bounds are derived: lower and upper bounds that require the evaluation of one square root and an upper bound that requires a constant number of exponentiations. This upper bound does not employ the balancing of server loadings and is especially useful for asymptotic analysis in the case of a large number of customers N. |
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Keywords: | Queueing Networks Time-Sharing Systems Throughput Bounds Response Time Bounds Asymptotic Analysis Performance Evaluation |
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