Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System |
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Authors: | Brandt Andreas Brandt Manfred |
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Institution: | (1) Wirtschaftswissenschaftliche Fakultät, Humboldt-Universität zu Berlin, Spandauer Str. 1, D-10178 Berlin, Germany;(2) Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, D-14195 Berlin, Germany |
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Abstract: | In this paper for the M(n)/M(n)/s+GI system, i.e. for a s-server queueing system where the calls in the queue may leave the system due to impatience, we present new asymptotic results for the intensities of calls leaving the system due to impatience and a Markovian system approximation where these results are applied. Furthermore, we present a new proof for the formulae of the conditional density of the virtual waiting time distributions, recently given by Movaghar for the less general M(n)/M/s+GI system. Also we obtain new explicit expressions for refined virtual waiting time characteristics as a byproduct. |
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Keywords: | M(n)/M(n)/s+GI system limited waiting times finite buffer virtual waiting times blocking- abandon probability impatience rates asymptotic results M(n)/M(n)/s system with waiting place dependent impatient rates Markovian approximation |
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