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Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System

Please always quote using this URN: urn:nbn:de:0297-zib-5801
  • 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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Metadaten
Author:Andreas Brandt, Manfred Brandt
Document Type:ZIB-Report
Tag:M(n)/M(n)/s+GI system; abandon probability; asymptotic; blocking-; finite buffer; impatience rates; limited waiting times; virtual waiting times
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G10 Stationary processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K25 Queueing theory [See also 68M20, 90B22]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Mxx Computer system organization / 68M20 Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
Date of first Publication:2000/04/05
Series (Serial Number):ZIB-Report (00-12)
ZIB-Reportnumber:00-12
Published in:Appeared in: Queuing Systems 41 (2002) 73-94
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