Konrad-Zuse-Zentrum für Informationstechnik Berlin ZIB PaperWeb

00-12

Andreas Brandt, Manfred Brandt Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System Appeared in: Queuing Systems 41 (2002) 73-94

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.
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 syst. with waiting place depend. impatient rates, Markovian approximation
MSC: 60K25, 68M20, 60G10