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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

An estimate for the loss probability in a queueing system of the $ MAP/G/m/0$ type in the case of light traffic


Authors: D. Baum and I. N. Kovalenko
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 17-24
MSC (2000): Primary 60K25
Published electronically: December 28, 2005
MathSciNet review: 2144317
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a queueing system with losses and with a general distribution of the service time. It is assumed that the input is of the $ MAP$ type and the phase process assumes values in a general measurable space. The asymptotic behavior of the loss probability is studied for the case where the mean service time tends to zero. In particular, we find conditions under which the loss probability is asymptotically invariant with respect to the shape of the service time.


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Additional Information

D. Baum
Affiliation: LG Stochastische Modellierung und Rechnernetze, FB4-Abteilung Informatik, Universität Trier, D-54286 Trier, Germany
Email: baum@info04.uni-trier.de

I. N. Kovalenko
Affiliation: Glushkov Institute for Cybernetics, Kyiv, Ukraine
Email: kovigo@yandex.ru

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00644-7
PII: S 0094-9000(05)00644-7
Received by editor(s): March 29, 2004
Published electronically: December 28, 2005
Additional Notes: The second author is partially supported by the DLR Foundation (project ADLON, Trier University, Germany).
Article copyright: © Copyright 2005 American Mathematical Society