An estimate for the loss probability in a queueing system of the 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), 1724
MSC (2000):
Primary 60K25
Published electronically:
December 28, 2005
MathSciNet review:
2144317
Fulltext PDF Free Access
Abstract 
References 
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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 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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 6.
 I. N. Kovalenko, J. B. Atkinson, and K. V. Mykhalevych, Three cases of lighttraffic insensitivity of the loss probability in a loss system to the shape of the service time distribution, Queueing Systems 45 (2003), 245271. MR 2024180 (2004k:60255)
 7.
 T. Erhardsson, On the number of lost customers in stationary loss systems in the light traffic case, KTH, INTERNET, Stockholm (2002), 119.
 8.
 V. Klimenok, C. S. Kim, D. Orlovsky, and A. Dudin, Lack of invariant property of Erlang loss model in case of the MAP input, QUESTA (to appear).
 9.
 Yu. V. Malinkovski, Invariance of the stationary distribution of the states of modified Jackson and GordonNewell networks, Avtomat. i Telemekh. 59 (1998), no. 9, 2936; English transl. in Automat. Remote Control 59 (1999), no. 9, 12261231. MR 1680017
 10.
 Yu. V. Malinkovskiand O. V. Yakubovich, Invariance in closed networks with bypasses, Mathematical Methods for Investigations for Telecommunication Networks, Proceedings of the 13th Belorussian Winter SchoolSeminar on the Theory of Queues, (International Conference BWWQT97), Minsk, February 35, 1997, Belorussian State University, Minsk, 1997, pp. 118119. (Russian)
 11.
 Yu. V. Malinkovskiand O. V. Yakubovich, Invariance of Markov queueing networks with bypasses of nodes and immediate service, Mathematical Methods for Investigations of Queueing Systems and Networks, Proceedings of the 14th Belorussian Winter SchoolSeminar on the Theory of Queues (International Conference BWWQT98), Minsk, January 2729, 1998, Belorussian State University, Minsk, 1998, pp. 121122. (Russian)
 12.
 A. V. Krylenko, Invariance of queueing networks with several types of nodes and customers, with immediate service, and bypasses of nodes, Mathematical Methods for Investigations of Queueing Systems and Networks, Proceedings of the 14th Belorussian Winter SchoolSeminar on the Theory of Queues (International Conference BWWQT98), Minsk, January 2729, 1998, Belorussian State University, Minsk, 1998, pp. 112115. (Russian)
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Additional Information
D. Baum
Affiliation:
LG Stochastische Modellierung und Rechnernetze, FB4Abteilung Informatik, Universität Trier, D54286 Trier, Germany
Email:
baum@info04.unitrier.de
I. N. Kovalenko
Affiliation:
Glushkov Institute for Cybernetics, Kyiv, Ukraine
Email:
kovigo@yandex.ru
DOI:
http://dx.doi.org/10.1090/S0094900005006447
PII:
S 00949000(05)006447
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
