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Sojourn times in single-server queues by negative customers

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

P. G. Harrison  and
E. Pitel
P. G. Harrison
Affiliation:
Imperial College, London
E. Pitel*
Affiliation:
Imperial College, London
*
∗ Postal address for both authors: Department of Computing, Imperial College, University of London, 180 Queen's Gate, London SW7 2BZ, UK.
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Abstract

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

Keywords

G-NETWORKSWAITING TIMESKILLING STRATEGIESGENERATING FUNCTIONS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 943 - 963
Copyright
Copyright © Applied Probability Trust 1993 

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References

Boxma, O. J. and Daduna, H. (1990) Sojourn times in queueing networks. In Stochastic Analysis of Computer and Communication Networks, ed. Takagi, H., pp. 401–450, North-Holland, Amsterdam.Google Scholar
Coffman, E. G. Jnr., Muntz, R. R. and Trotter, H. (1970) Waiting time distribution for processor-sharing systems. J. Assoc. Comput. Mach. 17, 123–130.Google Scholar
Daduna, H. (1982) Passage times for overtake-free paths in Gordon-Newell networks. Adv. Appl. Prob. 14, 672–686.Google Scholar
Gelenbe, E. (1991) Product form networks with negative and positive customers. J. Appl. Prob. 28, 656–663.CrossRefGoogle Scholar
Gelenbe, E., Glynn, P. and Sigman, K. (1991) Queues with negative arrivals. J. Appl. Prob. 28, 245–250.Google Scholar
Harrison, P. G. (1990) Laplace transform inversion and passage time distributions in Markov processes. J. Appl. Prob. 27, 74–87.CrossRefGoogle Scholar
Harrison, P. G. and Patel, N. M. (1992) Performance Modelling of Communication Networks and Computer Architectures. Addison-Wesley, Reading, MA.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Lerch, M. (1892) O vlastnostech nekonecne rady [On properties of infinite radius]. Casopis 21, 65–68.Google Scholar