Summary
The generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both positive and negative customers is investigated. The queueing discipline first come first served is chosen for the positive customers together with a killing strategy in which the last customer in the queue is removed by a negative customer. This killing strategy leads to complex mathematical analysis and, ultimately, to a Fredholm integral equation of the first kind. This type of equation has no known reliable numerical solution method except in special cases. We derive an alternative, iterative method involving the numerical inversion of Laplace transforms.
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References
H. Dubner and J. Abate, “Numerical inversion of Laplace transforms by relating them to the finite Fourier Cosine transform”, JACM, 1510, pp. 115–123, 1968.
E. Gelenbe, P. Glynn and K. Sigman, “Queues with negative arrivals”, J. Appl. Prob., 28, pp. 245–250, 1991.
E. Gelenbe, “Product form networks with negative and positive customers”, J. Appl. Prob., 28, pp. 656–663, 1991.
E. Gelenbe and R. Schassberger., “Stability of product form G-networks”, Probability in the Engineering and Informational Sciences, 6, pp. 271–276, 1992.
P.G. Harrison and E. Pitel, “Sojourn times in single server queues with negative customers”, Journal of Applied Probability, 30, pp. 943–963, 1993.
P.G. Harrison and E. Pitel, “The M/G/1 queue with negative customers”, Accepted for publication in Advances in Applied Probability, 33, June 1996.
W. Henderson, “Queueing networks with negative customers and negative queue length”, Journal of Applied Probability, 30 3, 1993.
E. Pitel, “Queues with negative customers”, PhD Thesis, Dept. of Computing, Imperial College, London, 1994.
S. Wolfram, “Mathematica”, Addison-Wesley, 1988.
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© 1995 ECSC-EC-EAEC, Brussels-Luxembourg
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Harrison, P.G., Pitel, E. (1995). M/G/1 Queues with FCFS Negative Arrivals. In: Baccelli, F., Jean-Marie, A., Mitrani, I. (eds) Quantitative Methods in Parallel Systems. Esprit Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79917-4_10
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DOI: https://doi.org/10.1007/978-3-642-79917-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-79919-8
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