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System Contents Versus System Delay for Discrete-Time Queueing Systems with Renewal Arrivals

  • Conference paper
Applying Formal Methods: Testing, Performance, and M/E-Commerce (FORTE 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3236))

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Abstract

This paper concerns discrete-time queueing systems operating with a first-come-first-served (FCFS) queueing discipline. Customers arrive in the system according to a renewal process; the inter-arrival times form a family of independent and identically distributed (i.i.d.) random variables. We establish a relationship between the probability generating function (pgf) of the system delay of an arbitrary customer and the pgf of the system contents during an arbitrary slot. Based on this result we derive relationships between the mean and variance, the mass function and the tail probabilities of the respective distributions. These relationships are valid irrespective of the characteristics of the servicing process, i.e., irrespective the number of servers, the distribution of the service times and possible correlation between the service times of consecutive customers.

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Author information

Authors and Affiliations

  1. Department TELIN, Research Group SMACS, Ghent University, Sint-Pietersnieuwstraat 41, B-9000, Gent, Belgium

    Bart Vinck & Herwig Bruneel

Authors
  1. Bart Vinck
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  2. Herwig Bruneel
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Editor information

Editors and Affiliations

  1. Dept. Sistemas Informáticos y Programación Facultad de Informática, Universidad Complutense de Madrid, 28040,, Madrid, Spain

    Manuel Núñez

  2. CIT, Zayed University, Dubai, United Arab Emirates, United Arab Emirates

    Zakaria Maamar

  3. Dept. de Sistemas Informáticos Escuela Politécnica Superior, Universidad Castilla-La Mancha, 02071, Albacete, Spain

    Fernando L. Pelayo

  4. Business Informatics and Systems Engineering, University of Augsburg, Universitätsstraße 16, 86135, Augsburg, Germany

    Key Pousttchi

  5. Dept. Sistemas Informáticos y Computación, Facultad de Informática, Universidad Complutense de Madrid, Madrid, Spain

    Fernando Rubio

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© 2004 Springer-Verlag Berlin Heidelberg

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Vinck, B., Bruneel, H. (2004). System Contents Versus System Delay for Discrete-Time Queueing Systems with Renewal Arrivals. In: Núñez, M., Maamar, Z., Pelayo, F.L., Pousttchi, K., Rubio, F. (eds) Applying Formal Methods: Testing, Performance, and M/E-Commerce. FORTE 2004. Lecture Notes in Computer Science, vol 3236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30233-9_13

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  • DOI: https://doi.org/10.1007/978-3-540-30233-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23169-1

  • Online ISBN: 978-3-540-30233-9

  • eBook Packages: Springer Book Archive

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