Systems with Queueing and their Simulation

In the queueing theory, it is assumed that customer arrivals correspond to a Poisson process and service time has the exponential distribution. Using these assumptions, the behaviour of the queueing system can be described by means of Markov chains and it is possible to derive the characteristics of the system. In the paper, these theoretical approaches are presented on several types of systems and it is also shown how to compute the characteristics in a situation when these assumptions are not satisfied

Authors:

• Miloš Šeda
• Pavel Ošmera
• Jindřich Petrucha

Keywords:

• Queueing theory
• Poisson process
• Markov chains.

References:

[1] G. Bolch, S. Greiner, H. Meer and K.S. Trivedi, Queueing Networks and
Markov Chains. John Wiley & Sons, New York, 2006.
[2] S.K. Bose, An Introduction to Queueing Systems. Springer-Verlag,
Berlin, 2001.
[3] R.B. Cooper, Introduction to Queueing Theory. North Holland, New
York, 1981.
[4] D. Gross, J.F. Shortle, J.M. Thompson and C.M. Harris, Fundamentals
of Queueing Theory. John Wiley & Sons, New York, 2008.
[5] K. Hrubina, A. Jadlovská, S. Hrehová., Optimisation Algorithms Using
Programme Systems. Technical University in Košice, Prešov-Košice,
2005.
[6] J. Klvaňa, Modelling. Czech Technical University Prague, 2005.
[7] I. RukovanskÛ, "Evolution of Complex Systems," in Proceedings of the
8th Joint Conference on Information Sciences, Salt Lake City, Utah,
USA, 2005.
[8] J. Virtamo, Queueing Theory. Lecture Notes. Helsinki University of
Technology, 2005.
[9] A. Willig, A Short Introduction to Queueing Theory. Lecture Notes.
Technical University Berlin, 1999, 42 pp.