Abstract
In this paper we consider various continuous/discrete time queueing models with general service time distribution. With an aim to identify queueing models we examine the structural properties like infinite divisibility of the stationary distribution of various characteristics of different queueing models and report some new results. Our investigation is further extended to bulk arrival models and multiple vacation queueing models, revealing the structural aspects of their steady state distributions.
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References
Burke PJ (1968) The output process of a stationary M / M / s queueing system. Ann Math Stat 39:1144–1152
Cox DR (1955) The analysis of non Markovian stochastic process by the inclusion of supplementary variables. In: Proceedings of the Cambridge Philosophical Society (vol 51, pp 433–441)
Doshi BT (1986) Queueing systems with vacations—a survey. Queueing Syst 1:29–66
Gross D, Haris CM (1985) Fundamentals of queueing theory. Wiley, New York
Hunter J (1983) Mathematical techniques of applied probability, vol 2. Academic Press, New York
Joby KJ, Manoharan M (2013) Some properties of the steady state characteristics of discrete time queueing models. J Stat Adv Theory Appl 10:189–197
Kendall DG (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of imbedded Markov chain. Ann Math Stat 24:338–354
Kingman JFC (1965) The heavy traffic approximation in the theory of queues. In: Proceedings symposium congestion theory, University of North Carolina Press, Chapel Hill, pp 137–169
Manoharan M (2009) Some preservation properties of Poisson mixtures, Bulletin of Kerala Mathematical Association, Special issue, Guest Editor: Professor S.R.S. Varadhan FRS, pp 67–86
Manoharan M, Alamatsaz MH, Shanbhag DN (2003) Departure and related characteristic in queueing models. In: Rao CR, shanbhag DN (eds) Hand book of statistics. Elsevier, Amsterdam, pp 557–572
Medhi J (2003) Stochastic models in queueing theory. Academic Press, Burlington
Mirasol NM (1963) The output of an \( M / G / \infty \) queueing system is poisson. In: Mathematical Proceedings of the Cambridge Philosophical Society (vol 72, pp 137–169)
Shanbhag DN (1973) Characterization for the queueing system \( M / G / \infty \). In: Mathematical Proceedings of the Cambridge Philosophical Society (vol 74, pp 141–143)
Shanbhag DN, Tambouratzis DG (1973) Erlang’s formula and some results on the departure process for a loss system. J Appl Probab 10:233–240
Steutel FW, Van Harn K (2004) Infinite divisibility of probability distributions on the real line. Marcel Dekker, New York
Takagi H (1993) Queueing analysis: a foundation of performance evaluation. Discrete time systems, vol 3. Elsevier, Amsterdam
Woodward ME (1994) Discrete time performance modeling of packet switching networks. Pentech Press, London
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Jose, J.K., Manoharan, M. Infinite Divisibility of Some Steady State Queue Characteristics. J Indian Soc Probab Stat 18, 215–224 (2017). https://doi.org/10.1007/s41096-017-0026-8
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DOI: https://doi.org/10.1007/s41096-017-0026-8