Manuel Alberto M. Ferreira
Modified peakedness in M|G|∞ queue busy cycle distribution
Manuel Alberto M. Ferreira. Modified peakedness in M|G|∞ queue busy cycle distribution. Acta Scientiae et Intellectus, 6(4)2020, 116-123.
REFERENCES
Modified peakedness in M|G|∞ queue busy cycle distribution
Abstract
We expose how a parameter, then called θ, analogous to the parameter η proposed in [1] to characterize the M|G|∞ queue busy period distribution, is also worthwhile to characterize the M|G|∞ queue busy cycle distribution. The parameters θ and η are both modifications of the peakedness proposed in [3].
Keywords: M|G|∞, busy cycle, peakedness, modified peakedness
Manuel Alberto M. Ferreira. Modified peakedness in M|G|∞ queue busy cycle distribution. Acta Scientiae et Intellectus, 6(4)2020, 116-123.
REFERENCES
- M.A.M. Ferreira. A M|G|∞ queue busy period distribution characterizing parameter. Computer and Information Science, 6 (1), 83-88, 2013. http://dx.doi.org/10.5539/cis.v6n1p83.
- M.A.M. Ferreira. The modified peakedness as a M|G|∞ busy cycle distribution characterizing parameter. International Journal of Academic Research, 5(2), 5-8, 2013. DOI: 10.7813/2075-4124.2013/5-2/a.1
- W. Whitt. On approximations for queues, I: extremal distributions. A T & T Bell Laboratories Technical Journal, 63(1), 115-138, 1984.
- L. Tackács. An introduction to queueing theory. Oxford University Press, New York, 1962.
- M.A.M. Ferreira. Application of Riccati equation to the busy period study of the M|G|∞ system. Statistical Review, 1st Quadrimester, INE, 23-28, 1998.
- M.A.M. Ferreira, M. Andrade. Looking to a M|G|∞ system occupation through a Riccati equation. Journal of Mathematics and Technology, 1 (2), 58-62, 2010.
- M.A.M. Ferreira, M. Andrade, J.A. Filipe. The age or excess of the M/G/∞ queue busy cycle mean value. Computer and Information Science, 5(5), 93-97, 2012. http://dx.doi.org/10.5539/cis.v5n5p93
- S. Ross. Stochastic Processes. Wiley, New York, 1983.
- M.A.M. Ferreira. M|G|∞ queue heavy-traffic situation busy period length distribution (power and Pareto service distributions). Statistical Review, 1st Quadrimester, INE, 27-36, 2001.
- M.A.M. Ferreira. The exponentiality of the M|G|∞ queue busy period. Actas das XII Jornadas Luso-Espanholas de Gestão Científica, Volume VIII-Economia da Empresa e Matemática Aplicada. UBI, Covilhã, Portugal, 267-272, 2002.
- J. Figueira, M.A.M. Ferreira. Representation of a pensions fund by a stochastic network with two nodes: an exercise. Portuguese Revue of Financial Markets, 1(3), 1999.
- J.C. Hershey, E.N. Weiss, A.C. Morris. A stochastic service network model with application to hospital facilities. Operations Research, 29(1), 1-22, 1981.
- L. Kleinrock. Queueing systems. Vol. I and Vol. II. Wiley- New York, 1985.
- M.J. Carrillo. Extensions of Palm’s theorem: a review. Management Science, 37(6), 739-744, 1991.
- M.A.M. Ferreira, M. Andrade, J.A. Filipe. Networks of queues with infinite servers in each node applied to the management of a two echelons repair system. China-USA Business Review, 8(8), 39-45 and 62, 2009.
- R. Syski. Introduction to congestion theory in telephone systems. Oliver and Boyd-London, 1960.
- R. Syski. Introduction to congestion theory in telephone systems. North Holland, Amsterdam, 1986.
- M.G. Kendall and A. Stuart: The advanced theory of statistics. Distributions theory. London, Charles Griffin and Co., Ltd. 4th Edition, 1979.
- M. Andrade. A note on foundations of probability. Journal of Mathematics and Technology, 1(1), 96-98, 2010.
- M.A.M. Ferreira. Computational simulation of infinite servers systems. Statistical Review, 3rd Quadrimester, INE, 23-28, 1998. M.A.M. Ferreira. Differential equations important in the M|G|∞ queue system transient behavior and busy period study. Proceedings of 4th International Conference APLIMAT 2005, Bratislava, Slovakia, 119-132, 2005.
- M.A.M. Ferreira. Laplace transform effectiveness in the M|G|∞ queue busy period probabilistic study. 18th Conference on Applied Mathematics, APLIMAT 2019, 1, 304-312, 2019.
- M.A.M. Ferreira, J. A. Filipe. A queue model to monitor the conversion from ICeV to EV, HEV and DV in a scarce oil environment. 18th Conference on Applied Mathematics, APLIMAT 2019,1, 313-322, 2019.
- M.A.M. Ferreira, M. Andrade. The ties between the M|G|∞ queue system transient behavior and the busy period. International Journal of Academic Research, 1(1), 84-92, 2009.
- M.A.M. Ferreira, M. Andrade. M|G|∞ system transient behavior with time origin at the beginning of a busy period mean and variance. APLIMAT-Journal of Applied Mathematics, 3(3), 213-221, 2010.
- M.A.M. Ferreira, M. Andrade. Fundaments of theory of queues. International Journal of Academic Research, 3(1), part II, 427-429, 2011.
- M.A.M. Ferreira, M. Andrade. Busy period and busy cycle distributions and parameters for a particular M|G|∞ queue system. American Journal of Mathematics and Statistics, 2(2), 10-15, 2012. http://article.sapub.org/10.5923.j.ajms.20120202.03.html
- M.A.M. Ferreira, M. Andrade. Queue networks models with more general arrival rates. International Journal of Academic Research, 4(1), part A, 5-11, 2012.
- M.A.M. Ferreira, M. Andrade. Transient behavior of the M|G|m and M|G|∞ system. International Journal of Academic Research, 4(3), part A, 24-33, 2012.
- M.A.M. Ferreira, M.F. Ramalhoto. Estudo dos parâmetros básicos do período de ocupação da fila de espera M|G|∞. A Estatística e o Futuro e o Futuro da Estatística. Actas do I Congresso Anual da S.P.E., Edições Salamandra, Lisboa, 1994.
- M.F. Ramalhoto, M. A. M. Ferreira. Some further properties of the busy period of an M|G|∞ queue. Central European Journal of Operations Research and Economics, 4(4), 251-278, 1996.
- W. Stadje. The busy period of the queueing system M|G|∞. Journal of Applied Probability, 22, 697-704, 1985.