Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
The consequences of heavy-tailed service time distribution on a basic queuing model and its performance indicators
Efecto del uso de tiempos de atención heavy-tailed sobre el modelo básico de líneas de espera y sus medidas de desempeño
DOI:
https://doi.org/10.15446/ing.investig.v30n2.15744Keywords:
queuing system, heavy-tailed distribution, service time, Pareto distribution, generative model (en)líneas de espera, distribuciones heavy-tailed, tiempos de servicio, distribución de Pareto, modelos generatrices (es)
Downloads
Recent research showing theoretical generative models for heavy-tailed service time queues and its empirical validation implies the need for a better knowledge of the key performance indicators' behaviour under such assumption. The behaviour of the average length of the queue (Lp) and the average waiting-time (Wp)were analysed through simulation, varying system capacity, average service utilisation factor (r) and the number of servers in the systems as parameters. Comparisons were also made with service times based on Poisson processes. The results showed more sensitive variations Lq and Wq heavy-tailed service times than for Poisson-based service times. Systems having a capacity of over 1,000 entities might be considered as being systems having infinity capacity and the number of servers has a greater importance in heavy-tailed ruled processes than in Poisson processes. There was a lack adequacy Lq and Wq as key performance indicators for heavy-tailed service times, leading to unexpected and unstable results.
La reciente aparición de modelos generatrices de líneas de espera con tiempos de atención heavy-tailed y su comprobación empírica implican la necesidad de conocer el comportamiento de las medidas clásicas de desempeño de una línea de espera bajo estas condiciones. El objetivo del estudio fue el de analizar el comportamiento de Lp (longitud promedio de la fila) y Wp (tiempo promedio de espera en fila) variando los parámetros capacidad del sistema, nivel de utilización promedio (r) y número de servidores para líneas de espera con tiempos de atención heavy-tailed, y contrastar dicho comportamiento con los resultados clásicos basados en procesos de Poisson, usando para ello la simulación de eventos discretos. Los resultados mostraron que la sensibilidad de los modelos con tiempos de atención heavy-tailed a variaciones en los parámetros es mayor que la de los modelos basados en procesos de Poisson. En particular, a partir de capacidades de sistema de 1.000 entidades ciertos procesos heay-tailed pueden considerarse infinitos, y la importancia del número de servidores es mayor en los procesos heavy-tailed analizados que en los procesos de Poisson. Por último, la utilización de Lp y Wp como medidas de desempeño es inadecuada para tiempos de atención heavy-tailed al generar resultados inestables y contraintuitivos.
Downloads
References
Alvarado, J. A., Montoya, J. R., Rangel, L. M., Analyse par simulation de l’impact de la modélisation du temps de service avec une distribution heavy-tailed: étude de Cas d’un atelier de maintenance automobile., Mosim 2008, Proceedings of the 7eme conference international de modelisation et Simulation, Paris, 2008.
Andriani, P., McKelvey, B., Why Gaussian statistics are mostly wrong for strategic organization., Strategic Organization, Vol. 3, 2005, pp. 219–223.
Barabási, A. L., The origin of bursts and heavy-tailed in human dynamics., Nature, Vol. 435, 2005, pp. 435–439.
Cohen, J. W., Some results on regular variation for distributions in queuing and fluctuations theory., Journal of Applied Probability, Vol. 10, 1973, pp. 343–353.
Embrechts, P., Kluppelberg, C., Mikosch, T., Modeling extremal events for Insurance and finance., New York, Springer-Verlag, 1997.
Gross, D., Fundamentals of queuing theory., 4th ed., New York, John Wiley & Sons, 2009.
Hillier, F., Lieberman, G. J., Operations Research., 8th ed., México, McGraw-Hill. 2005.
Janicki, H. P., Simpson, E., Changes in the size distribution of US Banks: 1960–2005., Economic Quarterly - Federal Reserve Bank of Richmond, Vol. 92, No. 4, 2005, pp. 291-316.
Kuehl, R., Diseño de experimentos: Principios estadísticos de diseño y análisis de investigación., México, International Thomson Editores, 2001.
Mitzenmacher, M., A brief history of generative models for power law and lognormal distributions., Internet Algorithms, Vol. 1, No. 2, 2004, pp. 226–251.
Montgomery, D., Design and analysis of experiments., 7th edition, 2008, Wiley.
Neuts, M. F., Computer experimentation in applied probability., Journal of applied probability, Vol. 25A,1988, pp. 31-43
Newman, M., Power laws, Pareto distributions and Zipf’s law., Contemporary Physics, Vol. 46, 2005, pp. 323-351.
Pakes, A. G., On the tails of waiting-time distributions., Journal of Applied Probability, Vol. 12, 1975, pp. 555–564.
Ross, S., A first course in probability., 7th ed., New Jersey, Pearson Prentice Hall, 2006.
Sigman, K., Apendix: A primer on heavy-tailed distributions., Queuing Systems, Vol. 33, No. 1-3, Dic., 1999, pp. 261–275.
Stidham, S., Analysis, Design, and Control of Queuing Systems., Operation research, Vol. 50, 2002, pp. 197-216.
Stewart, W. J., Introduction to the numerical solution of Markov chains, New Jersey, Princeton University Press, 1994.
Whitt, W., The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting time distribution., Queuing Systems, Vol. 36, 2000, pp. 71-87.
Willinger, W., Traffic modelling for high-speed networks: theory versus practice., Stochastic Networks, IMA Volumes in Mathematics and its applications 71, Springer-Verlag, New York, 1995, pp.169-181.
License
Copyright (c) 2010 Lina M. Rangel Martínez, Jorge A. Alvarado Valencia
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.
