New Queuing Theory Applied to Port Terminals and Proposal for Practical Application in Container and Bulk Terminals
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 146, Issue 1
Abstract
Queueing theory has been used in port management since the early 60s as a support, among others, to determine the optimal number of berths based on the occupation rate of the berths and the expected waiting time for vessels operating in them. Depending on the type of terminal involved, different authors have provided solutions for various systems. While the equations characterizing some of these systems can be analytically resolved, and it is possible to calculate exact solutions for them, other systems are not resolvable, and only approximate solutions are presented in the form of graphs or tables. In the present work, a simple analytical methodological scheme is presented for one of these systems with approximate solutions () deduced from a system in which the exact analytical solutions exist (). This new approach is proposed to be used in private container terminals without regular services and in bulk terminals in which quasi-constant size vessels arrive.
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References
Agerschou, H. 2004. Planning and design of port and marine terminals. London: Thomas Telford.
Agerschou, H., H. Lundgren, and T. Sorensen. 1983. Planning and design of port and marine Terminals. Chichester, UK: Wiley.
Brockmeyer, E., H. L. Halstrom, and A. Jensen. 1948. Vol. 2 of The life and works of A.K. Erlang: Transactions of the Danish Academy of Technical Sciences. København, Denmark: Akademiet for de Tekniske Videnskabe.
Cosmetatos, G. P. 1975. “Notes approximate explicit formulae for the average queueing time in the processes (M/D/r) and (D/M/r).” INFOR: Inf. Syst. Oper. Res. 13 (3): 328–331. https://doi.org/10.1080/03155986.1975.11731618.
Cosmetatos, G. P. 1976. “Some approximate equilibrium results for the multiserver queue (M/G/r).” Oper. Res. Q. 27 (3): 615–620. https://doi.org/10.1057/jors.1976.120.
Crow, E. L., A. D. Frances, and W. M. Margaret. 1960. Statistics manual with examples taken from ordnance development. New York: Dover.
de Weille, J. 1968. “The optimum number of berths of a port.” In Proc., Working Paper, No 19. Washington, DC: International Bank for Reconstruction and Development.
El-Naggar, M. E. 2010. “Application of queuing theory to the container terminal at Alexandria Port.” J. Soil Sci. Environ. Manage. 1 (4): 77–85.
EPPE (Ente Publico Puertos del Estado). 2012. ROM 2.1. Obras de Atraque y Amarre. Tomos I y II. Madrid, Spain: Organismo Público Puertos del Estado.
Frankel, E. G. 1987. Port planning and development. New York: Wiley.
Fratar, T. J., A. S. Goodman, and A. E. Brant. 1960. “Prediction of maximum practical berth occupancy.” J. Waterways Habours Div. 86 (2): 69–78.
González, J. M. 2006. ROM 2.1: Obras de Atraque y Amarre. Capítulo 3. Criterios de Proyecto. EROM2. Madrid, Spain: Ente Publico Puertos del Estado.
Jagerman, D., and T. Altiok. 2003. “Vessel arrival process and queueing in marine ports handling bulk materials.” Queueing Syst. 45 (3): 223–243. https://doi.org/10.1023/A:1027324618360.
Kendall, D. G. 1948. “On the role of variable generation time in the development of a stochastic birth process.” Biometrika 35 (3/4): 316–330. https://doi.org/10.2307/2332354.
Kendall, D. G. 1951. “Some problems in the theory of queues.” J. R. Stat. Soc. Ser. B (Methodol.) 13 (2): 151–185. https://doi.org/10.1111/j.2517-6161.1951.tb00080.x.
Kendall, D. G. 1953. “Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov Chain.” Ann. Math. Stat. 24 (3): 338–354. https://doi.org/10.1214/aoms/1177728975.
Khintchine, A. 1932. “Mathematisches über die Erwartung vor einem öffentlichen Schalter.” Rec. Math. 39 (4): 73–84.
Kia, M., E. Shayan, and F. Ghotb. 2002. “Investigation of port capacity under a new approach by computer simulation.” Comput. Ind. Eng. 42 (2–4): 533–540. https://doi.org/10.1016/S0360-8352(02)00051-7.
Kimura, T. 1991. “Refining Cosmetatos’ approximation for the mean waiting time in the M/D/s queue.” J. Oper. Res. Soc. 42 (7): 595–603. https://doi.org/10.1057/jors.1991.119.
Kuo, T.-C., W. C. Huang, S.-C. Wu, and P. L. Cheng. 2006. “A case study of inter-arrival time distributions of containers ships.” J. Mar. Sci. Technol. 14 (3): 155–164.
Lindley, D. V. 1952. “The theory of queues with a single server.” In Vol. 48 of Mathematical Proc. Cambridge Philosophical Society, 277–289. Cambridge, UK: Cambridge University Press.
López, I., A. Camarero, V. Negro, and N. González. 2011. “Terminales multicliente vs terminales dedicadas. Estudio del caso del puerto de Valencia.” In Proc., IAME 2011 Annual Conf. of the Int. Association of Maritime Economist. Gavelston, TX : International Association of Maritime Economist.
Nicolau, S. N. 1967. “Berth planning by evaluation of congestion and cost.” J. Waterways Harbours Div. 93 (4): 107–132.
Novaes, A., and E. Frankel. 1966. “A queuing modelling for unutilized cargo generation.” J. Oper. Res. 14 (1): 100–132. https://doi.org/10.1287/opre.14.1.100.
Peña-Zarzuelo, I. 2018. “Historia, Evolución y Perspectivas de Futuro en la utilización de técnicas de simulación en la Gestión Portuaria: Aplicaciones en el análisis de operaciones, estrategia y planificación portuaria.” Ph.D. thesis, Dept. of Economy, Universidade A Coruña.
Plumlee, C. H. 1966. “Optimum size seaport.” J. Waterways Harbours Div. 92 (3): 1–24.
Pollazzek, F. 1930a. “Über eine Aufgabe der Wahrscheinlichkeitstheorie.” Math. Z. 32 (1): 729–750. https://doi.org/10.1007/BF01194620.
Pollazzek, F. 1930b. “Über eine Aufgabe der Wahrscheinlichkeitstheorie II (Mitteilung aus dem Telegraphenteehnischen Reichsamt).” Math. Z. 32 (1): 64–100. https://doi.org/10.1007/BF01194663.
Pollazzek, F. 1934. “Uber dar Waterproblem.” Math. Z. 38 (1): 492–537.
Pollazzek, F. 1952. “Fonctions caractéristiques de certaines répartitions définies au moyen de la notion d’ordre.” C. R. Acad. Sci. 234 (1952): 2334–2336.
Rodríguez, F. 1985. Dirección y Explotación de Puertos. Bilbao, Spain: S.A. Puerto Aútonomo de Bilbao.
Saeeda, N., and O. I. Larsenb. 2016. “Application of queuing methodology to analyze congestion: A case study of the Manila International Container Terminal, Philippines.” Case Stud. Transp. Policy 4 (2): 143–149. https://doi.org/10.1016/j.cstp.2016.02.001.
Smith, W. L. 1953. “On the distribution queuing times.” In Vol. 49 of Mathematical Proc. Cambridge Philosophical Society, 449–461. Cambridge, UK: Cambridge Philosophical Society.
Tsinker, G. P. 2004. Port engineering: Planning, construction, maintenance, and security. New York: Wiley.
UNCTAD (United Nations Conference on Trade and Development). 1979. Port development: A handbook for planners in developing countries. New York: UNCTAD.
UNCTAD (United Nations Conference on Trade and Development). 1985. Port development: A handbook for planners in developing countries. 2nd ed. New York: UNCTAD.
van Vianen, T. A., J. A. Ottjes, and G. Lodewijks. 2012. “Modeling the arrival process at dry bulk terminals.” Transport Engineering and Logistics. Accessed October 18, 2018. http://www.exspecta.nl/wp-content/uploads/2015/10/Modeling-arrival-process-at-dry-bulk-terminals.pdf.
Volberg, O. 1939. “Problème de la queue stationnaire et no-stationnaire.” C. R. (Dokl.) Acad. Sci. URSS 24: 657–661.
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©2019 American Society of Civil Engineers.
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Received: Nov 2, 2018
Accepted: Apr 3, 2019
Published online: Oct 15, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 15, 2020
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