A method of determination of port terminal capacity under irregular cargo delivery and pickup
Keywords:a port terminal, a capacity, irregularity of delivery and pickup of cargoes, service system
There was built up and analyzed a stochastic model of a work of a port terminal that takes into consideration irregularity of delivery and pickup of a cargo. It is supposed that a terminal consists of n interchangeable moorages, in which there is carried out loading to ships. The ships arrive to a terminal to take a cargo independently on each other, their total number is equal to N. Time from departure of any loaded ship to the moment of its arrival to a terminal is a random variable that is distributed according to the exponentional law. All cargoes, that come to a terminal with a help of land transport, are immediately unloaded to a storehouse. It is supposed that a stream of incoming cargoes is described with a model of the compound Poisson process with zero drift. From a storehouse cargoes are loaded to any shipl that is in a moorage, with the rate W. With use of non-standard type of the Markov process with drift for finding of limit join distribution of number of ships, that are in moorages, and amount of cargo, that is in a storehouse, there is got a system of integral-differential equations together with relevant boundary conditions. There is given a method of solving of this boundary-value problem, that is based on use of the Laplace-Stieltjes transformation for getting of a solution in a closed form. It gives a possibility to get simple calculation formulae for assessment of indices of capacity of a terminal: the average number of ships in moorages, the average amount of cargo in a storehouse, possibility of demurrage of ships because of absence of cargoes in a storehouse and etc. There are given examples of practical use of the got theoretical results, namely: a method of calculation of necessary capacity of a storehouse, assessment of a term of recoupment of a project of construction of a terminal. They showed that the worked out method of calculation of capacity of a port terminal in conditions of irregularity of a work of transport can be used in project calculations.
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Copyright (c) 2016 Mykhaylo Postan, Lyudmyla Kushnir
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