# Modeling of a Coal Transshipment Complex Based on a Queuing Network
###### Abstract  
This article concerns the problem of estimating the throughput and forecasting the operation of a coal transshipment complex that comprises a marine coal terminal and a railway station. Scenario modeling is employed to address this issue. The mathematical model of the transshipment complex has the form of a queuing network, which allows us to take into account the impact of random factors on the arrival of trains and departure of vessels from the system and their handling. In the model, we use the batch marked Markovian arrival process (BMMAP), which allows for the batch arrival of several types of requests, to describe the arrival of different categories of trains. Various queuing systems model particular structural elements of the complex to consider peculiarities of their work. We investigate the coal transshipment complex, which includes one of the largest and most modern coal export terminals in Russia. Based on the results of a numerical study, we estimate its current and maximum throughput, find bottlenecks in the system structure, and forecast its performance after the planned modernization. We also discuss the advantages and limitations of the model presented and its potential extension. mathematical model; queuing theory; bulk terminal; traffic flow; simulation; computational experiment +
Footnote †: journal: Applied  
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operation of the port infrastructure and associated ground transport as a joint system. Such a model should necessarily take into account the impact of random factors (for example, weather) on the vessel movement and loading and unloading operations [1; 2]. Several mathematical models are known to consider the effect of random factors on the operation of maritime transport facilities; these include probabilistic statistical models [3], network models [4], and stochastic programming models [5; 6]. However, since the 1980s, queuing theory (QT) has traditionally been considered the most suitable tool for describing internal logistics operations in a port [7]; in particular, to determine the required fleet of transshipment equipment at the berths of container [8] and bulk marine terminals [9]. Let us note that queuing systems (QSs), as a rule, are not used for modeling individual events [10]. QSs are well suited for studying objects that regularly repeat similar operations, and the incoming material flow and its further processing are stochastic [10; 11]. At the same time, such models can be adapted to almost any transport facility in a relatively short time. Therefore, queueing theory (explicitly or implicitly) formed the basis of many methods and tools for designing marine infrastructure [1; 2; 7]. One of the first significant works concerning the application of QT for marine terminal planning appears to be the article by [PERSON] and [PERSON] [8]. This (and some other papers) deals with simple Markov QSs suitable for analytical research, i.e., single-phase QSs, in which the arrivals and services are stationary Poisson processes. In ref. [9], [PERSON] et al. apply QT to describe the operation of marine bulk terminals intending to handle bulk cargo. The authors use single-phase QSs with stationary Poisson incoming flow and deterministic service time to simulate a vessel loading system. Recent studies (see, for example, [12; 13; 14]) apply a similar approach. When using single-phase QSs with stationary or deterministic Poisson flow, researchers face the fact that the description of the arriving flow and the process of its servicing is unjustifiably simplified. Therefore, to simulate the operation of marine terminals, it is better to use more complex (non-Markov) QSs. [PERSON] [15] and [PERSON] [16] point out that cargo arrives on vessels in batches, so it is advisable to use QS with group request flow. [PERSON] et al. [17] present an approach based on the vacation queue model, which reduces the idle time for external trucks at the gate of the container terminal and internal trucks at the warehouse. [PERSON] et al.