## 2 Handling Loading Units in an Intermodal Handling Transshipment
### Issues Associated with Waiting Time in Light of the Queuing Theory  
The queuing theory is a field of probability calculus dealing with studying service processes. Based on applied statistics, it helps in assessing the relationship between decisions regarding the production capacity level and important issues associated with efficiency such as waiting time and queue length. The main objective of the theory is developing methods that enable determining the values characterizing a service process and assessing the system operation quality, as well as selecting an optimal service structure. From the perspective of a user, it is important to decide on the system utilization manner [44; 45].  
From the system administrator's standpoint, it is important to determine the conditions for effective system utilization. Searching for possible system operation improvements, e.g., through adding a new service channel or its appropriate reorganization, is often a priority in striving to increase the efficiency of a given system. Mass service systems are composed of such basic elements as request sources, queues, and service equipment. Optimal queue control involves shortening the handling waiting time, which leads to user satisfaction and increased effectiveness of a given system. It is also associated with reducing or expanding of handling station number. In the case of a container terminal, the queue can be shortened in several ways [44]:  
* shortening a transport task lead time inside the terminal (shorter cycle),increasing the number of handling equipment units, which are treated as new handling stations in this case,
* reducing the number of requests.  
The first of the factors is related to the rationalization of assigned tasks. This aspect was discussed in the previous paragraphs. Increasing the number of handling equipment units is a technically simple solution; however, finances are a fundamental barrier against its implementation. Purchasing (owning) another piece of equipment is cost-intensive and should be preceded by other technical activities that enable a fuller utilization of available resources. On the surface, reducing the number of requests within a transshipment system at a terminal can solely entail reduced demand for transshipment services. However, it should be notes that a stream of requests to a handling system also applies to these containers that must be translocated within a given terminal. These orders refer to unproductive moves, i.e., unproductivity reduction. Therefore, shortening the queue of pending requests is associated with adopting an appropriate order execution strategy so that there are as few requests to the system as possible [45].  
A mass service system mathematical functional model is primarily based on the theory of stochastic processes. The occurring random variables and their interpretation are presented in Table 1.  
Mathematical model assumptions define the type of random variable probability distribution, e.g., deterministic, exponential, Erlang or any distribution, independence or dependence of request waiting time and handling time random variables, finite or infinite number of handling stations, queue length, and the handling discipline applicable within a given system [46].