Results of the traffic simulation

The average waiting time in queue for one car for each area is presented in following graphs, which are the output of the one-year simulations with three different kinds of noise in arrival time, based on different kinds of probability distributions.

Figure 4. Daily average amount of waiting time in queue for one car from each area in case of ATN1

Figure 5. Daily average amount of waiting time in queue for one car from each area in case of ATN2

Figure 6. Daily average amount of waiting time in queue for one car from each area in case of ATN3

Figure 7. Total number of unserviced cars from each area after the annual simulation in case of ATN1

Figure 8. Total number of unserviced cars from each area after the annual simulation in case of ATN2

Figure 9. Total number of unserviced cars from each area after the annual simulation in case of ATN3

The main trend in all three cases is that for two regions the annual number of vehicles that were forced to return because of the lack of opportunity to get into the company is large enough. It is about 20 for one company and about 100 for another. Based on the data obtained, the obvious conclusion is that the system should be optimized in such a way that these numbers will be small enough. As the optimal result, the total amount of not served cars no larger than ten can be considered.

5 PROBLEM OF DYNAMICS OF THE SYSTEM OF LOADS

5.1 Methodology for solving the problem

The next problem that was raised in this paper relates to the studying of dynamics of the system of loads, where the amount of garbage transported by each region is understood as loads. As in case of a traffic problem, it is logical to assume that the first step in the studying of the features of the system of loads is to formulate the empirical model, that concentrates on the explanation of the processes related to the transportation of garbage.

The model will consider the key factors that affect the total amount of waste that produced by each area and this number will be considered as the output, dynamics of which will be studied under different conditions. The purpose of this study is to analyze the differ-ences between the assumed and really transported amount of garbage as well as to define the dependencies between the components of the system and these differences. Thus, the conditions under which the study will be implemented have to be defined before the fur-ther actions. After these settings, the second step in the target goal realization is similar to the second stage of the solution of the first problem. Quantitative simulations can be used in order to collect the statistics for the required analysis. Moreover, in dependence on the kind of conditions, the simulations can be performed separately for each of them, in case if they cannot be joint under one system or if it is necessary to study the unique effect of each of them on the outcome. As it was considered for the first problem, It is assumed that every simulation that characterizes one working day of the company will be repeated 365 times, providing the statistics for one year of company work.

5.2 Formulation of the empirical model

As in the previous case, the formulation of the main components of the model and their interactions is based on the initial data about the work performed. For the current prob-lem the day schedule Table 3 will be used, however additional information about loads is required. This requirement is raised due to the lack of a sufficient amount of data for comparative analysis. In addition to the aforementioned initial data, the information about the amount of garbage transported for each area during some period can be used in or-der to unor-derstand the real distribution of weights in loads for each region. Based on this data, annual work simulations can be constructed. The major company provided the

infor-mation about the total monthly amount of garbage transported from each region for nine months. Thus, the comparison of the amount of garbage computed as the monthly average of the real data multiplied by twelve months with the output of the simulations based on the real data features can be performed. Moreover, the major company has provided the information about the ”ideal” amount of garbage that is assumed to be transported from each region for one year. In addition, there is knowledge about the maximum loads for each car which is 50 tones. Considering all the information above it is possible to define one more task for data analysis. Comparison of the data related to the expected amount of garbage which is supposed to be transported for one year with the output of simulations realized with using of the information about maximal car loads can be done as well.

The next step is connected with the determination of the important characteristics that will be taken into account during the modelling of the transportation process. Due to the fact that for current problem detailed information related to the interconnections between cars or queue influence on the performance does not have high significance, the system will be concentrated just on the description of the information about the transported amount of garbage. The items that affect this number are the daily schedule of arrival and the loads for each car. Due to the two different sources of initial data for the loads generation, two systems for the simulations will be formulated. The first one will utilize the information about maximum loads for each car during the process of loads generation. The generator for the second system will use initial information about the monthly loads of trucks for nine months to study the distribution of the loads for one car separately for each region.

Resulting loads will be represented by the generated random values that follow this dis-tribution.

In order to approximate the model characteristics to the reality, in parallel with the mod-elling of the dynamics of systems with the conditions described above, simulations which will take into account the possibility of unforeseen circumstances will be performed. As unforeseen circumstances, the impossibility of arriving for some number of cars due to some unpredictable reasons is perceived.