# Improving the Functional Reliability of an Urban Public Transport Line
## 3 Results and Discussion
### Anticipated Occasional Overloads
#### 3.1.2 Numerical Experiment
Let us also admit that from the moment the passengers show up at the boarding stop in an estimated period \(\Omega_{d}=60\) min, the use of the line is of interest to the users. A longer duration would direct them either to other public transport offers or to walking (for their destinations, with times less or like \(\Omega_{d}\)). We assume that the 14 trams can be dispatched successively at an average interval of \(\tau_{u}=3\) min, higher than the boarding time of \(q\). \(\gamma=300\) passengers/tram (the trams are equipped with double doors and a lowered floor). It follows that this rate of dispatching of the 14 trams can be maintained for a duration of \(14\times 3=42\) min. According to Equation (18), the additional number of trams, \(\Delta N^{\prime}\), arrives in B from line I at the interval \(\overline{I^{\prime}_{I}}=75/6\) min. However, the additional trams \(\Delta N^{\prime}=\)3 trams can be dispatched in the same \(\tau_{u}=\)3 min. It means that, for a duration of \(\Delta\Omega_{d}=51\) min (according to Equation (17)) the number of 17 trams is dispatched at the interval of 3 min. Since \(\Delta\Omega_{d}>t^{\prime}\), it means that in end-stop B there are at least 3 trams to continue the 3-min pace of dispatches, in the remaining period \(\Omega_{d}-\Delta\Omega_{d}=9\) min. In conclusion, during the proposed outgoing flow period, \(\Omega_{d}\), the offer of the operator of the two lines makes it possible to take over a maximum of \(20\times 300=6000\) passengers (when the load level is \(\gamma<\gamma_{c}\)). The performance of the service is assured by correct management of dispatches; that is, by ensuring the planned load degree of the transport capacity of each tram (\(q\). \(\gamma\)). It should be noted that even after the expiration of the \(\Omega_{d}\) period, using the same active fleet, the same pace of dispatches can be maintained (especially since \(\overline{I^{\prime}_{I}}\) is gradually reduced to 7.5 min, by putting into circulation the number \(\Delta N^{\prime}\) of trams). Since the trams of lines I and II are identical, to avoid the frustrations of the differential pace of advancement of passengers waiting to board the two lines (corresponding to lines I and II), it is possible to maintain the same alternation of dispatches (every 6 min) to \(m_{1}\), respectively, B. That is the same number of dispatches to the two destinations. The total volume of passengers is the same. The invoked equity of the pace of advancement of the two boarding lines can also be achieved by allocating distinct platforms to each line (Figure 7). Boarding the tram of line I is performed simultaneously with boarding the tram of line II. The same number of terms are dispatched at the interval \(\tau_{u}^{\prime}=4\) min, which means that a headway on the common route is of 2 min and results in 7 trans being dispatched to B and the same number of 7 trans being dispatched to \(m_{1}\), for 28 min (according to note a), of the Equation (4). During this time, 2 other trans arrive from A to B, which means that in total 16 trans are dispatched in 32 min from B. Then (after these 16 trans dispatching) the following terms from A arrive in B at minutes 37.5 and 50, and from \(m_{1}\) at minutes 45, 49, 53, 57 (before 60, which it assumed to be the end of the \(\Omega_{d}\) period). Thus, there are additional 6 trans, for which the schedule and destination could be set according to the length of the queues in B platforms. These 22 trans can carry the maximum possible volume of dispatching of 6600 passengers (with the degree of loading \(\gamma<\gamma_{c}\)). Figure 8 illustrates the dynamics of the outgoing flow's requests from the arrival of the first applicants in the boarding area of A stop, until the moment \(\Omega_{\text{sos}}\).