# Simulation-Based Optimization of Transport Efficiency of an Urban Rail Transit Network
## 2 Calculation Method of Transport Efficiency
### Double Time Penalty Method  
1. System input  
In order to quantitatively study the shadow efficiency, the input and output of the system must be calculated. The cost of the rail transit network, stations, vehicles, and vehicle kilometers is shown in Table 1:  
Value description: the unit conversion cost of the network, station, and vehicle is calculated by multiplying its own unit cost by the annual interest rate of 5%. The total operating cost per running kilometer of each vehicle includes service cost, maintenance cost, and management cost. The time value is calculated according to the average wage in Beijing (CNY 36/hour), which means CNY 0.01/s.  
2. System output  
The main product provided by the urban rail transit system is the displacement of passengers. Passengers are most concerned about the number of passengers served by the system, the total travel time spent on rail transit, the reliability of arrival time, and other service quality indicators such as safety and comfort. Since a high level of punctuality and safety of urban rail transit under normal circumstances has been realized, and it is difficult to determine the comfort index, this paper focuses on the number of passengers transported by the system and the total travel time of passengers. When the number of passengers served is large and the total travel time is short, a new method is required to take the two indexes into account comprehensively.  
Generally speaking, urban rail transit has the most direct competition and substitution relationship with traditional public transport on the ground. The newly attracted passenger flow of urban rail transit is mainly transferred from buses (at present, the effect of attracting passenger flow from passenger cars is relatively limited in China). According to relevant research, the average travel speed of buses in big cities in China is only 15-18 km/h, while the average travel speed of urban rail transit can reach 30-35 km/h. It can be considered that a subway train travels at roughly twice the speed of buses. In other words, if a passenger abandons rail transit and opts for land transport, the travel time may be doubled.  
Based on the above analysis, this paper proposes that when some passengers of the urban rail transit system give up using rail transit because of capacity limitation, operation  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Character** & **Unit Cost** & **Unit Conversion Cost** \\ \hline Network & Underground (CNY/km) & 1,000,000,000 & 136,900 \\  & Elevated (CNY/km) & 300,000,000 & 41,000 \\  & Underground (CNY/station) & 200,000,000 & 27,300 \\  & Elevated (CNY/vehicle) & 100,000,000 & 13,600 \\  & Type A (CNY/vehicle) & 12,000,000 & 1600 \\  & Type B (CNY/vehicle) & 8,000,000 & 1000 \\  & Running kilometer (CNY/vehicle kilometer) & - & 16.74 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Cost of urban rail transit.  
interruption or other reasons, their travel time should be doubled, which is called \"double time penalty\". The \"double time penalty method\" is used in this paper to calculate total travel time, which solves the problem of two unified indexes by converting the number of people into travel time. The \"total travel time savings\" obtained by passengers can be regarded as the total utility provided by the urban rail transit network system to passengers.  
The specific method for calculating the total travel time by the \"double time penalty method\" is as follows:  
\[T_{total}=\sum T_{s}+\sum T_{p} \tag{1}\]  
where \(T_{total}\) is the total travel time generated by transport services provided by the system, and \(\sum T_{s}\) is the travel time of passengers who are served by the system.  
\(\sum T_{p}\) is the travel time of passengers who should have been served but did not, which can be calculated by:  
\[\sum T_{p}=\sum t\cdot 2 \tag{2}\]  
where \(t\) is the Actual travel time of the same OD passengers in the rail network.