# An Electric Fence-Based Intelligent Scheduling Method for Rebalancing Dockless Bike Sharing Systems
## 2 Methodology
### The Definitions of Intelligent Scheduling Objectives
#### 2.3.1 Mean Utilization (_Mui_)  
The _MU_ is the average service ratio of bikes and represents the average number of bikes used in a specific time, such as an hour, as expressed in (1).  
\[MUI=\frac{\sum_{i=1}^{N_{B}}s_{Bi}}{N_{B}} \tag{1}\]  
where \(N_{B}\) is the total number of bikes and \(s_{Bi}\) is the number of times that the \(i\)th bike is used in a period of time.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(N_{P}\) & the number of users \\ \hline \(S_{P}\) & \(S_{P}:(s_{h},s_{P2},\ldots,s_{Pi},\ldots,s_{Np_{P}})\) the states of the users (\(s_{Pi}\) denotes the number of times that the \(i\)thbise used in a period of time) \\ \hline \(V_{P}\) & the walking speed of a user \\ \hline \(T_{P}\) & the maximum walking time that can be accepted by users during a ride \\ \hline \(N_{B}\) & the number of bikes \\ \hline \(S_{B}\) & \(S_{B}:(s_{B1},s_{B2},\ldots,s_{B1},\ldots,s_{BN_{B}})\) the states of the bikes (\(s_{Bi}\) denotes the number of times that the \(i\)th bike is used in a period of time) \\ \hline \(V_{B}\) & the speed of a bike \\ \hline \(N_{R}\) & the number of electric fences \\ \hline \(S_{R}\) & \(S_{R}:(s_{R1},s_{R2},\ldots,s_{Ri},\ldots,s_{RN_{B}})\) the states of the electric fences: \(s_{R1}\) is the state of the target electric fence (\(s_{R1}\) represents the total number of bikes dispatched from the dispatch electric fences); \(s_{R2},\ldots,s_{Ri},\ldots,s_{RN_{B}}\) represent the states of the dispatch electric fences (\(s_{Ri}\) represents the total number of bikes dispatched to the target electric fence from the \(i\)th electric fence). The initial states of the electric fences are (0, 0, \(\ldots\), 0) \\ \hline \(a_{R}\) & \(a_{R}:(a_{R1},a_{R2},\ldots,a_{Ri},\ldots,a_{RN_{B}})\) the actions of the electric fences: \(a_{R1}\) is the action of the target electric fence (\(a_{R1}\) represents the number of bikes dispatched to the target electric fence ); \(a_{R2},\ldots,a_{Ri},\ldots,a_{RN_{B}}\) represent the actions of the dispatch electric fences (\(a_{Ri}\) represents the number of bikes dispatched from the \(i\)th dispatch electric fence). The initial states of the actions are (0, 0, \(\ldots\), 0). Since the bikes entering the target electric fence come from other dispatch electric fences, we have \(a_{R1}+a_{R2}+\ldots+a_{RN_{B}}=0\) \\ \hline \(D_{w}\) & the distance from the departure location to the destination \\ \hline \(t_{w}\) & the time it takes for users to walk from the departure location to the destination, \(t_{w}=D_{w}/V_{P}\) \\ \hline \(D_{g}\) & the distance from the departure location to the nearest available bike \\ \hline \(t_{g}\) & the time it takes for users to find an available bike, \(t_{g}=D_{g}/V_{P}\) \\ \hline \(D_{r}\) & the distance from the nearest available bike to the target electric fence \\ \hline \(t_{r}\) & the time it takes for users to ride from the closest bike to the target fence, \(t_{r}=D_{r}/V_{B}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The mathematical model of a bike sharing system.  
Assuming that there are \(N_{P}\) users in the system, \(s_{Pi}\) denotes the number of times that the \(i\)th user wants to use the bike in a period of time. Then, the total number of times all bikes are used in a certain period of time is \(\sum_{i=1}^{N_{P}}s_{Pi}\), so (1) can be rewritten as:  
\[MUI=\frac{\sum_{i=1}^{N_{P}}s_{Pi}}{N_{P}} \tag{2}\]