## 3 Models and Preliminaries  
### System Models  
Unlike other public transport carriers, there are no fixed stations for shared bicycles and their location is influenced by the tidal movement of users. Because of the complexity and mass of cycling, the distribution of shared bicycles is unbalanced and is difficult to rebalance, particularly for the shared bicycle with no piles. The importance of a high-efficiency strategy for bicycle dispatching is as follows:  
* Reduce scheduling work and time;
* Alleviate cycling mess;
* Boost users' satisfaction with using shared bicycles. Consider a scenario of shared bicycle system, as shown in Figure 1. With no fixed pile for parking, we conducted a cluster analysis on all cycling travel points, and extracted the central point of the cluster as the travel station that was illustrated by dots in Figure 1.  
The travel stations in Figure 1 are modeled as the vertexes in an undirected graph \(G=(V,E)\), where \(V\) and \(E\) represent all vertex sets and edge sets in undirected Graph \(G\), respectively (\(|E|\geq 1\)). The \(E\) in graph \(G\) represents the paths between the shared bicycle stations, and the weight of \(E\) represents the relationship between the two shared bicycle points connected with them. In addition, a two-tuple \(S_{i}(t)=(num_{i}(t),pred_{i}(t))\) is used to describe the status of station \(i\) at time \(t\)(\(i\in[0,|V|-1]\)). The station status \(S\) includes two parts:  
* The number of bicycles initially in station \(i\) at time \(t\) is defined as \(num_{i}(t)\);
* The Demand of station \(i\) in next period predicted at time \(t\) is defined as \(pred_{i}(t)\). To further describe the imbalance of station \(i\) at time \(t\), we introduce a new parameter \(imb_{i}(t)=pred_{i}(t)-num_{i}(t)\). The unbalanced station in \(G\) are divided into two types: overflow station (\(imb_{i}(t)<0\)) and underflow station (\(imb_{i}(t)>0\)). Next, in order to alleviate unbalanced stations, we assign the dispatching task to operator and users via hybrid dispatching scheme proposed in Section 4 to allocate the excess bicycles in overflow station to other stations that are underflow. Firstly, we delegated some overcrowded dispatching tasks that needed to be dispatched to the operator immediately, which are called manual dispatching. Manual dispatching is direct and fast, which belongs to a macro level of dispatching scheme. Here, we introduce a parameter \(Max\) to describe the overflow threshold of the station, which means when \(num_{i}(t)\geq Max\), the station \(i\) needs to be dispatched immediately by the operator. More details about manual dispatching are shown in Section 4. Secondly, we give users a small number of less urgent dispatching tasks and pay them back rewards recognizing user flexibility and confusion, which are called user incentive dispatching and is a microscopic dispatch. Whether the user recognizes the tasks of dispatching is linked to the circumstance, time, environment, and other conditions of the user. After accepting the dispatch task, the user can choose a midpoint near his destination to park the bicycle, whose midpoint is here called _detour_node_. Taking into account the distance of the user walks, we select _detour_node_ from the adjacent node set of the user's final destination. The adjacent node set of station \(i\) is defined as \(adj^{(i)}\). Node set \(adj\_{low^{(i)}}(t)\) represents the node set in the adjacent nodes of station \(i\) where \(imb_{i}(t)>0\), and is defined as \(adj\_{low^{(i)}}(t)=\{n|num_{n}(t)\leq\ pred_{n}(t),n\in adj^{(i)}\}\). Finally, we create a discrete-time simulation system to analyze the above hybrid dispatching strategy. In our simulation system, trip record data work as the input data and are formed as a quad \(Items=\{t, depart, arrive,if\_detour\}\), where \(t\) is the moment when the trip record occurred, depart and arrive respectively represent the beginning and end of the trip record (\(depart\
eq arrive\)). \(if\_detour\)  
Figure 1: The dispatching model.