# Multi-Satellite Observation-Relay Transmission-Downloading Coupling Scheduling Method
## 2 Problem Description
### Rule-Based Dijkstra Data Transmission Path Scheduling Method
#### 3.4.2 State-Strategy Select Rules  
In the Dijkstra algorithm, the total distance \(d\) determines how the next node is selected from the current node. In conventional routing algorithms, the inter-node distance \(a\) is calculated based on metrics such as transmission delay and remaining bandwidth. In the multi-satellite observation-relay transmission-downloading coupling scheduling problem, the objective function is the total profit of observation and downloading targets. During the data transmission path planning process, the choice of data transmission path affects the electric energy consumption, the occupancy of storage memory, and the occupancy of the satellite-ground data transmission time window, which in turn affects the number of observation and downloading targets, thus impacting the total value of observation and downloading targets. Specifically, when a mission completes the downloading to the ground earlier, more memory and a subsequent data transmission time window become available for transmitting data to other observation targets. Inter-satellite transmission consumes electrical energy, and if a mission completes data downloading by passing through more satellites for inter-satellite data transmission, it will consume more electrical energy for the entire satellite cluster. Based on the analysis, two strategies for calculating total distance \(d\) and inter-node distance \(a\) are proposed: one is the strategy of minimizing the data transmission node number, called the min-node strategy, and the other is the strategy of minimizing the data downloading start time, called the min-download time strategy. The calculation process is introduced below. Firstly, the satellite-cluster state factors are calculated. The state factors of the satellite cluster include a data transmission state factor \(c_{D}\) and an electricity state factor \(c_{E}\). Their formulas are described as  
\[c_{E}=\psi_{E}\min\frac{W_{k}\min}{P_{Camk}+\frac{P_{Camk}\left(\frac{M_{ Lagal}-M_{max}}{M_{e}K_{cam}}\right)}{R_{GramalDataTransk}+\Delta t_{ AttitudeMissink}P_{Attitudek}+c_{SolarConv}(\Delta t_{AttitudeMissink}+\Delta t_{o})P_{Ink}}}, \tag{21}\]  
\[c_{D}=\min\left(\psi_{M}\min\left(\frac{M_{ Lagal}-M_{max}}{M_{e}K_{cam}}\right),\psi_{D}\min\left(\sum\limits_{m=1}^{n_{e}} \sum\limits_{q=1}^{n_{day}}\left(t_{dwebmq}-t_{dwebmq}\right)-\sum\limits_{i=1 }^{n_{e}}\sum\limits_{m=1}^{n_{e}}(t_{dkmi}-t_{dsbmi})\right)\right)\quad z_{ ikm}=1. \tag{22}\]  
In the equation of the electricity state factor \(c_{E}\), \(W_{k}\min\) represents the minimum electric energy of satellite \(k\) during the scheduling period. The denominator of the fraction encompasses the total electric energy consumption for observation, data transmission, and attitude maneuvering for a single mission, where \(\Delta t_{AttitudeMissink}\) is the estimated attitude maneuver time for a single mission, and \(c_{SolarConv}\) represents the loss coefficient of solar array Power. \(\psi_{E}\) represents the electricity influence coefficient. The electricity state factor \(c_{E}\) reflects the abundance of electric energy resources in the satellite cluster. For the data transmission state factor \(c_{D}\), the left term indicates the abundance of memory in the satellite cluster, where \(M_{k\max}\) represents the maximum occupied memory of satellite k during the scheduling period, \(\psi_{M}\) and \(\psi_{D}\) represents the memory and data transmission time window influence coefficient. represents the electricity influence coefficient. The right term indicates the abundance of available satellite-ground transmission time in the satellite cluster. The data transmission state factor \(c_{D}\) reflects the abundance of both available memory and available satellite-ground transmission time in the satellite cluster.