###### Abstract
More exactly, the ISLs are used to assist in the data download process by scheduling packets between different feeder links, thus achieving better load balancing. A MFMC routing algorithm is presented to calculate routes for traffic demands. Two linear programs (LPs) are required by the routing algorithm, the first LP finds a maximum flow between the visible satellites, and the second LP minimizes the routing cost given a fixed maximum flow. The above process is repeated until all capacities of feeder links are completely utilized, or until all data from visible satellites can be downloaded to the ESs. In this case, the increased packet delay or packet loss rate caused by a long queue of data in those feeder links with insufficient bandwidth can be alleviated. At present, many routing algorithms have been proposed to solve the problem of data transmission on LEO satellite networks. In 2001, [PERSON] et al. depicted the network structure of the satellite as a virtual logical topology [4]. By introducing virtual topology, the high dynamic of satellite network can be masked when calculating the route, so that the lightweight goal of routing algorithm can be achieved. Using this work as a foundation, [PERSON] improved the traditional method and proposed a better link connection strategy between satellites to resolve the asynchronous switches caused by the phase difference between satellite orbit planes [5]. Afterwards, [PERSON] et.e. proposed a temporary netgrid model to describe the topology of LEO satellite networks, and utilized the shortest path calculation between grids instead of the shortest path calculation between satellite nodes to make the routing algorithm more efficient [6]. Furthermore, aiming at the challenges of routing protocol convergence and network maintenance in software defined satellite networks, an elastic routing framework is proposed to establish a stable forwarding path  
Figure 1: (**a**) Geometrical representation of a LEO satellites network system. (**b**) Schematic diagram of beam coverage. for signaling in Ref. [7]. To find the best method for forwarding a packet in the LEO satellite network, [PERSON] et al. proposed a new routing protocol named GomHop in which the packet is forwarded to the target orbit as soon as possible [8]. Nevertheless, none of these studies have ever taken into account the feeder links' constrained capacity, which is a significant bottleneck for the throughput of the LEO constellation networks. In order to increase system throughput, we investigate in this paper how to employ the ISLs to fully use the feeder link. To increase the throughput of the LEO satellite network, feeder link resources must be utilized effectively. In 1996, [PERSON] et al. first modeled the Satellite Range Scheduling Problem (SRSP) for time window allocation between satellites and ground stations, when satellites need to transmit data to the ground, and developed an automated scheduling module using mixed-integer programming [9]. In 2004, [PERSON] et al. independently proposed the Single-Resource Range Scheduling (SiRRS) based method and the Multi-Resource Range Scheduling (MuRRS) based method after thoroughly examining the SRSP problem [10]. ISLs-based methods for downloading data to ESs have been proposed in recent years. In Ref. [11], [PERSON] et al. considered that the traditional satellite scheduling algorithms have very limited improvement on the system throughput due to the inconsistency between the amount of data to be downloaded and the contact time of the satellite. Therefore, a data downloading scheme based on ISLs is proposed to make the satellite download more data during the contact time. On this basis, [PERSON] et al. proposed an iterative optimization strategy to calculate the data transmission demand between satellites according to the length of contact time of each satellite, and modeled the data offloading between satellites as a bipartite graph maximum matching problem in Ref. [12]. In Ref. [13], [PERSON] et al.