In this paper, we consider traffic offloading of integrated low earth orbit (LEO) satellite-terrestrial network. We first derive traffic offloading probability from the terrestrial network to the LEO satellite network based on the instantaneous radio signal strength. Then to overcome limited coverage and also traffic congestion of the terrestrial network, we design an optimal satellite network in which the minimum number of LEO satellites maximizes the traffic offloading probability, while probability of a generic LEO satellite being idle is close to zero. Since the satellite network is optimized regarding the intensities of the base stations (BSs) and the users, it can control the terrestrial traffic. Numerical results show that an appropriate number of LEO satellites overcomes the limited coverage in a region with low intensity of the BSs and also the traffic congestion by controlling the traffic in a region that the intensity of the users increases.
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