## 2 System Model  
We consider that a very large number of clustered devices are under the coverage of \(K\) LEO satellites, then, following the related literature, we focus on the uplink, where most of the data traffic is concentrated and where contention can be very high. Devices transmit data packets to the satellites following a simple slotted Aloha policy [20]. Although this is out of the scope of this work, the LEO satellites can forward the data to an Earth station in a following phase. Moreover, we assume that there is minimum, if any, coordination among satellites, so that they do not exchange information among them regarding the received messages. The channel between the devices and the satellites is modelled considering on-off fading [36; 38], so that the satellites perceive a given erasure probability \(\varepsilon_{k},k\in\{1,2,...,K\}\). The erasure probabilities \(\varepsilon_{1},\varepsilon_{2},...,\varepsilon_{K}\) depend on the position of the satellite with respect to the cluster of IoT devices. Note that the on-off fading model has been extensively used in the analysis of Aloha-based multiple access schemes, as for instance in [15; 23; 25; 33; 36]. Such model describes well the behavior of channels whose losses are mainly dominated by fading and short-term blocking due to the presence of obstacles [33; 36], as in the case of IoT applications supported by end-devices transferring data via LEO satellites. Moreover, the on-off fading model brings the bonus of mathematical tractability, without loss of generality. We use the term position to refer to the continuous segment within the satellite's trajectory where the erasure probability does not vary significantly, while we call iteration the time it takes for a LEO satellite to transit from one position to the next. Then, the positions associated with a satellite constellation with respect to a cluster of IoT devices are the set of all those in which at least one satellite of said constellation is visible to the cluster. Thus, the first position is that in which the first satellite is seen, and the last position is the one in which the last satellite is seen before disappearing from the cluster range. Moreover, every passing of the satellite constellation over the IoT cluster is termed a lap. Since the satellites may be in different positions with respect to the IoT cluster, it is natural to assume that the erasure probabilities may be different at the different satellites. For the sake of simplicity, we assume that there is a finite number \(n\) of different erasure probabilities experienced by the satellites, such that \(\epsilon_{k}\in\{\epsilon_{1},\epsilon_{2},\cdots,\epsilon_{n}\}\). Moreover, also for the sake of simplicity, we assume that every segment associated with the different positions has the same length and then all iterations are of equal duration. Each iteration is associated with a fixed angular variation \(\Delta\theta\), such that the number of positions located around the Earth is equal to \(\frac{360^{\circ}}{\Delta\theta}\). Finally, note that the lowest erasure probability happens at the position associated with the zenith, and the highest erasure probabilities are associated with positions close to the horizon. Unlike [36], where all satellites perceive the same erasure probability (which would only happen if orbiting together or very close to each other), in this paper we exploit a model where the erasure probability depends on the satellite's orbital position with respect to the cluster of IoT devices. In order to determine the impact of the satellite constellation design on the system performance, we consider different topologies, given according to a fixed _spacing_\(s\in\{0,1,2\cdots 9\}\), in number of positions, between consecutive satellites. **Example 1**.