## 4 Intelligent Traffic Load Distribution  
From the analysis in Section 3, we can conclude that the system throughput and the packet loss rate depend on the traffic load offered by the IoT devices and on the uplink erasure probabilities at the satellites. Moreover, from the system model definitions in Section 2, we know that the erasure probabilities at the satellites in each iteration depend on the position of the satellites within the constellation. Consequently, we can deduce that the optimal traffic loads (in terms of system throughput) for each position of the satellite constellation are not the same. Based on this fact, we can predict that a non-uniform traffic load distribution should outperform uniform traffic load distribution in terms of the average system throughput. Note that the cluster of IoT devices can only communicate while some of the satellites within the constellation are visible to the cluster. Assuming a uniform load distribution, the total traffic load, \(G_{T}\), to be offered during a complete lap of the satellite constellation, considering (1), can be written as  
\[G_{i}^{(u)}=\frac{G_{T}}{M}, \tag{11}\]  
where \(G_{i}^{(u)}\), \(i\in\{1,...,M\}\), is the traffic load uniformly distributed per position. With the uniform load distribution in (11), considering both fixed total traffic load \(G_{T}\) and number of satellites in the constellation, topologies with larger numbers of positions \(M\) allocate lower traffic loads in each position; and topologies with less positions have to allocate a higher traffic load to each position. However, such a uniform distribution does not take into consideration the location of the satellites, nor the number of satellites visible to the cluster at each position in the satellite constellation, and therefore limits performance,as in some positions the offered load may be too optimistic or too pessimistic depending on the particular erasure probabilities. In order to increase the average system throughput, we propose an intelligent traffic load distribution (ITLD) strategy, where the system is aware of the overall throughput achievable by the uniform distribution and by a given non-uniform distribution for that total traffic load. In this proposed non-uniform distribution the traffic load offered in each position of the satellite constellation is proportional to the normalized system throughput that would be achieved in the same position with uniform load distribution. The total traffic load in a complete lap is the sum of the traffic load of all the IoT devices. So, in order to achieve a specific traffic load distribution according to the constellation positions, we estimate the load factor \(Q_{i}\) in each position \(i\) of the satellite constellation as  
\[Q_{i}=\frac{\mathcal{T}_{i}\big{(}C_{i}^{(u)}\big{)}}{\sum_{i=1}^{M}\mathcal{ T}_{i}\big{(}G_{i}^{(u)}\big{)}}, \tag{12}\]  
which represents in what proportion each position of the satellite constellation contributes to the overall system throughput, when the traffic load is uniformly distributed. Following the hypothesis that higher performing positions can successfully take on higher traffic load, we propose to use this load factor as the appropriate weight to conveniently distribute the traffic load in a simple and effective manner. Then, the non-uniform traffic load, per position, is defined as follows:  
\[G_{i}^{(mu)}=Q_{i}\,G_{T}. \tag{13}\]  
Finally, to establish a fair comparison between both traffic load distribution strategies, we use the overall system throughput, which is computed as  
\[\mathcal{T}^{(x)}=\sum_{i=1}^{M}\mathcal{T}_{i}\big{(}G_{i}^{(x)}\big{)}, \tag{14}\]  
where \(x=\{u,nu\}\) in the case of uniform or non-uniform distribution strategy, respectively. The implementation and comparison of both uniform and non-uniform distributions are described in Algorithm 1. The erasure probabilities of all the satellite positions visible from the IoT devices cluster are assumed to be known, along with the simultaneous positions visited by the \(K\) satellites of the constellation.