## 3 Reference Scenario and Problem Statement  
In this work, we will focus on the application of OEC to EO missions. In this scenario, we have several satellites arranged in different orbital planes. All satellites belonging to the same constellation--that is, to the same EO mission--are assumed to have identical characteristics in terms of processing resources, energy availability, and storage capacity. By taking advantage of ISLs, it is possible to enable communication between pairs of satellites, even displaced on different orbital planes. Notice that in this way it is possible to obtain satellite networks, enabling the data exchange between satellites and the possibility to offload task processing. Finally, we will consider each satellite to have the ability to process data on board thanks to a processing capacity, to store data in an on-board memory, and to have an amount of energy to be dedicated to OEC applications. Moreover, in this work, we consider EO tasks that can be processed either on board the satellite or at a GS, with no difference in functionality or output. In EO missions, services are related to the processing of images acquired by satellites. In particular, every time a satellite flies over a region of interest, it acquires an image which can be processed by the acquiring satellite itself, can be kept in its memory, or can be sent to another node (either a satellite or a ground station). In case data are sent to another node, the receiving node can in turn process the received data, store it in its memory, or send it to another node, and so forth. It is important to underline that in EO missions, just as the service source is always a satellite, the destination is always on Earth; specifically, it is any of the ground stations capable of receiving data, without any distinction among them. In addition, this process is completely known a priori due to the deterministic motion of the satellites that lead to a deterministic EO service. A clarification of the described scenario is given by the example shown in Figure 1, where the satellite \(A\) flies over a region of interest and acquires images. \(A\) can then transfer data to the ground station \(GS_{1}\) passing through satellite \(B\), thanks to the ISL \(A\)-\(B\), leading to a lower delay than the current state-of-the-art operations providing for the satellite \(A\) storing the acquired information in its memory until reaching the point \(A^{{}^{\prime}}\), when it has the possibility of transferring data to ground station \(GS_{2}\). It is also important to underline that, in the scenario, we consider in this work any of the nodes \(A\), \(B\), and \(GS_{1}\) can process the data. This is particularly important in case, for example, the bandwidth on link \(B\)-\(GS_{1}\) is enough to transmit processed data, but not to carry unprocessed data. In this case, by processing on either \(A\) or \(B\), the link \(B\)-\(GS_{1}\) would be able to carry data and, thus, would again allow us to obtain a reduction in the delay in information delivery with respect to the state-of-the-art operations. Figure 1: A generic example of the reference scenario, providing for two satellites (in blue and grey, initially placed in positions A and B) and two ground stations (in red and yellow). In this figure, satellites are moving on the same orbit, but in general they can occupy different orbits, even with a different altitude. After some time, satellite A occupies position A’ (light grey satellite in A). Satellites can communicate with each other by means of optical or radio-frequency ISLs, represented by the black dashed arrow. Instead, communication with the ground is made possible by radio-frequency links, represented by red dashed arrows. From the described scenario, it follows that by designing appropriate strategies to decide how each satellite has to deal with each image at every moment (i.e., to determine whether it shall process it, store it, or transmit it), it would be possible to optimize desired metrics.