# The Optimal Deployment Strategy of Mega-Constellation Based on Markov Decision Process
## 1 Introduction  
Mega-constellations consist of hundreds or even thousands of satellites providing communication and internet services for global customers with various applying scenarios [1]. Given the optimistic commercial prospects and important strategic positions, there are already many mega-constellation projects deployed to harness the opportunities in the potential customer market, such as Starlink, OneWeb, and Kuiper. Three LEO constellation systems providing broadband service have been compared to introduce the development situation of high-throughput satellites [2]. As more satellites are launched, the orbital resources are more intense due to the low orbital congestion problem and collision possibility [3; 4; 5; 6]. The current status of the LEO environment, as shown as Figure 1, intuitively demonstrates the above problem. When collisions occur during operation periods of satellites, it is important to bring the failure outcome to project owners and stakeholders because the systems cannot provide service anymore [7; 8; 9; 10; 11]. Therefore, it is necessary to launch additional satellites to replenish and make inventory for tge constellations [12]. In [13], [PERSON] discussed the impact of space debris in detail. He demonstrated the risk of the increasing number of debris and proposed a framework to manage the system by considering potential damage. In [14; 15], [PERSON] treated orbital debris as a huge threat to space operations. The future environment needs additional methods to recognize the damages of debris and reduce the hazards of potential orbital debris. Given the launch rate, the satellites' growth would result in random collision and the number density of satellites was above a critical spatial density in LEO. [PERSON] [16] conducted a review of previous collisions through an on-orbit examination of the catastrophic fragmentationconcept. Considering the observational records and the basic assumptions usually in the long-term debris evolution models, they discussed the concept of collision in detail. Based on this work, [PERSON] and [PERSON] [17] made a revision to the collision risk for satellite constellation. They pointed out that the population of debris increased more than 56% of the debris objects in just years and that the next missions would be impacted by the previous launch activities. [PERSON] and [PERSON] [18; 19] analyzed the chances provided by the mega-constellations and demonstrated the space economics through the delivery of world-wide and innovative services. In their work, the potential impact was also studied on the space debris environment due to the huge scale of launch activities. The process of a mega-constellation is full of uncertainty and the demand by customers is also stochastic. In [20], the models of determined and stochastic demand were built to provide a comprehensive review, and, in [21], the optimization method of resources was proposed based on the determined and stochastic model. [PERSON] [22] made a contribution to the multidisciplinary design optimization in the complex system management of satellite constellation. Given all of the stages of the development process, he proposed an overall method for the design and deployment of a satellite constellation. In [23], a staged deployment method was proposed for the uncertainty of demand in the development process of satellite constellations. By deploying the initial stage with a low capability, the next stages could be deployed when the demand increased or the investment was sufficient. The optimal inventory control method was proposed in [24] based on stochastic return flows. The optimal policy of periodic inventory was solved using dynamic programming equations. For performance optimization, the channel characterization is important especially under the uncertain and dynamic circumstances. [PERSON] [25] provided an elaborate overview of channel modeling methods.