Operation_Research_Assignment (10).pdf

This paper investigates the mathematical relationship between buffer system capacity (threshold m) and the number of servers (s) in the context of the IRIDIUM® Low Earth Orbit (LEO) satellite network, utilizing models from queuing theory. Focusing specifically on the (M/M/s) : (F CF S/m/∞) queuing system, the study aims to determine the minimum buffer size required such that the system’s performance closely approximates that of an infinite-capacity queue, a critical consideration for resource-constrained satellite systems. The research first provides a foundational overview of queuing theory, introducing essential notations, performance metrics, and model assumptions commonly applied in telecommunications and space networking. It then delves into the operational specifics of the IRIDIUM® satellite constellation, detailing its hybrid TDMA/FDMA access scheme, spot beam technology, inter-satellite links, and network-level traffic characteristics. Realistic network parameters—such as packet arrival rates, service rates, and traffic intensities—are derived based on published IRIDIUM® technical data. Analytically, the study presents complete derivations for steady-state probabilities, queue lengths, waiting times, and blocking probabilities for both infinite and finite buffer systems. The relationship between buffer threshold m and the number of servers s is investigated via numerical modeling using Python. By plotting key system metrics (queue length, waiting time, system occupancy) against increasing buffer sizes for varying numbers of servers, the research identifies the convergence point (mth) where system performance is indistinguishable from that of an ideal infinite-buffer system. Results show a pronounced non-linear reduction in required buffer capacity with the initial addition of servers in small systems, transitioning to a near-linear relationship (m ≈ s) in larger constellations. These findings are further contextualized with insights from modern reinforcement learning-based network optimization, emphasizing the practical design implications for satellite mega-constellations. The work concludes with actionable recommendations for buffer sizing in satellite communication design, balancing the trade-offs between resource expenditure, packet loss (blocking probability), and service latency. The methodology and code provided are broadly applicable to other multi-server, limited-buffer queuing systems found in both terrestrial and non-terrestrial networks.