Modeling of Geographic Greedy Routing in Sparse LDACS Air-to-Air Networks Using Absorbing Markov Chains

L-band Digital Aeronautical Communications System (LDACS) is the selected Air-to-Ground (A2G) technology for future aeronautical communications and a proposed candidate for Air-to-Air (A2A) links. Geographic greedy routing in sparse LDACS A2A networks, typical during gradual system deployment, frequently encounters local minima, necessitating backup mechanisms that are inefficient. Previous research has primarily focused on refining backup mechanisms, neglecting the root cause of geographic greedy routing failures. This paper investigates why geographic greedy routing performance deteriorates in sparse network scenarios, where failures occur more frequently than in dense deployments. We introduce a novel metric to quantify the quality of hop-by-hop forwarding decisions in geographic greedy routing. Furthermore, we develop a second-order absorbing Markov chain model to predict the success ratio and hop stretch factor. The model is validated through Monte-Carlo simulations over the French airspace with varying LDACS equipage fractions, achieving an average difference from simulation results of less than 3.4% for the success ratio and 1.5% for the hop stretch factor. The proposed model demonstrates high accuracy and can be generalized to evaluate other geographic routing protocols. Consequently, the outcomes provide valuable insights toward designing optimized geographic greedy routing protocols.