Abstract. This paper considers the mathematical modeling problem of traffic transmission in mobile networks under high user mobility and spatially heterogeneous coverage, including signal degradation (“dead”) zones. Traffic aggregation at the channel level is applied to increase the reliability and stability of data transmission. A Markov model of a communication channel is proposed to study the effectiveness of aggregation algorithms and adapt them to network operating parameters and user velocity. The model is based on a periodic affine motion of a mobile device between base stations (BSs) uniformly distributed along a straight line. Within this model, the concepts of stable coverage zones and transition zones are introduced in terms of the distances to the nearest and next BSs. The channel state is described by a Markov chain with states corresponding to signal quality sampling: stable connection, degraded connection, and disconnection. Transitions between states are governed by a continuous-time Markov process with constant rates, and the parameters of this process are determined from empirical network data. An extension of the model to incorporate the time dependence of channel states is also considered, leading to a semi-Markov framework. For both cases (Markov and semi-Markov chains), explicit expressions are derived for the stationary probabilities of states, and system stability conditions are formulated to ensure bounded traffic queues. In addition, an adaptive control model of the channel throughput is proposed; this model optimizes transmission parameters depending on the current channel state, request queue length, and user velocity. The effectiveness of the approach is demonstrated by numerical simulations: the network has stable performance across a wide range of mobility levels and coverage parameters. The model can be applied to the reliability analysis and optimization of network protocols in highly mobile environments, including high-speed railway transport, vehicle networks, and mobile platforms.
Keywords: mobile networks, Markov model, semi-Markov process, system stability, Laplace transform.
A Mathematical Model of Adaptive Traffic Control in Mobile Networks with Variable Signal Quality