An algorithm of bandwidth increment capture based on martingales with statistical delay QoS constraints for mine mobile robots

In the communication scenario of mining mobile robots, statistical delay quality of service (QoS) guarantee is particularly critical. The traffic carried by robots is the interweaving of heterogeneous flows and imposes extremely strict requirements on delay reliability. The reliability provisioning depends directly on the reasonable allocation of network bandwidth. In this paper, an elegant delay performance analysis framework is constructed and a bandwidth increment capture scheme is designed. The queuing system with aggregated traffic, which consists of an independent identically distributed flow and a bursty flow, is introduced. Based on martingale theory and queuing theory, a modularized modeling method of heterogeneous arrivals is proposed. The arrival-martingale process is defined. The martingale parameters are determined by considering the heterogeneous stochastic features of flows, which can reveal the impacts of complex arrival behavior on delay performance and facilitate the modeling of aggregated traffic. A delay-related martingale process is defined, and a special stopping time event about delay violation is observed. A new system stability condition is constructed in the martingale domain. Further leveraging the stopping time theory of martingales, rigorous probabilistic bounds for delay violations of the aggregated traffic are derived. Based on the theoretical delay analysis, an optimal problem of the bandwidth increment capture is formulated under statistical delay QoS constraints. The bandwidth increment is obtained using the bisection search method, which decouples QoS provisioning from bandwidth demands while considering the randomness of aggregated traffic. The tightness of the derived upper bound of delay violation probability is highlighted by comparison with state-of-the-art methods. The universality and availability of the martingale-based delay analysis framework are validated under five representative arrival models, including the Markov-modulated on–off process, the Poisson process, the Markov-modulated Bernoulli process, the interrupted Bernoulli process, and the Markov-modulated Poisson process. The effectiveness of the proposed bandwidth increment capture algorithm in guaranteeing delay QoS requirements is demonstrated.