This chapter significantly expands the analytical model of DC-like systems by introducing realistic input flows governed by Batch Markovian Arrival Processes (BMAP). These traffic patterns better capture the correlated, bursty, and heterogeneous nature of data in contemporary 5G-IoT infrastructures. The chapter begins with a comparative analysis of BMAP against classical Poisson-based models and proceeds to integrate BMAP flows into queuing systems of varying complexity. Mathematical representations using two-dimensional Markov chains are constructed for both single-channel and multi-channel systems. Specific focus is placed on custom configurations and adaptive queueing policies, enabling fine-grained modelling of service dynamics. The matrix-geometric method is applied to derive stationary distributions and conditional performance measures under constraints such as bounded buffers and blocking rules. Analytical derivations are supported by the use of order statistics to compute upper and lower bounds for response time, variance, and synchronization delay. This rigorous generalization of input models allows for a robust analysis of system behaviour in scenarios where traffic characteristics deviate significantly from ideal assumptions, offering a closer alignment with empirical observations in real-world communication networks.

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DC-Like Systems with BMAP-Flow as a Realistic Platform for Modelling Information and Communication Processes

  • Viacheslav Kovtun

摘要

This chapter significantly expands the analytical model of DC-like systems by introducing realistic input flows governed by Batch Markovian Arrival Processes (BMAP). These traffic patterns better capture the correlated, bursty, and heterogeneous nature of data in contemporary 5G-IoT infrastructures. The chapter begins with a comparative analysis of BMAP against classical Poisson-based models and proceeds to integrate BMAP flows into queuing systems of varying complexity. Mathematical representations using two-dimensional Markov chains are constructed for both single-channel and multi-channel systems. Specific focus is placed on custom configurations and adaptive queueing policies, enabling fine-grained modelling of service dynamics. The matrix-geometric method is applied to derive stationary distributions and conditional performance measures under constraints such as bounded buffers and blocking rules. Analytical derivations are supported by the use of order statistics to compute upper and lower bounds for response time, variance, and synchronization delay. This rigorous generalization of input models allows for a robust analysis of system behaviour in scenarios where traffic characteristics deviate significantly from ideal assumptions, offering a closer alignment with empirical observations in real-world communication networks.