Stochastic modelling of delays and buffering in 5G-IoT ecosystems with programmable P4 switches based on BMAP

This study presents a hybrid stochastic model for evaluating delays and buffering in 5G-IoT ecosystems with programmable P4 switches, where traffic patterns exhibit strong batch-like properties. The proposed approach integrates a batch Markovian arrival process (BMAP) with a phase-type service structure and semi-Markov modelling of control-plane interactions, thereby capturing both the temporal variability of IoT traffic and the hybrid nature of routing logic. Analytical expressions for the expected processing time and queue length were derived using extended G/G/1, H₂/H₂/1, M/G/1, and M/N/1 queueing frameworks. Unlike traditional queueing models, the proposed framework is the first to simultaneously incorporate BMAP-driven bursty arrivals, phase-type service distributions, and semi-Markov representation of control-plane interaction dynamics. This integrated design enables more accurate characterisation of real IoT traffic and significantly improves predictive accuracy. The model was validated on real-world traffic datasets, demonstrating that BMAP more accurately reflects the structure of IoT traffic than classical Poisson or MMPP models. Notably, the BMAP-based approach reduced the modelling error by up to 38% compared to Poisson-based approximations and by 22% compared to MMPP-based ones under bursty traffic conditions. Simulation results confirm that increasing the control-plane involvement probability from 0.2 to 0.7, under a fixed average batch size of 12 requests, leads to a 2.6-fold increase in processing delay. Furthermore, the H₂/H₂/1 model showed the highest alignment with empirical data, accurately reflecting the multi-phase service structure and control flow saturation effects. Additional 3D analyses revealed strong nonlinear dependencies of delay on the batchiness factor, dispersion in processing times, and phase asymmetry parameters.