Journal of Applied Mechanics Reviews and Reports

Stochastic Modeling and Identification of Spatio Temporal Arrival Processes in SMAP(t)/M/c/c Queueing Systems

Abstract

Sihem Saadi and Amar Aissani

This study addresses the stochastic modeling and identification of spatio-temporal arrival processes in queueing systems. We introduce a novel point process frame- work for characterizing customer arrivals in both space and time domains, cou- pled with a Bayesian inference methodology for robust parameter estimation. Our approach explicitly models the interdependence between arrival timings and spa- tial locations while quantifying parameter uncertainty. Specifically, we develop the SMAP(t)/M/c/c queue model, incorporating a Spatially-Marked Arrival Process with time-varying service rates and finite capacity constraints. Validation using empirical queue datasets demonstrates the model’s efficacy in capturing complex spatio-temporal arrival patterns. This research advances space-time queueing the- ory with applications in transportation networks, telecommunications, healthcare systems, and environmental monitoring

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