Abstract: International Journal of Blockchain Applications and Financial Technology

Abstract:
This study addresses the stochastic modeling and identification of spatio-temporal arrival processes in queue ing systems. We introduce a novel point process frame- work for characterizing customer arrivals in both space and time domains, coupled with a Bayesian inference methodology for robust parameter estimation. Our approach explicitly models the interdependence between arrival timings and spatial 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 arriv al patterns. This research advances space-time queueing theory with applications in transportation networks, telecommunications, healthcare systems, and environmental monitoring.