Sample path large deviations for marked point processes in the many sources asymptotic with small buffers: Heavily and lightly loaded systems

2019/02/26 by James R. Cruise, Fraser Daly, Cruise, James R. +3
Mathematics · #60F10 #60G55 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1902.10084

openalex publication_date 2019/02/26 · openalex created_date 2019/03/02 · openalex updated_date 2026/07/28

Abstract

Consider a queueing system fed by traffic from N independent and identically distributed marked point processes. We establish several novel sample path large deviations results in the scaled uniform topology for such a system with a small buffer. This includes both the heavily loaded case (the load grows as N→∞) and the previously unexplored lightly loaded case (the load vanishes as N→∞); this latter case requires the introduction of novel speed scalings for such queueing systems. Alongside these sample path large deviations results, we introduce a new framework to explore the range of scalings in the many sources asymptotic for these systems.

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