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math.PR2026
On Recurrence of the Infinite Server Queue
Sergey Foss, Peter Glynn
This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in t…
math.PR2025
The Law of Large Numbers and CLT for Non-stationary Markov Jump Processes Exhibiting Time-of-Day Effects
Monte Fischer, Peter W. Glynn
In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stati…
math.PR2025
Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime
Jin Guang, Xinyun Chen, J. G. Dai +1
Inspired by Dai et al. [2023], we develop a novel multi-scaling asymptotic regime for semimartingale reflecting Brownian motion (SRBM). In this regime, we establish the steady-stat…