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arXiv · 2511.07650

Fluid Limits for Time-Varying Many-Server Loss Systems via Discontinuous Volterra Equations

Mingrui Wang·Prakash Chakraborty
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Abstract

This paper develops fluid limits for nonstationary many-server loss systems with general service-time distributions. For the zero-buffer $M_t/G/n/n$ queueing model, we prove a functional strong law of large numbers for the fraction of busy servers and characterize the limit by a nonlinear Volterra integral equation with discontinuous coefficients induced by instantaneous blocking. Well-posedness is established through an appropriate solution concept, yielding the time-varying acceptance probability without heuristic approximations. We then treat the finite-buffer $M_t/G/n/(n+b_n)$ regime, proving a functional strong law of large numbers for the triplet of fractions of busy servers, occupied buffers, and cumulative departures, whose limit satisfies a coupled system of three discontinuous Volterra equations capturing the interaction of service completions, buffer occupancy, and admission control at the capacity boundary. We establish well-posedness and convergence of the time-varying acceptance probability weakly in $L^1$ weighted by the arrival rate, and locally uniformly on the set of times at which the system is not full. Our theoretical results are supported by numerical simulations for both zero and finite-buffer regimes, illustrating the convergence of transient acceptance probabilities guaranteed by our theory. Finally, we use the fluid limits to derive optimal staffing and buffer-capacity for both time-varying loss systems.

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Mingrui Wang, Prakash Chakraborty. 2026-09-19. Fluid Limits for Time-Varying Many-Server Loss Systems via Discontinuous Volterra Equations. https://arxiv.org/abs/2511.07650

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