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arXiv · 2609.01559

Erlang Loss Model with Energy Constrained Servers

Elijah Kulikov·Eliezer Fuentes-Quezada·Jamol Pender
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Abstract

In this paper, we study an Erlang-type loss system with energy-constrained servers. Each server is equipped with a finite battery and becomes temporarily unavailable for service when its energy is depleted, entering a charging phase before returning to operation upon full recharge. Customers who arrive to find all servers unavailable are blocked and lost immediately. We characterize the steady-state behavior of this two-dimensional Markov process by extending classical truncation results for Jackson networks to incorporate energy dynamics. This yields a closed-form product-form stationary distribution, from which we derive explicit expressions for the steady-state moments and the blocking probability. Finally, we establish that the corresponding M/G/$k$/$k$ queue with stochastic charging is insensitive to both the service-time and charging-time distributions, depending only on their means. Thus, we extend the insensitivity property of the Erlang loss queue to the stochastic server setting.

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Elijah Kulikov, Eliezer Fuentes-Quezada, Jamol Pender. 2026-09-01. Erlang Loss Model with Energy Constrained Servers. https://arxiv.org/abs/2609.01559

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