Erlang Loss Model with Energy Constrained Servers
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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BibTeX
@misc{kulikov2026erlang,
title = {{Erlang Loss Model with Energy Constrained Servers}},
author = {Elijah Kulikov and Eliezer Fuentes-Quezada and Jamol Pender},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01559},
eprint = {2609.01559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01559},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Erlang Loss Model with Energy Constrained Servers
AU - Elijah Kulikov
AU - Eliezer Fuentes-Quezada
AU - Jamol Pender
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01559
UR - https://arxiv.org/abs/2609.01559
AB - 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.
ER -