发表机构
Bronx High School of Science（布朗克斯科学高中）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究带能量受限服务器的Erlang型损失系统，扩展Jackson网络截断结果得到闭式平稳分布，证明对应带随机充电的M/G/k/k队列具有不敏感性，将Erlang损失队列的不敏感性扩展到随机服务器场景。
AI 中文摘要
本文研究一种带能量受限服务器的Erlang型损失系统。每台服务器配备有限电池，能量耗尽时会暂时无法提供服务，进入充电阶段，充满电后返回运行状态；到达时发现所有服务器均不可用的客户会被立即阻塞并丢失。我们通过将Jackson网络的经典截断结果扩展以纳入能量动态，刻画了该二维马尔可夫过程的稳态行为，得到了闭式乘积形式的平稳分布，据此推导了稳态矩和阻塞概率的显式表达式。最后，我们证明对应的带随机充电的M/G/k/k队列对服务时间和充电时间分布均具有不敏感性，仅依赖于它们的均值，因此将Erlang损失队列的不敏感性性质扩展到了随机服务器场景。
英文摘要
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.
