Original title: Erlang Loss Model with Energy Constrained Servers
Elijah Kulikov, Eliezer Fuentes-Quezada, Jamol Pender · September 2026
Think of a service center where every worker uses a battery that runs out. The researchers studied a system where servers shut down when their energy drains. While recharging to full battery, these servers cannot help anyone. If a new customer arrives when every single server is busy or recharging, that customer is turned away and lost immediately. The researchers built a mathematical model to track both the busy servers and recharging servers over time. They figured out exact formulas to calculate how often customers get turned away. They discovered that the system only cares about the average service and recharge times. The specific shapes of the time distributions do not matter at all.
Imagine a busy café where baristas need to take recharging breaks. If all baristas are either making drinks or recharging, customers have to leave without being served. The hard part is predicting how many customers are lost without knowing exactly how long each drink takes or how long each break lasts. In this paper, the servers are like baristas with battery-powered tools, and the model shows that the loss rate depends only on the average drink time and average break time, not their variation.
This helps in designing networks or data centers with battery-powered servers. Engineers can predict customer loss rates using just average service and charge times, simplifying system management.
The work is limited to a specific queueing model with energy constraints. It does not address systems with multiple energy sources or non-Markovian processes. The insensitivity result applies only to the M/G/k/k queue with stochastic charging, as stated in the abstract.
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Erlang Loss Model with Energy Constrained Servers — Elijah Kulikov, Eliezer Fuentes-Quezada, Jamol Pender
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.