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.