Hitting time in Erlang loss systems with moving boundaries

Abstract

When the boundary—the total number of servers— in an Erlang loss system is a function of time, customers may also be lost due to boundary variations. On condition that these customers are selected independently of their history, we solve for the hitting-time distribution and transient distribution of busy servers. We derive concise asymptotic expressions in the time domain for normal loads in the heavy-traffic limit, i.e., when the offered load ρ is high, and the number of servers scales as ρ+Oρ. The solutions are computationally efficient, and simulations confirm the theoretical results.