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Hitting time in Erlang loss systems with moving boundaries
When the boundaryâthe total number of serversâin 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 Ï is high, and the number of servers scales as Ï+O(âÏ). The solutions are computationally efficient, and simulations confirm the theoretical results.TH