Hitting time in Erlang loss systems with moving boundaries

Nilsson, Martin (2014) Hitting time in Erlang loss systems with moving boundaries. Queueing Systems, 78 (3). pp. 225-254. ISSN 1572-9443

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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+O(√ρ). The solutions are computationally efficient, and simulations confirm the theoretical results.

Item Type:Article
Uncontrolled Keywords:Mathematics Subject Classification Primary: 60K25 Queueing theory, 90B22 Queues and service; Secondary: 60J80 Branching processes First passage time, Spectral decomposition, Charlier polynomial, Hermite function, Diffusion Colored noise
ID Code:5783
Deposited By:Martin Nilsson
Deposited On:29 Dec 2014 13:15
Last Modified:29 Dec 2014 13:15

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