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Hitting time in Erlang loss systems with moving boundaries.

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Title: Hitting time in Erlang loss systems with moving boundaries.
Authors: Nilsson, Martin1 hitting.time@drnil.com
Source: Queueing Systems. Nov2014, Vol. 78 Issue 3, p225-254. 30p.
Subjects: ERLANG (Computer program language), Internet servers, Client/server computing, Queuing theory, Polynomials, Boundary value problems
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 $$\rho $$ is high, and the number of servers scales as $$\rho +O\left( \sqrt{\rho }\right) $$ . The solutions are computationally efficient, and simulations confirm the theoretical results. [ABSTRACT FROM AUTHOR]
Copyright of Queueing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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 $$\rho $$ is high, and the number of servers scales as $$\rho +O\left( \sqrt{\rho }\right) $$ . The solutions are computationally efficient, and simulations confirm the theoretical results. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Queueing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s11134-014-9399-5
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      – TitleFull: Hitting time in Erlang loss systems with moving boundaries.
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