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arXiv · 1912.13067

A Many-Server Functional Strong Law For A Non-Stationary Loss Model

Prakash Chakraborty·Harsha Honnappa
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Abstract

The purpose of this note is to show that it is possible to establish a many-server functional strong law of large numbers (FSLLN) for the fraction of occupied servers (i.e., the scaled number-in-system) without explicitly tracking either the age or the residual service times of the jobs in a non-Markovian, non-stationary loss model. This considerable analytical simplification is achieved by exploiting a semimartingale representation. The fluid limit is shown to be the unique solution of a Volterra integral equation.

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Prakash Chakraborty, Harsha Honnappa. 2019-12-30. A Many-Server Functional Strong Law For A Non-Stationary Loss Model. https://arxiv.org/abs/1912.13067

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