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

Probability 2020-01-01 v1

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.

Keywords

Cite

@article{arxiv.1912.13067,
  title  = {A Many-Server Functional Strong Law For A Non-Stationary Loss Model},
  author = {Prakash Chakraborty and Harsha Honnappa},
  journal= {arXiv preprint arXiv:1912.13067},
  year   = {2020}
}