A Note on the Correspondence Pattern for Ordinary People

DOI

10.2991/ammsa-17.2017.42How to use a DOI?

Keywords

M/M/1 queue; last in first out; waiting time; tail probability; Laplace transforms

Abstract

This paper focuses on the problem of modeling the correspondence pattern for ordinary people. Suppose that letters arrive at a rate and answered at a rate . Furthermore, we assume that, for a constant T, and the remains are answered in last in first out order. Let W_n be the waiting time of the n-th answered letter. It is proved that W_n converges weekly to W _T, a non-negative random variable which possesses a density with power-law tail when = and with exponential otherwise. Note that this may provide a reasonable explanation to the phenomenon reported by Oliveira and Barab si in [16].

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Feng Wang
AU  - Xianyuan Wu
PY  - 2017/05
DA  - 2017/05
TI  - A Note on the Correspondence Pattern for Ordinary People
BT  - Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017)
PB  - Atlantis Press
SP  - 195
EP  - 199
SN  - 1951-6851
UR  - https://doi.org/10.2991/ammsa-17.2017.42
DO  - 10.2991/ammsa-17.2017.42
ID  - Wang2017/05
ER  -