# A State Dependent Chat System Model

### Per Enqvist, Göran Svensson

#### Abstract

The main purpose of this paper is to introduce a model of a chat based communication system, as well as developing the necessary tools to enable resource optimization with regards to a measure of the service quality. The system is modeled by a Markov process in continuous time and with a countable state space. The construction of the intensity matrix corresponding to this system is outlined and proofs of a stationary state distribution and an efficient way of calculating it are introduced. A numerical example for system optimization when the service measure is the average sojourn time is included as well as a heuristic algorithm for quicker solution generation.

Download#### Paper Citation

#### in Harvard Style

Enqvist P. and Svensson G. (2019). **A State Dependent Chat System Model**.In *Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-352-0, pages 121-132. DOI: 10.5220/0007391001210132

#### in Bibtex Style

@conference{icores19,

author={Per Enqvist and Göran Svensson},

title={A State Dependent Chat System Model},

booktitle={Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2019},

pages={121-132},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007391001210132},

isbn={978-989-758-352-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - A State Dependent Chat System Model

SN - 978-989-758-352-0

AU - Enqvist P.

AU - Svensson G.

PY - 2019

SP - 121

EP - 132

DO - 10.5220/0007391001210132