A State Dependent Chat System Model

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.