User-centric Markov reward model for state-dependent Erlang loss systems

Abstract

Markov reward models are commonly used in the analysis of systems by integrating a reward rate to each system state. Typically, rewards are defined based on system states and reflect the system’s perspective. From a user’s point of view, it is important to consider the changing system conditions and dynamics while the user consumes a service. The key contributions of this paper are proper definitions for (i) system-centric reward and (ii) user-centric reward of the Erlang loss model M/M/n-0 and M/M(x)/n with state-dependent service rates, as well as (iii) the analysis of the relationships between those metrics. Our key result allows a simple computation of the user-centric rewards. The differences between the system-centric and the user-centric rewards are demonstrated for a real-world cloud gaming use case. To the best of our knowledge, this is the first analysis showing the relationship between user-centric rewards and system-centric rewards. This work gives relevant and important insights in how to integrate the user’s perspective in the analysis of Markov reward models and is a blueprint for the analysis of other services beyond cloud gaming while also considering user engagement.