Second-order Markov reward models driven by QBD processes

作者：Bean Nigel G; O' Reilly Malgorzata M; Ren Yong

来源：Performance Evaluation, 2012, 69(9): 440-455.

DOI：10.1016/j.peva.2012.05.002

• Reward model
• Quasi-birth-and-death (QBD) process
• RG-factorization
• Brownian motion

Second-order reward models are an important class of models for evaluating the performance of real-life systems in which the reward measure fluctuates according to some underlying noise. These models consist of a Markov chain driving the evolution of the system, and a continuous reward variable representing its performance. Thus far, only models with a finite number of states have been studied. We consider second-order reward models driven by Quasi-birth-and-death processes, a class of block-structured Markov chains with infinitely many states. We derive the expressions for the Laplace-Stieltjes transforms of the accumulated reward and demonstrate how they can be efficiently evaluated. We use our results to analyse a simple example and, in doing so, show that the second-order feature can make a significant difference to the accumulated reward. The inclusion of the second-order feature also creates new difficulties which require the development of new conditions in the analysis.

• 出版日期2012-9