Advertisement
Published in:
2020 | OriginalPaper | Chapter
5. The Average Cost Model
Authors : Alexey Piunovskiy, Yi Zhang
Published in: Continuous-Time Markov Decision Processes
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
In this chapter, restricted to the class of \(\pi \)-strategies, we consider the following long-run average cost as the performance measure of the system: for each initial distribution \(\gamma \), \(j=0,1,\dots ,J\) and \(\pi \)-strategy \(S\in \mathbf{S} _\pi \). Recall that the convention of \(c_j(x_\infty ,a):=0\) for each \(a\in \mathbf{A} \) is in use.
$$\begin{aligned} W_j(S,\gamma ):= & {} \mathop {\overline{\lim }}_{T\rightarrow \infty }\frac{1}{T}\mathrm{E}_\gamma ^S\left[ \int _{(0,T]} \int _\mathbf{A } c_j(X(t),a)\Pi (da|t)dt \right] \nonumber \\= & {} \mathop {\overline{\lim }}_{T\rightarrow \infty }\frac{1}{T}\mathrm{E}_\gamma ^S\left[ \int _{(0,\min \{T,~T_\infty \}]} \int _\mathbf{A } c_j(X(t),a)\Pi (da|t)dt \right] \end{aligned}$$