We consider an extension to the restless multi-armed bandit (RMAB) problem with unknown arm dynamics, where exogenous global Markov process governs rewards distribution of each arm. Under state, evolves according Markovian rule, which is non-identical among different arms. At time, a player chooses out $N$ arms play, and receives random reward from finite set states. The are restless, that is, ...

It is well known that various characteristics in risk and queuing process can be formulated as Markov Renewal function. We study the max-position of finitely many Markov Renewal Reward process with countable state space. We define Markov Renewal equation associated with max-posed process. The solutions of the Markov Renewal Reward equation are derived and the asymptotic behaviors of the equatio...