Renewal Reward Process With Uncertain Interarrival Times and Random Rewards

Abstract

Renewal reward process is used to measure the cumulative occasional rewards up to some given time. So far, two basic types of renewal reward processes with only random parameters or with only uncertain parameters have been proposed. This paper aims at proposing a new type of renewal reward process, which has uncertain interarrival times and random rewards in the framework of the chance theory. The chance distribution of such an uncertain random renewal reward process is obtained, and the reward rate is derived. A renewal reward theorem is verified to show that the reward rate converges in distribution to an uncertain variable, which is highly related to the interarrival times and the expected values of random rewards.