Asymptotic Properties of Alternating Renewal Process with Instantaneous Rewards Suyono- Ibnu Hadi
Depertment of Mathematics, Universitas Negeri Jakarta, Indonesia
Abstract
Consider an alternating renewal process starting at time 0 at up state where to each its uptime and downtime, including the incomplete uptime or downtime, we associate rewards which depend on the uptime and downtime lengths. The total reward earned in the time interval [0,t] is called an alternating renewal process with instantaneous rewards. The distributional properties of this process in the bounded time interval [0,t] is known in the literature. In this paper we derive asymptotic properties of the process. Firstly, we obtain the limit in probability of the process, and secondly, we get the limiting behaviour of the mean of the process. In a special case, when the Laplace transform of the mean of the process is a rational function, we get a finer result of its asymptotic mean.
