A correction term for the covariance of renewal-reward processes with multivariate rewards

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...

Limiting Covariance in Markov-renewal Processes

General additive functions called rewards are defined on a "regular" finite-state Markov-renewal process. The asymptotic form of the mean total reward in [0,t] has previously been obtained, and it is known that the total rewards are joint-normally distributed as t -► oo. This paper finds the dominant asymptotic term in the covariance of the total rewetrds as a simple function of the moments of ...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Renewal Processes with Costs and Rewards

We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the elementary renewal theorem and avoids the technicalities in the proof that is presented in most textbooks. Moreover, we mention briefly the extension of the theor...

Some properties of fuzzy alternating renewal processes

The alternating renewal process is one of the renewal processes in renewal theory. It is widely used in inventory systems and queueing systems. In classical alternating renewal processes, one of the assumptions is that the on times and off times are independent random variables. The notion of a fuzzy set was introduced by Zadeh [1] who defined it as a generalized characteristic function. Recent...