Moment-Based Approximations for the Moments of a Renewal-Reward Process with Asymmetric Triangular Distributed Interference of Chance

This paper presents an effective approximation for the n^th order moments of the ergodic distribution of a renewal-reward process X(t) with asymmetric triangular distributed interference of chance. Many studies have investigated these processes and proposed asymptotic results in which they represented the remaining terms after the second or third term by big Oh (O) or small oh (o) notations. This method does not clarify how these terms convergence to zero. To overcome the ambiguity of the asymptotic expansion we propose approximation formulas to compute n^th order moments of the ergodic distribution of the considered process based only on the moments of random variables that produce the renewal process. The proposed approximation provides closed-form expression and can be used when the distribution functions of the random variables that produce the renewal process are unknown. Furthermore, a simulation study has been conducted to validate the proposed approach, demonstrating its high accuracy across a wide range of parameter configurations.