Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance

Abstract This study investigates the renewal reward process under the assumption that the random variables describing the discrete interference of chance follow a generalized gamma distribution. A moment-based approximation method is employed to derive novel results for the renewal function, enabling an approximation of the ergodic distribution of the process. Furthermore, the limiting distribution of the ergodic distribution is also derived. The theoretical findings are illustrated through a specific example in which the demand random variable <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>η</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:math> {\eta }_{1} is represented by a third-order Erlang distribution with parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>θ</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> \theta =1 .