I am trying to find the time $T$ between two job completions in a G/G/1 queue. I derived the following expression:
\begin{equation} E[T] = \rho \cdot E[S] + (1-\rho)(E[A'] + E[S]), \end{equation}
where $\rho$ denotes the utilization of the server, $S$ the service time and $A'$ the time until arrival of the next job. However, I have no clue how to compute $E[A']$, since the interarrival times are not exponentially distributed. The only things I know about the distribution of the interarrival time is the mean and the squared coefficient of variation. Can anyone help me out? Thank you in advance!