The objective of this paper is to develop a stochastic inventory system model under the so-called continuous-review <Q,r> policy with a Poisson one-at-a-time demand process, iid customer inter-arrival times {Xi}, backorders allowed, and constant procurement lead time $gamma$. The distributions of the so-called inventory position process {$IP_{(t-r)}$} and lead time demand process {$D_{(t-r,t)}$} are formulated in terms of cumulative demand by time t, {$N_t$}. Then, for the long-run expected average annual inventory cost expression, the "ensemble" average is estimated, where the cost variations for stock ordering, holding and backorders are considered stationary.