We consider a two-echelon, continuous review inventory system under Poisson demand and a one-for-one replenishment policy. Demand is lost if no items are available at the local warehouse, the central depot, or in the pipeline in between. We give a simple, fast and accurate approach to approximate the service levels in this system. In contrast to other methods, we do not need an iterative analysis scheme. Our method works very well for a broad set of cases, with deviations to simulation below 0.1% on average and below 0.36% for 95% of all test instances. 
On two-echelon inventory systems with Poisson demand and lost sales