We investigate a fundamental model from open-pit mining which is a cyclic system consisting of an (unreliable) shovel, trucks travelling loaded, unloading facility, and trucks travelling back empty. The interaction of these subsystems determines the mean number of trucks loaded per time unit — the capacity of the shovel, which is a fundamental quantity of interest. To determine this capacity we need the stationary probability that the shovel is idle. Because an exact analysis of the performance of the system is out of reach, besides of simulations there are various approximation algorithms proposed in the literature, which stem from computer science and can be characterized as general purpose algorithms. We propose for solving the special problem under mining conditions an extremely simple alternative algorithm. Comparison with several general purpose algorithms shows that for realistic situations in the open-pit mining application the special algorithm outperforms the precision of general purpose algorithms. This holds even if the general purpose algorithms incorporate more details of the underlying models than our simple algorithm, which is based on a strongly reduced model. The comparison and assessment is done with extensive simulations on a level of detail which the general purpose algorithms are able to cover. We discuss the application of our proposed algorithms to other applications. It turns out that our algorithms are analogues to Norton's Theorem for a large class of general transportation systems.