We consider the performance of a distributed, three-tier, client-server architecture, typical for large, Java-supported, Internet applications. An analytical model is developed for the central schedulers in such systems, which can be applied at various levels in a hierarchical modelling approach. The system involves a form of blocking in which clients must wait for one of a number of parallel ‘instance servers’ to clear its outstanding work in order that a new instance may be activated. Thus, blocking time is the minimum of sojourn times at the parallel queues. We solve this model for the probability distribution of blocking time and obtain a simple formula for its mean value. We then use this result in a flow-equivalent server model of the whole system and compare our approximate results with simulation data. This numerical validation indicates good accuracy for the blocking approach per se as well as for system throughput, the performance objective chosen for the exercise.