Summary form only given. In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determine the system performance. Jackson networks have been very successful in modeling parallel and distributed systems. However, they have their limitations. In particular, the product-form solution of Jackson networks assumes steady state and exponential service centers or certain specialized queueing disciplines. We use a transient model studying distributed systems with finite workload (no new arrivals). Using some nonexponential distributions we show to what extent the exponential distribution can be used to approximate other distributions. When the number of tasks to be executed is large enough, the model approaches the product-form solution in those cases where the Jackson networks can be applied. We also study some cases where Jackson networks can't be applied (the nonexponential servers have queueing). The model can be used for reliability analysis of systems that allow failures without repair (fail-stop).