Stochastic rendezvous networks (SRVN) are models for the throughput of distributed programs executed concurrently and synchronously on distributed computing nodes. Server tasks respond to requests from user tasks and execute in a two-phase pattern (in-rendezvous phase, then postrendezvous phase), and may themselves act as user tasks to further servers, to any depth. The authors extend the model to permit the execution time and the occurrence of nested rendezvous calls to depend on the identity of the calling user task. An iterative approximation method is developed, and compared to exact throughput calculations found with timed Petri nets. The approximation has errors of a few percent in most cases, and executes very much faster than the Petri-net calculation.>