We consider a form of blocking, which is typical in client-server systems including those implemented under the Enterprise JavaBean (EJB) specification. The novel feature is that tasks must wait for one of a number of parallel queues to clear its outstanding work. Thus, blocking time is the minimum of sojourn times at the parallel queues. Under certain simplifying assumptions, 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 an aggregate server model of a larger queueing network in which further non-standard techniques are included to represent this form of blocking. We compare our approximate results against simulation data, obtaining good agreement for both system throughput and queue length probability distributions at equilibrium.
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