This paper addresses the problem of optimum allocation of distributed real-time workflows with probabilistic service guarantees over a Grid of physical resources made available by a provider. The discussion focuses on how such a problem may be mathematically formalised, both in terms of constraints and objective function to be optimized, which also accounts for possible business rules for regulating the deployment of the workflows. The presented formal problem constitutes a probabilistic admission control test that may be run by a provider in order to decide whether or not it is worth to admit new workflows into the system, and to decide what the optimum allocation of the workflow to the available resources is. Various options are presented...