The purpose of this paper is to present and solve a particular class of a telecommunications related Process Allocation Problem. The problem deals with the allocation of processes to a network of processors with the aim to minimize a "trade off"objective function composed of (a) the queueing delays overhead which is formed in the underlying queueing network. (b)the communication costs incurred between processes residing on different processors.Various application constraints are also taken into account. A cost function id first constructed to reflect the queueing delay "felt" by a subscriber and a simulated annealing algorithm is then used to minimize the trade off objective function.