Transient Model for Jackson Networks and its Approximation Ahmed M. Mohamed, Lester Lipsky and Reda Ammar {ahmed, lester, reda@engr.uconn.edu} Dept. of Computer Science and Engineering University of Connecticut, Storrs, CT 06269 Abstract. Jackson networks have been very successful in so many areas in modeling parallel and distributed systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since Jackson networks do not apply to systems where there are population size constraints. Also, the product-form solution of Jackson networks assumes steady state systems exponential service centers with FCFS queueing discipline. In this paper, we present a transient model for Jackson networks. The model is applicable under any population size. This model can be used to study the transient behavior of Jackson networks and if the number of customers in the network is large enough, the model accurately approaches the product-form solution (steady state solution). Finally, an approximation to the transient model using the steady state solution is presented. 1. Introduction Since the early 1970s, networks of queues have been studied and applied to numerous areas in computer science and engineering with a high degree of success. General exponential queueing network models were first solved by Jackson [10] and by Gordon and Newell [9] who showed that certain classes of steady state queueing networks with any number of service centers could be solved using a product-form solution. A substantial contribution to the theory was made by Buzen [5,6] who showed that the ominous-looking formulas the previous researchers had derived were actually computationally manageable. Basket et al [13] summarized under what generalizations the product form solution could be used (e.g., processor sharing, multiple classes, ……). Thereafter the performance analysis of queueing networks began to be considered as a research field of its own. Chandy et. al [14] and others developed many of the basic notions concerning several job streams, as well as some notions concerning non-exponential holding times. Jackson networks have been so successful in so many areas that it is hard to see where they do not apply. However, the ability of Jackson networks to predict remains an open question. It is important to state that Jackson networks do not apply to systems where there are population size constraints. Also, the product-form solution of Jackson networks assumes steady state systems (number of customers is much greater than number of service centers). Finally, the model assumes exponential