Transient approximation for Jackson networks

Two closure approximations for the M/M/1 queue are extended to a Jackson network. These approximations were tested on networks ranging in size from 4 to 61 nodes, under various initial conditions and loading. The approximations are compared to a discrete-event simulation of a Jackson network. Results of the comparison are presented in terms of the maximum and average errors obtained with the approximations. The approximations are shown to provide accuracy comparable to that of the simulation, with significant savings in computer time and implementation effort. It is believed that this class of approximations holds considerable promise for modeling queuing systems when steady-state results are inadequate