Approximate Analysis of General Queuing Networks by Decomposition

In this paper an approximate method for the analysis of general queuing networks is proposed. The queuing network is of the open network type, having single server queuing stations with arbitrary interconnections. Customers may enter the network at any queuing station. The interarrival times of the exogenous arrival processes and the service times at the queuing stations are generally distributed. The analysis is based on the method of decomposition where the total network is broken up into subsystems; e.g., queuing stations of the type or subnets. The subsystems are analyzed individually by assuming renewal arrival and departure processes. All related processes are considered with respect to their first two moments only. An analysis procedure is reported which reduces the total problem to a number of elementary operations which can be performed efficiently with the aid of a computer. Numerical results are reported together with simulation results to demonstrate the accuracy of the new method. The paper concludes with a short discussion of possible extensions of the method.