Open, closed, and mixed networks of queues with different classes of customers

The authors derived the equilibrium distribution of states of a model containing four different types of service centers and R different classes of customers. From this steady state distribution one can compute the moments of the queue sizes for different classes of customers at different service centers, the usage of the service centers, the 'cycle time' or response time for different classes of customers, the 'throughput' of different classes of customers, and other measures of system performance. The model allows different classes of customers to have different arrival rates and different routing probabilities. For open networks some very simple formulas give the marginal distribution of customers at the service centers of the network. Allowing different classes of customers should answer one of the principal objections to queueing models as models of computer systems. The example given indicates how significant different classes of customers can be in the safe levels predicted by model analysis. (Modified author abstract).