Using Fractional Numbers of Customers to Achieve Throughputs in Queueing Networks

One of the design parameters in closed queueing networks is Np, the number of customers of class p. It has been assumed that Np must be an integer. However, integer choices will usually not achieve the target throughput for each class simultaneously. We use Mean Value Analysis with the Schweitzer-Bard approximation and nonlinear programming to determine the value of Np needed to achieve the production targets exactly, although the values of Np may be fractional. We interpret these values to represent the average number of customers of each class in the network. We implement a control rule to achieve these averages and verify our approach through simulation.