A Matlab Toolkit for the Analysis of Two-Level Processor Sharing Queues

This paper presents a Matlab toolkit for the numerical analysis of the two-level processor sharing queue (2LPS). The job sizes are expressed in terms of acyclic phase type distributions which can approximate any distribution arbitrary well while arrivals occur according to a homogeneous Poisson process. The toolkit provides a simple yet efficient way to find the optimal parametrization of the 2LPS queueing disciplines given the job size distributions and the intensity of the workload. In practice, the tool can be used to configure the 2LPS scheduler for TCP flows. The time complexity of the solution depends on the cube of the number of phases of the distribution describing the flow sizes.