Delay Analysis of Switches in Heavy Traffic

Recently, heavy-traffic theory has been applied for understanding behavior of delay in switches. The next section explains the heavy traffic scaling. With some toy examples, it discusses how Brownian motion arises in delay analysis and the idea of state-space collapse. Section 2 defines a switch and sketches a standard method for its stability analysis using the fluid scaling. For fluid scaling, the steady state behavior of switches is also discussed. Section 3 first discusses the relations between the heavy traffic scaling and the fluid scaling. Second, the results by Stolyar [1] are sketched out, where only one of the resources of a switch is in heavy traffic (say an input port or an output port). Then it discusses the results from Shah’s thesis [2], where all the resources are in heavy traffic. It shows an optimal (in heavy traffic scaling) algorithm for minimizing the average delay in a switch and also compares delays of other common algorithms.