Queue Behavior with ON-OFF Input Processes: An Intuitive Approach

Experimental results with standard ON-OFF sources, as input to a one server queue, indicate that the M/D/1 model is adequate below a certain utilization, ρ* (say), and plain wrong above. Moreover, as the output capacity increases, ρ* increases towards 1. We provide simple engineering formulae, together with computable conditions of their applicability, to physically explain these facts. We also propose two rules/methods to determine quite accurately ρ*. One of these approaches is adequate to approximately predict the average queue length above ρ*.