Response Time of Queueing Mechanisms

We study response time, a key performance characteristic of queueing mechanisms. The studied model incorporates both active and passive queue management, arbitrary service time distribution, as well as a complex model of arrivals. Therefore, the obtained formulas can be used to calculate the response time of many real queueing mechanisms with different features, by parameterizing adequately the general model considered here. The paper consists of two parts. In the first, mathematical part, we derive the distribution function for the response time, its density, and the mean value. This is done by constructing two systems of integral equations, for the distribution function and the mean value, respectively, and solving these systems with transform techniques. All the characteristics are derived both in the time-dependent and steady-state cases. In the second part, we present numerical values of the response time for a few system parameterizations and point out several of its properties, some rather counterintuitive.