Analysis of input control with control delay

Many studies have been carried out on input regulation control in queueing models, which is a basic congestion control. Most of the studies assumed that there is no control delay, which means the time from when the control message starts to be sent until the effect of the control appears. However, in real systems, the control delay time cannot be neglected. This paper analyzes a two-level input control queueing model with control delay based on sampling monitoring. The model can deal with cases where the monitoring interval distribution is arbitrary. Steady state probabilities are analyzed using piecewise Markov process theory and some performance measures are shown. Through several numerical results, the influences of control parameters such as the control delay, threshold values for control, and the monitoring interval distribution on the system performance, are investigated. In particular, we get the remarkable result that there is a mean control delay which gives a minimum loss probability for uncontrolled calls in some cases. Furthermore, from the numerical results, we conjecture that periodically monitoring gives a minimum loss probability for uncontrolled calls under the condition that the system and the control parameters are fixed.