On continuous-time optimal deterministic traffic regulation

We study the continuous-time deterministic traffic regulation problem. We propose a regulation form shown to be the optimal deterministic traffic regulator in the sense that it outputs the most packets while satisfying the constraint on the output process. We further investigate the subtle relation between continuous-time and discrete-time optimal deterministic regulators, and reduce our general regulation form to the known discrete-time optimal deterministic regulator when restricting arrival (departure) instants to integers and packet size to unity. Therefore, by extending traffic-regulation theory to continuous time, our work provides a fundamental framework for future research regarding quality-of-service (QoS) guaranteed network design/analysis in continuous-time.