Control of queueing systems in a class of delays

The paper considers systems with cyclic instants of service start, i.e., systems where the sequence of service start instants is set. Such models arise in the analysis of transport systems. It is interesting to study control policies for such systems that minimize the mean waiting time of requests. One of the simplest control policies is the introduction of service start delays that can be easily implemented in practice. There is an interest in studying models in which delay of one service start instants alters the next service start instant-as occurs in real systems. This note is concerned with the study of such systems. It outlines the class of systems for which the delay introduction is expedient, and finds the form of the optimal function minimizing the mean waiting time of a request before service.