Message transmission with timing constraints in ring networks

We consider the message transmission problem in unidirectional slotted ring networks. We consider two operation modes: 1) the evacuation mode, in which all messages arrive before system initialization and no new message arrives during system operation; and 2) the continuation mode, in which new messages may arrive after system initialization. We study the performance of several message scheduling policies with respect to three performance measures: meeting all message deadlines, minimizing the maximum delay or the total length of busy periods, and minimizing the average delay. We show that the least-slack-time-first (LSF) scheduling policy is optimal in evacuation mode operation with respect to meeting all message deadlines, while no optimal scheduling policy can possibly exist for continuation mode operation. For the other two performance measures, we show that in the case when messages may be of variable lengths: 1) the farthest-destination-first (FDF) policy is optimal in terms of minimizing the maximum delay and minimizing the total length of busy periods for evacuation mode and for continuation mode operation, respectively, and 2) no optimal scheduling policy can possibly exist in terms of minimizing the average delay under either evacuation mode or continuation mode operation.