Optimal scheduling with strict deadlines

The problem of dynamic scheduling of customers (messages) in time-critical environments is discussed. A single station (communication node) is considered, and it is assumed that each customer (message) must begin service (transmission) by an individually varying extinction time or else it is lost. Interest is in minimizing, in the sense of stochastic order, the number of messages lost over any time interval. A variety of results is proved that establishes the optimality of the shortest-time-to-extinction policy under rather general conditions. Similar results are found when messages have constraints on their complete transmission times. A network of M stations in tandem is considered under the hypothesis that a message is never lost and is scheduled irrespective of whether its extinction time (also called due date in this case) has expired or not. Under fairly general assumptions on the arrivals, deadlines, and services, it is shown that the earliest-due-date policy minimizes a form of average tardiness incurred over a finite operating horizon among all non-idling nonpreemptive policies. These problems are formulated in the context of stochastic dominance, and simple interchange arguments are used to establish all results