Optimality of the Stochastic Earliest Deadline Policy for the G/M/c Queue Serving Customers with Deadlines

• Authors: Don Towsley;S. S. Panwar
• Venue: Optimality of the Stochastic Earliest Deadline Policy for the G/M/c Queue Serving Customers with Deadlines
• Year: 1991

We consider the problem of scheduling customers with deadlines in the G/M/c queue. We assume that customer deadlines are not known but that the scheduling policy has available to it partial information regarding stochastic relationships between the deadlines of eligible customers. We prove three main results, 1) in the case that deadlines are until the beginning of service, the nonpreemptive, non-idling policy that stochastically minimizes the number of customers lost during an interval of time belongs to the class of non-idling stochastic earliest deadline (SED) policies, 2) in the case that deadlines are until the end of service, the optimum policy belongs to the class of SED policies, and 3) in the case of deadlines until the end of service, the optimum non-preemptive policy belongs to the class of non- preemptive, non-idling SED policies. The last result assumes that a customer in service that misses its deadline is always removed and thrown away. Here a policy belongs to the class of SED policies if it never schedules a customer whose deadline is known to be stochastically larger than that of some other customer in the queue. We describe several applications for which these classes contain exactly one policy. These include queues where i) deadlines are known exactly, ii) deadlines are characterized by distributions with increasing failure rate, iii) deadlines are characterized by distributions with decreasing failure rate, iv) customers fall into several classes, each with its own exponential deadline distribution, and v) certain combinations of the previous three applications. The optimal policies for the first four applications are the earliest deadline first come first serve, last come first serve, and head of the line priority scheduling. The scheduling policy for the last application combines elements of head of the line priority, first come first serve, and last come first serve. The paper concludes with some generalizations to discrete time systems, finite buffers and vacation models.