Comparison of Service and Buffer Overflow Policies for Multiple Server

MANY PROBLEMS IN REAL-TIME SYSTEMS CAN BE MODELED BY FINITE OR INFINITE CAPACITY MULTIPLE SERVER QUEUES SERVING CUSTOMERS WITH DEADLINES. IF A CUSTOMER IS NOT COMPLETED WITHIN A CERTAIN TIME INTERVAL OF ITS ARRIVAL TO SUCH A SYSTEM, IT IS CONSIDERED USELESS AND NEED NOT BE SERVED. IT IS THEREFORE DESIRABLE TO SCHEDULE CUSTOMERS SO THAT THE FRACTION OF CUSTOMERS SERVED WITHIN THEIR RESPECTIVE DEADLINES IS MAXIMIZED. IN THIS PAPER WE SHOW THAT OUT OF THE CLASS OF NON-IDLING SERVICE TIME INDEPENDENT POLICIES, THE SHORTEST TIME TO EXTINCTION POLICY (STE) MAXIMIZES THIS FRACTION AND THAT THE LONGEST TIME TO EXTINCTION POLICY (LTE) MINIMIZES THIS FRACTION FOR THE CONTINUOUS AND DISCRETE TIME NON-PREEMPTIVE, G/M/C/K QUEUES WHEN CUSTOMERS MUST EITHER BEGIN SERVICE BY THEIR DEADLINE OR COMPLETE SERVICE BY THEIR DEADLINE. FOR THE PREEMPTIVE G/M/C/K QUEUE WITH DEADLINES UNTIL THE END OF SERVICE, STE MAXIMIZES THE FRACTION OF CUSTOMERS COMPLETING BY THEIR DEADLINES OUT OF THE CLASS OF SERVICE INDEPENDENT POLICIES AND LTE MINIMIZES THE FRACTION COMPLETING BY THEIR DEADLINES OUT OF THE CLASS OF NON-IDLING, SERVICE INDEPENDENT POLICIES. IN ALL OF THESE SYSTEMS, STE IS THE POLICY THAT SCHEDULES CUSTOMERS CLOSEST TO THEIR DEADLINES AND, IN THE CASE OF BUFFER OVERFLOW REMOVES THE CUSTOMER CLOSEST TO ITS DEADLINE. LTE, ON THE OTHER HAND, SCHEDULES AND REMOVES CUSTOMERS FARTHEST FROM THEIR DEADLINES. WE FURTHER SHOW IN THE CASE OF THE NONPREEMPTIVE G/M/C/K QUEUE