It is known that foreground-background processor sharing (FBPS) stochastically minimizes the number in the system with a single server when task processing times follow a Decreasing Failure Rate(DFR) distribution. Based on this, we derive an optimal policy for a system with a common queue for several identical servers. The performance of such a system will provide a lower bound for the loosely coupled servers case -a system with several identical servers, where a routing decision must be made immediately on a task's arrival. When system load and task variance are high, we propose maximum-least-elapsed-time (MLET) or join-the-shortest-queue (JSQ) for routing followed by foreground-background processor sharing scheduling at each server. Simulation results show good performance of the proposed policies.
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