Efficiency and Optimality of Largest Deficit First Prioritization: Resource Allocation for Real-Time Applications

An increasing number of real-time applications with compute and/or communication deadlines are being supported on shared infrastructure. Such applications can often tolerate occasional deadline violations without substantially impacting their Quality of Service (QoS). A fundamental problem in such systems is deciding how to allocate shared resources so as to meet applications' QoS requirements. A simple framework to address this problem is to, (1) dynamically prioritize users as a possibly complex function of their deficits (difference of achieved vs required QoS), and (2) allocate resources so to expedite users with higher priority. This paper focuses on a general class of systems using such priority-based resource allocation. We first characterize the set of feasible QoS requirements and show the optimality of max weight-like prioritization. We then consider simple weighted Largest Deficit First (w-LDF) prioritization policies, where users with higher weighted QoS deficits are given higher priority. The paper gives an inner bound for the feasible set under w-LDF policies, and, under an additional monotonicity assumption, characterizes its geometry leading to a sufficient condition for optimality. Additional insights on the efficiency ratio of w-LDF policies, the optimality of hierarchical-LDF and characterization of clustering of failures are also discussed.