A Method for Performance Analysis of Earliest-Deadline-First Scheduling Policy

This paper introduces an analytical method to approximate the fraction of jobs missing their deadlines in a soft real-time system when the earliest-deadline-first (EDF) scheduling policy is used. In the system, jobs either all have deadlines until the beginning of service (DBS) and are non-preemptive, or have deadlines until the end of service (DES) and are preemptive. In the former case, the system is represented by an M/M/m/EDF+G model, i.e., a multi-sever queue with Poisson arrival, exponential service, and generally distributed relative deadlines. In the latter case, it is represented by an M/M/1/EDF+G model, i.e., a single-server queue with the same specifications as before. EDF is known to be optimal in both of the above cases. The optimality property of EDF scheduling policy is used for the estimation of a key parameter, namely the loss rate when there are n jobs in the system. The estimation is possible by assuming an upper bound and a lower bound for this parameter and then linearly combining these two bounds together. The resulting Markov chains can then be easily solved numerically. Comparing numerical and simulation results, we find that the existing errors are relatively small.

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