Speedup Bounds for Global Scheduling

Abstract

In the preceding chapters, we have seen a variety of global schedulability analysis tests for the fixed job priority (FJP) scheduling algorithm $\textsf{EDF}$, the fixed task priority (FTP) scheduling algorithm deadline monotonic (DM), and the dynamic priority scheduling algorithm [EDZL]. When applied to systems of sporadic three-parameter task systems, the only one of these tests for which a quantitative metric of worst-case performance was obtained is the sc [bak] test (Chap. 16): Corollary 16.1 showed that the processor speedup factor of the [bak] test is no larger than $(3+\sqrt{5})/2$, or $\approx 2.6181$. In this chapter, we will describe the results of [63] deriving a tight speedup bound of $(2-\frac{1}{m})$ for global $\textsf{EDF}$ scheduling of three-parameter sporadic task systems upon m processors, and a tight speedup bound of $(3-\frac{1}{m})$ for global DM scheduling of three-parameter sporadic task systems upon m processors. We will also describe how these speedup bounds were used [62, 36, 37] to derive pseudopolynomial time schedulability tests that are within a factor ϵ away from optimal, for ϵ an arbitrarily small positive number.

Sources

The forced-forward demand bound function was proposed in [63] as a refinement to the demand bound function; ideas leading up to it were previously suggested in [24]. The speedup bounds for $\textsf{EDF}$ and DM presented here were derived in [63]. The $\textsf{EDF}$ schedulability test we describe here was first presented in [36, 37].