Efficient Online Schedulability Tests for Real-Time Systems Tei-Wei Kuo, Senior Member, IEEE, Li-Pin Chang, Yu-Hua Liu, and Kwei-Jay Lin, Senior Member, IEEE
Schedulability Test Liu & Layland first introduced the concept of achievable utilization factor U Online v.s. offline Kuo & Mok, Han & Tyan, ......
Utilization factor Proposed by Liu & Layland Under the process model Preemptive processes Periodically request Parameters : (Ci, Pi) U = Σ (Ci/Pi) Sufficient condition for schedulablily test
Schedulability Test Based on the Liu and Layland Model Some definition Division Graph Offspring set Root Reduced set & RSR
Division Graph
Offspring set
Root
Reduced Set
Example {τi | i = 1~5 } = {3, 5, 15, 20, 60} Root :60 Sevreal offspring of τ5 , e.g. {3,5}, {3,5,60} For {τ1,τ2, τ3} , τ (which period is τ3 and utilization factor is equal to the sum of utilization factor of τ1,τ2, τ3) is an RSR of {τ1,τ2, τ3} . {τ1,τ2, τ3} is a reduced set of τ
Schedulability Theorems
Schedulability Theorems
Schedulablility Test Algorithm
example T3 is schedulable according to utilization bound, but T4, T5 is not guaranteed schedulable because U4 > U(4), U5 > U(5), where Ui Is the utilization factor of Ti and U(i) is the achievable utilization of i processes Actually, T4 and T5 is schedulable ! Why and How ?
Schedulability test for multiframe model Multiframe ? τ: ((C0, C1, … CN), pi) Peak execution time Peak utilization factor
AM Multiframe model AM means Accumulative monotonic
AM multiframe model Critical instant : same as LL model Root & offspring : same as LL model RSR :