(12) We can find that mean (DMA (λ, m)) and mean (DMB (λ, are same as obtained in mA, eA, mB) subsection 2.1. As parameters using in two analyses are the same but leff, i = li, - mi, two deadline uses meet ratios computed in 2.1 and 2.3 must be the same. (One li > mi while the other leff, i = which is basically same, to compute deadline meet ratio.) > 0, 2.3 O-ELST (Optimal Effective Least Slack Time First) As the ELST algorithm cannot improve real-time performance, we consider the optimal algorithm which changes schedule for two tasks (task A and task B) when the changed schedule can improve the real-time performance. Let p be probability of meeting deadline of firstly scheduled task (task A). (13) Let q be probability of meeting deadline of the secondly scheduled task (task B). (14) We use somewhat different approach from LST and ELST scheduling to compute deadline meet ratio for O-ELST scheduling. O-ELST scheduling considers moving time as well as slack time to improve deadline meet ratio. When task A and task B conflict, O-ELST schedules tasks (A followed by B or B followed by A), which maximizes a deadline meet ratio. On a schedule of A followed by B, there are four cases: Both A and B meet the deadline (probability of pq): In this case, O-ELST does not change • schedule (choose schedule of A followed by B) A only meets the deadline (probability of p (1-q)): In this case, O-ELST changes schedule (B • followed by A) if both A and B meet the deadline. Probability of meeting deadline for both A and B
(12) We can find that mean (DMA (λ, m)) and mean (DMB (λ, mA, eA, mB) are same as obtained in subsection 2.1. As parameters using in two analyses are the same but leff, i = li, - mi, two deadline meet ratios computed in 2.1 and 2.3 must be the same. (One uses li > mi while the other leff, i = > 0, which is basically same, to compute deadline meet ratio.) 2.3 O-ELST (Optimal Effective Least Slack Time First) As the ELST algorithm cannot improve real-time performance, we consider the optimal algorithm which changes schedule for two tasks (task A and task B) when the changed schedule can improve the real-time performance. Let p be probability of meeting deadline of firstly scheduled task (task A). (13) Let q be probability of meeting deadline of the secondly scheduled task (task B). (14) We use somewhat different approach from LST and ELST scheduling to compute deadline meet ratio for O-ELST scheduling. O-ELST scheduling considers moving time as well as slack time to improve deadline meet ratio. When task A and task B conflict, O-ELST schedules tasks (A followed by B or B followed by A), which maximizes a deadline meet ratio. On a schedule of A followed by B, there are four cases: • Both A and B meet the deadline (probability of pq): In this case, O-ELST does not change schedule (choose schedule of A followed by B) • A only meets the deadline (probability of p (1-q)): In this case, O-ELST changes schedule (B followed by A) if both A and B meet the deadline. Probability of meeting deadline for both A and B
Effective%20Real-Time%20Scheduling%20Algorithm%20for%20Cyber%20Physical%20Systems%20-%2020130828-%203rd%20rev..docx