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@@ -133,7 +133,7 @@ CONTENTS
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arrival time r_j (the time when the job starts), an amount of computation
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time c_j needed to finish the job, and a job absolute deadline d_j, which
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is the time within which the job should be finished. The maximum execution
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- time max_j{c_j} is called "Worst Case Execution Time" (WCET) for the task.
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+ time max{c_j} is called "Worst Case Execution Time" (WCET) for the task.
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A real-time task can be periodic with period P if r_{j+1} = r_j + P, or
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sporadic with minimum inter-arrival time P is r_{j+1} >= r_j + P. Finally,
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d_j = r_j + D, where D is the task's relative deadline.
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@@ -141,7 +141,7 @@ CONTENTS
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WCET and its period (or minimum inter-arrival time), and represents
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the fraction of CPU time needed to execute the task.
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- If the total utilization sum_i(WCET_i/P_i) is larger than M (with M equal
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+ If the total utilization U=sum(WCET_i/P_i) is larger than M (with M equal
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to the number of CPUs), then the scheduler is unable to respect all the
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deadlines.
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Note that total utilization is defined as the sum of the utilizations
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@@ -159,8 +159,8 @@ CONTENTS
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More precisely, it can be proven that using a global EDF scheduler the
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maximum tardiness of each task is smaller or equal than
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((M − 1) · WCET_max − WCET_min)/(M − (M − 2) · U_max) + WCET_max
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- where WCET_max = max_i{WCET_i} is the maximum WCET, WCET_min=min_i{WCET_i}
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- is the minimum WCET, and U_max = max_i{WCET_i/P_i} is the maximum utilization.
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+ where WCET_max = max{WCET_i} is the maximum WCET, WCET_min=min{WCET_i}
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+ is the minimum WCET, and U_max = max{WCET_i/P_i} is the maximum utilization.
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If M=1 (uniprocessor system), or in case of partitioned scheduling (each
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real-time task is statically assigned to one and only one CPU), it is
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@@ -170,7 +170,7 @@ CONTENTS
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of the tasks running on such a CPU is smaller or equal than 1.
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If D_i != P_i for some task, then it is possible to define the density of
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a task as WCET_i/min{D_i,P_i}, and EDF is able to respect all the deadlines
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- of all the tasks running on a CPU if the sum sum_i WCET_i/min{D_i,P_i} of the
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+ of all the tasks running on a CPU if the sum sum(WCET_i/min{D_i,P_i}) of the
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densities of the tasks running on such a CPU is smaller or equal than 1
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(notice that this condition is only sufficient, and not necessary).
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