# Rate Monotonic Scheduling

Rate-monotonic scheduling (German about, advise monotonic scheduling 'in short, RMS ) is a priority scheduling method for interruptible, periodic jobs and is often in real-time systems used. The priorities are statically determined based on the period duration of a job: the shorter the period duration of a job, the higher its priority.

Aperiodic jobs can be run using a fictitious periodic job that runs them when needed or takes no action otherwise. This technique is also known as the server principle.

## Can be planned

A number of jobs can be guaranteed to be scheduled using Rate Monotonic Scheduling under the following conditions:

• Sufficient condition according to Liu and Layland : If the workload isless than or equal to a workload limit, the number of jobs can be planned. The limit onlydepends onthe numberof jobs:${\ displaystyle u}$${\ displaystyle n}$
${\ displaystyle u = \ sum \ limits _ {i = 1} ^ {n} {\ frac {C_ {i}} {T_ {i}}} \ leq n \ cdot \ left ({\ sqrt [{n} ] {2}} - 1 \ right)}$
${\ displaystyle C_ {i}}$: Execution times
${\ displaystyle T_ {i}}$: Period lengths
${\ displaystyle n}$: Number of jobs
As the number of jobs ( ) increases, the limit approaches the value ln 2 ≈ 0.693. So if the calculated utilization is below 69.3%, all jobs can be safely scheduled. If the actual workload is greater than , however, a schedule can still exist under RMS with which no job violates its deadline.${\ displaystyle n \ to \ infty}$${\ displaystyle u}$${\ displaystyle n \ cdot \ left ({\ sqrt [{n}] {2}} - 1 \ right)}$
• Harmonic periods . If the period durations are multiples of each other (harmonic), the jobs can be scheduled, if . So RMS is optimal under this condition.${\ displaystyle u \ leq 1}$