Earliest deadline first scheduling

Earliest deadline first (EDF) or least time to go is a dynamic priority scheduling algorithm used in real-time operating systems to place processes in a priority queue. Whenever a scheduling event occurs (task finishes, new task released, etc.) the queue will be searched for the process closest to its deadline. This process is the next to be scheduled for execution.
EDF is an "optimal" scheduling algorithm on preemptive uniprocessors, in the following sense: if a collection of independent "jobs," each characterized by an arrival time, an execution requirement and a deadline, can be scheduled (by any algorithm) in a way that ensures all the jobs complete by their deadline, the EDF will schedule this collection of jobs so they all complete by their deadline.
With scheduling periodic processes that have deadlines equal to their periods, EDF has a utilization bound of 100%. Thus, the schedulability test for EDF is:
where the formula_2 are the worst-case computation-times of the formula_3 processes and the formula_4 are their respective inter-arrival periods (assumed to be equal to the relative deadlines).
That is, EDF can guarantee that all deadlines are met provided that the total CPU utilization is not more than 100%. Compared to fixed priority scheduling techniques like rate-monotonic scheduling, EDF can guarantee all the deadlines in the system at higher loading.
EDF is also an "optimal" scheduling algorithm on non-preemptive uniprocessors, but only among the class of scheduling algorithms that do not allow inserted idle time. When scheduling periodic processes that have deadlines equal to their periods, a sufficient (but not necessary) schedulability test for EDF becomes:
Where "p" represents the penalty for non-preemption, given by "max" formula_2 / "min" formula_4. If this factor can be kept small, non-preemptive EDF can be beneficial as it has low implementation overhead.
However, when the system is overloaded, the set of processes that will miss deadlines is largely unpredictable (it will be a function of the exact deadlines and time at which the overload occurs.) This is a considerable disadvantage to a real time systems designer. The algorithm is also difficult to implement in hardware and there is a tricky issue of representing deadlines in different ranges (deadlines can not be more precise than the granularity of the clock used for the scheduling). If a modular arithmetic is used to calculate future deadlines relative to now, the field storing a future relative deadline must accommodate at least the value of the (("duration" {of the longest expected time to completion} * 2) + "now"). Therefore EDF is not commonly found in industrial real-time computer systems.
Instead, most real-time computer systems use fixed priority scheduling (usually rate-monotonic scheduling). With fixed priorities, it is easy to predict that overload conditions will cause the low-priority processes to miss deadlines, while the highest-priority process will still meet its deadline.
There is a significant body of research dealing with EDF scheduling in real-time computing; it is possible to calculate worst case response times of processes in EDF, to deal with other types of processes than periodic processes and to use servers to regulate overloads.
Example.
Consider 3 periodic processes scheduled on a preemptive uniprocessor. The execution times and periods are as shown in the following table:
In this example, the units of time may be considered to be schedulable time slices. The deadlines are that each periodic process must complete within its period.
Timing diagram.
In the timing diagram, the columns represent time slices with time increasing to the right, and the processes all start their periods at time slice 0. The timing diagram's alternating blue and white shading indicates each process's periods, with deadlines at the color changes.
The first process scheduled by EDF is P2, because its period is shortest, and therefore it has the earliest deadline. Likewise, when P2 completes, P1 is scheduled, followed by P3.
At time slice 5, both P2 and P3 have the same deadline, needing to complete before time slice 10, so EDF may schedule either one.
Utilization.
The utilization will be:
formula_8
Since the least common multiple of the periods is 40, the scheduling pattern can repeat every 40 time slices. But, only 37 of those 40 time slices are used by P1, P2, or P3. Since the utilization, 92.5%, is not greater than 100%, the system is schedulable with EDF.
Deadline interchange.
Undesirable deadline interchanges may occur with EDF scheduling. A process may use a shared resource inside a critical section, to prevent it from being pre-emptively descheduled in favour of another process with an earlier deadline. If so, it becomes important for the scheduler to assign the running process the earliest deadline from among the other processes waiting for the resource. Otherwise the processes with earlier deadlines might miss them.
This is especially important if the process running the critical section has a much longer time to complete and exit from its critical section, which will delay releasing the shared resource. But the process might still be pre-empted in favour of others that have earlier deadlines but do not share the critical resource. This hazard of deadline interchange is analogous to priority inversion when using fixed priority pre-emptive scheduling.
To speed up the deadline search within the ready queue, the queue entries be sorted according to their deadlines. When a new process or a periodic process is given a new deadline, it is inserted before the first process with a later deadline. This way, the processes with the earliest deadlines are always at the beginning of the queue.
Heavy traffic analysis for EDF queues with reneging.
In a heavy-traffic analysis of the behavior of a single-server queue under an Earliest-Deadline-First (EDF) scheduling policy with reneging, the processes have deadlines and are served only until their deadlines elapse. The fraction of “reneged work,” defined as the residual work not serviced due to elapsed deadlines, is an important performance measure.
Comparison with Fixed-priority schedulers.
It is commonly accepted that an implementation of a Fixed-priority pre-emptive scheduling (FPS) is simpler than a dynamic priority scheduler, like the EDF. However, when comparing the maximum usage of an optimal scheduling under fixed priority (with the priority of each thread given by the Rate-monotonic scheduling), the EDF can reach 100% while the theorical maximum value for Rate-monotonic scheduling is around 69%.
Note that EDF does not make any specific assumption on the periodicity of the tasks; hence, it can be used for scheduling periodic as well as aperiodic tasks.
Kernels implementing EDF scheduling.
Although EDF implementations are not common in commercial real-time kernels, here are a few links of open-source and real-time kernels implementing EDF: