  This paper proposes a new scheduler applying the concept of non-uniform
laxity to Earliest deadline first (EDF) approach for aperiodic tasks. This
scheduler improves task utilisation (Execution time / deadline) and also
increases the number of tasks that are being scheduled. Laxity is a measure of
the spare time permitted for the task before it misses its deadline, and is
computed using the expression (deadline - (current time + execution time)).
Weight decides the priority of the task and is defined by the expression
(quantum slice time / allocated time)*total core time for the task. Quantum
slice time is the time actually used, allocated time is the time allocated by
the scheduler, and total core time is the time actually reserved by the core
for execution of one quantum of the task. Non-uniform laxity enables scheduling
of tasks that have higher priority before the normal execution of other tasks
and is computed by multiplying the weight of the task with its laxity. The
algorithm presented in the paper has been simulated on Cheddar, a real time
scheduling tool and also on SESC, an architectural simulator for multicore
platforms, for upto 5000 random task sets, and upto 5000 cores. This scheduler
improves task utilisation by 35% and the number of tasks being scheduled by
36%, compared to conventional EDF.
