Do implementations of the HPC server (based on a priority queue)

A High Performance Computing (HPC) server receives requests from users, running computationally intensive programs. For simplicity, we adopt an abstract time period between [0,19], i.e. a total of 20 time units. User requests could arrive at any point as follows:

At time 0, Program A is submitted requiring 2 time units to run

At time 0, Program B is submitted requiring 1 time units to run

At time 2, Program C is submitted requiring 2 time units to run

At time 3, Program D is submitted requiring 4 time units to run

At time 3, Program E is submitted requiring 1 time units to run

At time 3, Program F is submitted requiring 3 time units to run

At time 7, Program G is submitted requiring 1 time units to run

At time 11, Program H is submitted requiring 2 time units to run

At time 12, Program I is submitted requiring 1 time units to run

At time 15, Program J is submitted requiring 3 time units to run