Short package for plotting real-time scheduling of tasksets.

Features

• Plot a taskset with the informations about releases and deadlines
• Plot the scheduling of a taskset;
  • Execution and deadlines are diplayed and,
  • A different scheduler’s implementation can be given to the plotting function.
• Implicit, constrained and arbitrary deadlines are supported, as well as synchronous and asynchronous systems.
• Configure the layout of the plot (width of steps, height of task, colors of the tasks).

Getting started

#import "@preview/rt-sched:0.0.1": print-taskset, scheduler, plot

// Declare a taskset
// o: offset (optionnal, default=0)
// c: worst-case execution time
// d: deadline
// t: period
#let taskset = (
  (c: 7, d: 10, t: 10),
  (c: 1, d: 16, t: 16),
  (o: 4, c: 3, d: 15, t: 15),
)

#print-taskset(taskset)

// Plot the interval [0, 20) of the taskset with RM
#plot(
    from: 0,
    to: 20,
    tasks: taskset,
    scheduler: scheduler.rm,
)

API Reference

Configuration

The configuration is represented as an array of three values:

• the width of a task (step-width: length)
• the height of a task (task-height: length)
• the color set from which the task choose a color (colors: array of colors)

#let config = (
  task-height: 0.8cm,
  step-width: 2em,
  colors: none,
)

If you want the scheduler some colors you could do:

#import "@preview/rt-sched:0.0.1": config, plot
config.colors = (red, blue, green)

and pass the config to the plot function.

Plot

plot(
  // start of the interval
  from: int,
  // end of the interval (included)
  to: int,
  // number of step used on the x-axis (default: 1)
  step: 1,
  // the taskset display on the plot, the order of the tasks depend on their
  // order in the array (element at index i has index i + 1)
  // each task contains at least the following fields:
  // - o: int, the offset (optional)
  // - c: int, the wcet (mandatory)
  // - d: int, the deadline (mandatory)
  // - t: int, the period (mandatory)
  tasks: array,
  // the configuration of the plot (array)
  // contains the following fields
  // - config.task-height (mandatory)
  //   the height of the tasks
  // - config.step-width (mandatory)
  //   the width of the tasks
  // - config.colors (optional)
  //   the colors from which each task get their color (by index modulo
  //   the number of colors)
  config: (
    task-height: 0.8cm,
    step-width: 2em,
    colors: none,
  ),
  // the scheduling function, if none only the plot is displayed
  // the function take the array of running_jobs and the instant t
  // and return the array sorted with the highest priority task in first
  // position
  scheduler: none,
  // display a mark to indicate an idle unit (default: false)
  display-idle: false,
  // try to find a step-width that enable the plot to be printed on a a4 page
  auto-width: true,
)

Scheduling functions

A scheduling function must take array of running jobs as parameter and the instant t at which it’s called and return a sorted array where the highest priority job is put at the first position.

The scheduler namespace contains the implementation of the following scheduling algorithm:

• rm: Rate Monotonic
• dm: Deadline Monotonic
• edf: Earliest Deadline First
• llf: Least Laxity First
• priority_assignment: Priority based on the task index (lower the index, higher the priority) $\tau_1 \succ \tau_2 \succ … \succ \tau_n$.
• reversed_priority_assignement: Priority based on the task index (lower the index, lower the priority) $\tau_n \succ \tau_{n-1} \succ … \succ \tau_1$.

The scheduling function is then passed as a parameter of the plot function.

Examples

1. Plot a tasket without scheduling it.

#import "@preview/rt-sched:0.0.1": *
#let taskset = (
  (c: 1, d: 5, t: 5),
  (c: 2, d: 4, t: 4),
)

#plot(from: 0, to: 20, tasks: taskset)

2. Plot a tasket and scheduling it (with RM).

#import "@preview/rt-sched:0.0.1": *
#let taskset = (
  (c: 1, d: 5, t: 5),
  (c: 2, d: 4, t: 4),
)

#plot(from: 0, to: 20, tasks: taskset, scheduler: scheduler.rm)

3. Use colors for plotting

#import "@preview/rt-sched:0.0.1": *
#let taskset = (
  (c: 1, d: 5, t: 5),
  (c: 2, d: 4, t: 4),
)

#{config.colors = (red.lighten(40%), green.lighten(40%))}

#plot(from: 0, to: 20, tasks: taskset, scheduler: scheduler.rm, config:config)