TORSCHE Scheduling
Toolbox for Matlab


1. Introduction

Task is a basic term in scheduling problems describing a unit of work to be scheduled. The terminology is adopted from the following publications: I – [Błażewicz01], II – [Butazo97], III – [Liu00]. Graphic representation of task parameters is shown in Figure 3.1, “Graphics representation of task parameters”. Task Tj in the toolbox is described by the following properties:

Name (Name)

label of the task

Processing timeI pj (ProcTime)

is the time necessary to execute task Tj on the processor without interruption

(Computation time II)

Release timeIII rj (ReleaseTime)

is the time at which a task becomes ready for execution

(Arrival time I,II, Ready time I, Request time II)

DeadlineI dj (Deadline)

specifies a time limit by which the task has to be completed, otherwise the scheduling is assumed to fail

Due dateI d~j (DueDate)

specifies a time limit by which the task should be completed, otherwise the criterion function is charged by penalty

WeightI (Weight)

expresses the priority of the task with respect to other tasks (Priority II)

Processor (Processor)

specifies dedicated processor on which the task must be executed

Graphics representation of task parameters

Figure 3.1. Graphics representation of task parameters

Rest of the task properties shown in Figure 3.1, “Graphics representation of task parameters” are related to start time of task sj, i.e. result of scheduling (see sections Section 4.1, “Start Time of Task” and Section 3.2, “Schedule”). Properties completion time Cj (Cj=sj+pj), waiting time wj (wj=sj+rj), flow time Fj (Fj=Cj-rj), lateness Lj (Lj=Cj+dj) and tardiness Dj (Dj=max{Cj-dj,0}) can be derived from start time sj.

2. Creating the task Object

In the toolbox, task is represented by the object task. This object is created by the command with the following syntax rule (properties contained inside the square brackets are optional):

t1 = task([Name,]ProcTime[,ReleaseTime[,Deadline[,DueDate

Command task is a constructor of object task and returns the object. In the syntax rule above the object is the variable t1. Examples of the object task creating are shown in Figure 3.2, “Creating task objects”.

>> t1 = task(5)
Task ""
 Processing time: 5
 Release time:    0
>> t2 = task('task2',5,3,12)
Task "task2"
 Processing time: 5
 Release time:    3
 Deadline:        12
>> t3 = task('task3',2,6,18,15,2,2)
Task "task3"
 Processing time: 2
 Release time:    6
 Deadline:        18
 Due date:        15
 Weight:          2
 Processor:       2

Figure 3.2. Creating task objects

3. Graphical Representation of the task Object

Parameters of a task can be graphically displayed using command plot. For example parameters of task t3, created above, can be displayed by command:

>> plot(t3)

For more details see Reference Guide @task/plot.m.

Plot example

Figure 3.3. Plot example

4. Object task Modifications

Command get returns the value of the specified property or values of all properties. Command set sets the value of the specified property. These two commands has the same syntax as is described in Matlab user's guide. Property access is allowed using the . (dot) operator too.


To obtain a list of all accessible properties use command get. Note that some private and virtual properties aren't accessible using the . (dot) operator, although they are presented when the automatic completion by Tab key is used.

An example of task modification:

>> get(t3)
          Name: 'task3'
      ProcTime: 2
   ReleaseTime: 6
      Deadline: 18
       DueDate: 15
        Weight: 2
     Processor: 2
         Notes: ''
>> set(t3,'ProcTime',4)
>> get(t3,'ProcTime')

ans =


4.1. Start Time of Task

Command add_scht adds the start time into an object task. Schedule of a task is described by three arrays (start, length, processor). The length of array is equal to number of task preemptions minus one. Opposite command to get_scht is appointed for getting a schedule from the task object. For more details see Reference Guide @task/add_scht.m , @task/get_scht.m.

4.2. Color Modification

Commands set_graphic_param and get_graphic_param can be used to define color of tasks. If color of task is set, command plot will use it. Use of these commands is shoved on the following example:

>> t = task('task',5);
>> set_graphic_param(t,'color','red')
>> get_graphic_param(t,'color')

ans =


5. Periodic Tasks

Periodic tasks are tasks, which are released periodically with a fixed period. There is a ptask object in TORSCHE™ that allows users to work with periodic tasks. Periodic tasks are mainly used in real-time scheduling area (see Chapter 8, Real-Time Scheduling).

5.1. Creating the ptask Object

The syntax of ptask constructor is:

pt = ptask([Name,]ProcTime,Period[,ReleaseTime[,Deadline[,Duedate[,Weight[,Processor]]]]])

Almost all parameters are the same as for task object except for Period, which specifies the period of the task.

5.2. Working with ptask Objects

The way of manipulating ptask objects is the same as for task objects. It is possible to change their properties using set and get methods as well as by dot notation. In addition, there is util method which returns CPU utilization factor of the task.

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