Tasks in Real Time systems

The system is subjected to real time, i.e. response should be guaranteed within a specified timing constraint or system should meet the specified deadline. For example flight control system, real-time monitors etc.
There are two types of tasks in real-time systems:

  1. Periodic tasks
  2. Dynamic tasks

Jitter: Sometimes actual release time of a job is not known. Only know that ri is in a range [ ri-, ri+ ]. This range is known as release time jitter. Here ri– is how early a job can be released and ri+ is how late a job can be released. Only range [ ei-, ei+ ] of the execution time of a job is known. Here ei– is the minimum amount of time required by a job to complete its execution and ei+ the maximum amount of time required by a job to complete its execution.

Precedence Constraint of Jobs: Jobs in a task are independent if they can be executed in any order. If there is a specific order in which jobs in a task have to be executed then jobs are said to have precedence constraints. For representing precedence constraints of jobs a partial order relation < is used. This is called precedence relation. A job Ji is a predecessor of job Jj if Ji < Jj i.e. Jj cannot begin its execution until Ji completes. Ji is an immediate predecessor of Jj if Ji < Jj and there is no other job Jk such that Ji < Jk < Jj. Ji and Jj are independent if neither Ji < Jj nor Jj < Ji is true.
An efficient way to represent precedence constraints is by using a directed graph G = (J, <) where J is the set of jobs. This graph is known as the precedence graph. Jobs are represented by vertices of graph and precedence constraints are represented using directed edges. If there is a directed edge from Ji to Jj then it means that Ji is immediate predecessor of Jj. For example: Consider a task T having 5 jobs J1, J2, J3, J4 and J5 such that J2 and J5 cannot begin their execution until J1 completes and there are no other constraints.
The precedence constraints for this example are:
J1 < J2 and J1 < J5



Set representation of precedence graph:

  1. < (1) = { }
  2. < (2) = {1}
  3. < (3) = { }
  4. < (4) = { }
  5. < (5) = {1}

Consider another example where precedence graph is given and you have to find precedence constraints

From the above graph, we derive the following precedence constraints:

  1. J1 < J2
  2. J2 < J3
  3. J2 < J4
  4. J3 < J4

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