The document presents a model for real-time systems that includes three main elements: a workload model describing the applications and their timing parameters, dependencies, and functional parameters; a resource model describing the available system resources; and scheduling algorithms defining how resources are allocated over time. It discusses different types of real-time tasks and their temporal parameters, dependencies between tasks, and how precedence and resource constraints are represented in task graphs. The document also covers scheduling hierarchy, valid schedules, and performance measures for evaluating real-time schedulers.

1. MODEL OF
REAL-TIME
SYSTEM
PRESENTED
BY:
MANOJ
KHADKA
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2. ACCORDING TO REFERENCE MODEL, A
SYSTEM IS CHARACTERIZED BY THREE
ELEMENTS:-
(1)a workload model that describes the applications supported by the system,
 Temporal parameters
 Precedence constraints and dependencies
 Functional parameters
(1)a resource model that describes the system resources available to the applications,
(2)algorithms that define how the application system uses the resources at all times
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3. PROCESSORS AND
RESOURCES
servers and active resources;
computers, transmission links,
disks, and database server are
examples of processors
 Every job must have one or more
processors in order to execute
and make progress toward
completion
resources are memory, sequence
numbers, mutexes, and
database lock
 A job may need some resources in
addition to the processor in
order to make progress
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4. Temporal Parameters of Real-Time
Workload
Its temporal parameters that tell us its timing constraints
and behavior. Its interconnection parameters describe how
it depends on other jobs and how other jobs depend on it.
Release time (ri)
Relative deadline(Di)
Absolute deadline(di)
Execution time(ei)
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5. Fixed, Jittered, and Sporadic
Release Times
Fixed: we do know the actual release time ri of each job .
Jitter: we do not know the actual release time ri of each job Ji ; only that ri is in a range [ri− , ri+ ].
Sporadic/aperiodic : they are released at random time instants.
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6. APERIODIC AND SPORADIC TASKS
 a task is aperiodic if the jobs in it have either soft deadlines or no deadlines.
 Tasks containing jobs that are released at random time instants and have
hard deadlines are sporadic tasks.
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7. PERIODIC TASK MODEL
 each computation or data transmission that is executed
repeatly at regular or semiregular time intervals in order
to provide a function of the system on a continuing basis
is modeled as a period task
 such as digital control, real-time monitoring, and constant
bit-rate voice/video transmission
 Four tuples (φi(phase), pi(periods), ei, Di(relative deadline))
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8. PRECEDENCE CONSTRAINTS
• jobs are said to have precedence constraints if they are constrained to execute in some order
Example:
• For example, in a radar surveillance system, the signal-processing task is the producer of track records,
while the tracker task is the consumer. In particular, each tracker job processes the track records
generated by a signal-processing job. The designer may choose to synchronize the tasks so that the
execution of the kth tracker job does not begin until the kth signal-processing job completes.
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9. PRECEDENCE GRAPH AND TASK
GRAPH
• Jobs are either precedence constrained or independent
• Precedence relation:
->partial ordering operator <
->Ji < Jk : Ji is a predecessor of Jk , Jk a successor of Ji
->directed graph : G=(J,<)
• Task graph is an extended precedence graph
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10. TASK GRAPH
• gives us a general way to describe the application system
• the vertices in a task graph represent jobs
• shown as circles and squares
• numbers in the bracket above each job give its feasible interval
• edges in the graph represent dependencies among jobs
• If all the edges are precedence edges, representing precedence constraints, then the graph is a
precedence graph
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11. DATA DEPENDENCY
• a situation in which a program statement (instruction) refers to the data of a preceding statement
• there is a data-dependency edge from a vertex Ji to vertex Jk in the task graph if the job Jk consumes
data generated by Ji or the job Ji sends messages to Jk
• A parameter of an edge from Ji to Jk is the volume of data from Ji to Jk
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12. OTHER DEPENDENCIES
• Temporal Dependency
• AND/OR Precedence Constraints
• Conditional Branches
• Pipeline Relationship
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13. TEMPORAL DEPENDENCY
• In task graph, temporal distance constraints among jobs are represented by temporal-dependency edge
• There is a temporal dependency edge from a vertex Ji to Jk if the job Jk must be completed within a
certain time after Ji completes.
• The value of this parameter is infinite if jobs have no temporal distance constraints or there is no
temporal dependency edge among the jobs
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14. AND/OR PRECEDENCE
CONSTRAINTS
• A job with one or more than one immediate predecessor that must wait until all of its predecessor are
executed is AND jobs
• The dependencies among theme AND precedence constraints
• These are represented by unfilled circles in the task graph
• OR jobs are the job that can begin execution at or after its release time provided one or more of its
immediate predecessor has been completed
• It is represented by square vertices
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15. CONDITIONAL BRANCHES
• all the immediate successors of a job must be completed before the job to be executed
• This convention makes it inconvenient for us to represent conditional execution of job
• Let us consider the program shown below:
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16. A Program with conditional branches 16

17. PIPELINE RELATIONSHIP
• In task graph, the vertices are granules of producer and consumer
• Each consumer granule can begin execution when previous granules of job and the producer job have
been completed
• We represent the pipeline relationship between edges with the dotted lines
• There is an pipeline edge from Ji to Jk if o/p of Ji is piped into Jk and execution of Jk can proceed as long
as there are data for it to proceed
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18. FUNCTIONAL PARAMETERS
• Main function parameters include:-
• Preemptivity of jobs
• Criticality of jobs
• Optional execution
• Laxity type and laxity function
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19. PREEMPTIVITY OF JOBS
• Preemptable:-Can be suspended and resumed form the suspension point
• Non-preemptable jobs:-it must be implemented from start time to completion time without
preemption
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20. CRITICALITY OF THE JOBS
• Criticality of jobs:-positive number indicating how critical the job is
• Value increases with importance of job
• Here we don’t use the terms priority and weight
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21. OPTIONAL EXECUTION
• If an optional job or optional portion completes late or is not executed at all, the system still functions
satisfactorily
• Non-optional job:- mandatory
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22. LAXITY TYPE AND LAXITY FUNCTIONS
• Laxity type of a job means whether its timing constraints are hard or soft.
• Laxity type is supplemented by a usefulness function
• This function gives the usefulness of the result produced by the job as a function of its tardiness
• The tardiness is the difference between the completion time and deadline of the job.
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23. USEFULNESS OF THE FUNCTION
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24. RESOURCE PARAMETER OF JOBS AND PARAMETER OF
RESOURCES
• Preemptivity of resource
• Resource Graph
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25. PREEMPTIVITY
• If a job can use every unit of resource in a interleaved fashion, the resource is called preemptable
• A resource is non-preemptable if each unit of the resource is constrained to be used serially
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26. RESOURCE GRAPH
• A graph that is used to describe the configuration of the resources
• Vertex Ri for every processor or resource Ri in the system
• Attributes of the vertex are the parameters of the resources
• p- processor R- passive resources
• Parameters
 Type
 No. of available units
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27. SCHEDULING HIERARCHY
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28. SCHEDULING HIERARCHY
• Task Graph
 Representation of application system
 Processor time
 Resource requirement
 Timing constraints & dependencies of the job
• Resource graph
 Amount of attributes
 Resource attributes
 Usage rules
• Scheduling and resource access control algorithm used by the operating system
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29. SCHEDULER AND SCHEDULE
• Scheduler
 Implements scheduling algorithm
 Schedule jobs
 Allocate resources
Example :-processor assignments on jobs(or vice-versa)
• Schedule
 A schedule is an assignment of all jobs in the system on the available processors.
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30. VALID SCHEDULES
• Every processor is assigned at most one job at any time.
• Every job is assigned at most one processor at any time.
• No job is scheduled before its release time.
• The total amount of processor time assigned to every job is equal to its maximum or actual execution
time.
• All the precedence and resource usage constraints are satisfied.
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31. FEASIBILITY, OPTIMALITY AND PERFORMANCE MEASURES OF
SCHEDULING
• A valid schedule is also a feasible schedule if every job meets its timing constraints or completes by its
deadline
• A job is a schedulable according to a scheduling algorithm, if the scheduler always produces a feasible
schedule
• Miss Rate: The percentage of jobs that are executed but completed too late
• Loss Rate: The percentage of jobs that are not executed at all or discarded
The other performance measures are maximum and average tardiness, response time, miss/loss and invalid rates
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32. BIBLIOGRAPHY
• https://www.kullabs.com/classes/subjects/units/lessons/notes/note-detail/4508
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