This document provides an overview of a reference model for real-time systems. It describes the key components of the model including the workload model (tasks and jobs), resource model (processors and resources), and scheduling algorithms. It defines temporal parameters for jobs, periodic and sporadic task models, and different types of dependencies. It also covers functional parameters, resource requirements, and defines concepts like feasibility and optimality for schedules. The goal is to characterize real-time systems and provide a framework for analyzing scheduling and resource allocation algorithms.

1. PROCESSOR AND RESOURCES
TEMPORAL PARAMETERS OF REAL -TIME WORKLOAD
PERIODIC TASK MODEL
PRECEDENCE CONSTRAINTS AND DATA DEPENDENCY
OTHER DEPENDENCIES
FUNCTIONAL PARAMETERS
RESOURCE PARAMETERS OF JOBS
PARAMETERS OF RESOURCES
SCHEDULING HIERARCHY
Reference Model of Real time
System

2. Introduction
 The model that focuses the relevant characteristic
such as the timing properties, resource requirements
of system components and the way in which OS
allocates the available system resources among them
is called reference model.
 Its main goal is to move away from functional
characteristics and focus on timing properties and
resource requirements.

3.  Our reference model is characterized by
 A workload model that describes the application supported by
the system.
 A resource model that describe the system resource available
to the application.
 Algorithms that define how the application system uses the
resources at all times.

4. Reference Model
Task Graph
Scheduling of
Resources
Resource Graph
Application
System
AlgorithmsAvailable System
Resource

5. Processor and Resources
 We divide all the system resources into two major
types:
 Processors
 Resources
 Processors are active resources e.g. computers,
transmission links, disks , database servers etc.
 Every job must have one or more processor in order
to execute and make progress towards completion.
 Two processor can be called of same type if they are
identical and can be used interchangeably.

6.  We will denote the processor with letter P and call
represent m processor in the system P1,P2…..Pm
 By resource we mean passive resources. E.g.
memory, sequence number , semaphore, database
lock etc.
 A job may need some resources in addition to the
processor in order to make progress.
 We will use the letter R to denote the resources.

8. Temporal Parameters of real time workload
 Each job Ji is characterized by its temporal
parameters, functional parameters, resource
parameters and interconnection parameters.
 The temporal parameters of a job is the parameters
which describes its timing constraints and behavior.
 It includes the release time(ri), absolute deadline(di),
relative deadline(Di) and Execution time(Ei).
 The interval between the release time and absolute
deadline of the job(Ji) is represented as[ri,di] and it is
called feasible interval

9. Fixed, Jittered and sporadic release times
 The release time may not be exactly known, only the
range may be known[ri- ri+].
 When only the range of ri is known then this range is
called release time.
 If the jitter is negligible, then the actual release time
of the job is given by either earliest or the latest
release time. This release time of the job is called
fixed release time.
 Every real time system is required to response to
unexpected external events which occur at random
instant which are called sporadic or aperiodic jobs.

10.  The release time of such jobs are random variables
and can be described in terms of probability
distribution A(x).
 A(x) gives the probability that the release time of job
is at or earlier than x for all valid values of x.

11. Execution Time
 It is the amount of time required to execute the job
when it executes alone and has all the resources it
required.
 The execution time depends on the complexity of the
job, speed of processor but not on how the job is
scheduled.
 The execution time may vary. It can only be known
in terms of maximum and minimum value of time
require to compute each job. Its range is [ei- ei+]

12.  For most of the deterministic models in hard real
time systems, the execution time means maximum
execution time. The deterministic models are used
for two reasons:
 Hard real time system are safety critical in which variation in
execution time is kept as small as possible.
 Hard real time portion of the system is generally very small
rest of the system is soft. A hard real time sub-system based on
its worst case processor time and resource requirements even
though their actual requirement may be much smaller. We can
then use the method and tools to allocate processor and
resources to other application when not in used.

13. Periodic Task Model
 It is well known deterministic workload model.
 This model characterizes accurately many traditional
hard real time application like digital control, real
time monitoring and constant bit rate voice/video
transmission.
 A set of jobs are executed repeatedly at regular time
intervals in order to provide function of the system
are called periodic tasks.
 Each periodic task denoted by Ti is sequence of jobs.

14.  Periodic task can also be define in terms of phase,
periods, execution time , hyper period and utilization
factor.
 The release time ri,1 of the first job Ji,1 in each task is
called the phase of Ti. It is denoted by фi=ri,1
 Different tasks may have different phases and if all
the tasks have same phase, then they are in-phase.

15.  The period(Pi) of task(Ti) is the minimum lengths of
all time interval between release time of consecutive
jobs.
 The execution time(ei) of a task Ti is the maximum
execution time of all the jobs in the periodic task,
 The period and execution time of a periodic task in
the system must be known with reasonable accuracy.
 The hyper period of periodic task is least common
multiple of their periods.

16.  The maximum number of jobs in hyper period is
equal to ∑H/Pi.
 This is the time after which the pattern of job release
or execution time start to repeat.
 The length of hyper period of 3 periodic tasks with
period 3,4 and 10 is 60.
 No of jobs=60/3 + 60/4 + 60/10 = 41

17. Utilization Function
 Utilization of task Ti is the ration of execution time
and period i.e Ui = ei/pi.
 It is the fraction of time periodic task(Pi) having
execution time(ei) keep busy the processor.
 The total utilization of all task is sum of the
utilization of individual task in the system. U=∑Ui
 If execution time of three periodic tasks are 1,1 and 3
with periods 3,4 and 10 respectively than U=0.33+
0.25+0.3= 0.88
 This means processor is busy 88% of time.

18. A periodic and Sporadic Tasks
 In addition to periodic task, RTS executes aperiodic
or sporadic task. E.g. pilot switch to auto pilot mode,
operator adjustment sensitivity of setting of radar
etc.
 The jobs in each aperiodic task are same in the sense
that they are identically distributed random variables
with some probability distribution A(x).

20. Precedence Graph and Task Graph
 Precedence Graph can represent the precedence
constraints among jobs in a set J using a directed
graph G=(J,<).
 Each vertex in the graph represent the job.
 There is directed edge from vertex Ji to Jk when job Ji
is an immediate predecessor of job Jk
 This graph is called precedence graph.
 Task graph is an extended precedence graph.
 It is used different types of edges to represent the
different dependencies.

22. Data Dependency
 Data dependency cannot be captured by a
precedence graph.
 In task graph, data dependencies among the jobs are
represented by edged among the jobs.
 There is data dependency edge from a vertex Ji to Jk
in task graph if the job Jk consumes data generated
by Ji or Ji sends messages to Jk.

23. Other types of Dependencies
 The various types of extended dependencies in
precedence graph are:
 Temporal Dependency
 AND/OR Precedence Constraints
 Conditional Branches
 Pipeline Relationship

24. Temporal Dependencies
 Some jobs may be constrained to complete within a
certain amount of time relative to one another.
 The difference in the completion times of two jobs is
the temporal distance between them.
 Jobs are said to have temporal distance constraint if
their temporal distance must be no more than
certain finite value.
 Jobs with temporal distance constraints may or may
not have deadlines.

25.  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.

26. 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.

27. Conditional Branches
 In classical model, 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:

29.  This system can be modeled by a task graph that has
edges expressing OR constraints.
 Only one of all the immediate successors of a job
whose outgoing edges represent OR constraints is to
be executed.
 Such a job is called branch job and associated with it
is the join job both of them are represented by the
filled circle.
 The sub graph that begins from a branch job and
ends at join job is called a conditional block.

30.  Only one conditional branch in each conditional
block is to be executed.
 Above figure has two conditional branches.
 Either the upper conditional branch containing
chain of jobs or lower conditional branch, containing
one job is to be executed.

31. 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.

32. Functional Parameters
 While scheduling and resource access control
decision are being made certain functional
parameters do affect the job.
 These are:
 Preemptivity of Jobs
 Criticality of Jobs
 Optional Execution
 Laxity Type and laxity Functions

33. Preemptivity Of Jobs
 The scheduler may suspend the execution of less
important job and give the processor to more urgent
job.
 When the urgent jobs completes, the scheduler
returns the process to less urgent job so the job can
resume execution.
 This interruption of job execution is called
preemption.
 A job is preemptable if its execution can be
suspended at any time to allow the execution of other
jobs and later on can be resumed.

34.  A job is non-preemtable if it must be executed from
start to completion without interruption.
 Computational jobs in CPU are preemptable jobs.
 Transmission of frames in token ring is non-
preemptable. If transmission of frame is interrupted
before it is completed, the partially transmitted
frame is discarded by the receiver.
 To avoid wasting of bandwidth we make execution of
this job preemptable.

35. Criticality of Jobs
 In any system, jobs are not equally important.
 The importance(criticality) of a job is a positive
number that indicates how critical the job is with
respect to other jobs.
 The more critical means the job is more important.
 Priority and weight are used to indicate the
importance.
 If a job is important, then the priority or weight is
large.

36.  During the overload period, the less critical jobs can
be sacrificed so that more critical jobs can meat the
deadlines.
 Sometimes the weighted performance measures such
as weighted average response time(average response
time * importance) or tardiness are used to optimize
the resource control algorithm.

37. Optional Execution
 The optional jobs or optional part of the can be
discarded even when it is executing.
 But the jobs which are not optional or are mandatory
must be executed to completion.
 Optional means job is not critical .
 The discarding of optional job may degrade the
system performance but the obtained result is still
satisfactorily.
 System can trade between the quality of result it
produces and timeliness of the result.

38. Laxity Type and Laxity Function
 Laxity type of a job indicates whether its timing
constraints are soft or hard.
 Laxity type is measured in terms of usefulness
function.
 This function gives the usefulness of the result
produced by the job as a function of its tardiness.
 In the figure, the solid lines represent the hard real
time job.
 In these jobs, the result become negative or zero as
soon as job become tardy.

40.  The dotted lines give the usefulness of the job which
decreases gradually and become 0 if tardiness
become large.
 The dashed line shows the function that decreases
faster and becomes negative. E.g. is stock price
update transaction.
 It may be tolerable if the update completes slightly
late and price written in database is slightly old. But
if the transaction complete so late the current price
differ significantly and result may be negative.

41.  We can use the usefulness function to describe
qualitatively the real time performance objectives of
the system.
 They can guide the choice and implementation of
scheduling strategies.

42. Resource Parameter of Job and Parameter
Resources
 The resource parameter of the job is its resource
requirement.
 The resource can be processor, memory or other
resources.
 The resource parameter give the type of processor
and units of each resource type required by the job
and the time interval during its execution when units
are required.
 This parameter provides the information that is
needed to support resource management decision.

43.  The two resource parameters are:
 Preemptivity of Resources
 Resource Graph

44. Preemptivity of Resource
 A resource in non-preemptable if each unit of
resource is constrained to be used serially.
 Once the unit of non-preemptable resource is
allocated to a job, the other job needing the unit
must wait until the job completes its use.
 If a job can use every resource in an interleaved
manner, then the resource is called preemptable.

45. Resource Graph
 Resource graph is used to describe the configuration
of the resources.
 In a resource graph, there is a vertex for every
processor or resource Ri in the system.
 The attributes of the vertex are the parameter of the
resources.
 Resource type of a resource tell if the resource is
processor or passive resource and number gives the
available number of units.

46.  There are two types of edges in resource graphs.
 An edge from vertex Ri to Rk can mean Rk is
component of Ri(memory is a part of computer).
 This edge is an is-a-part-of-edge.
 Some edges in resource graph represent the
connectivity between the components.
 These edges are called accessibility
edges.(Connection between two CPUs)

47. Scheduling Hierarchy

48.  The figure shows the three elements of our model of
real time system together.
 The application system is represented by task graph
on the top of the diagram.
 This graph gives the processor time and resource
requirements of jobs, the timing constraints of each
job and dependencies of jobs.
 The resource graph describes the amounts of the
resources available to execute the application
system, attributes of resources and rule governing
their usage.

49.  Between them are the scheduling and the resource
access-control algorithms used by Operating System.

50. Scheduler and Schedules
 Jobs are scheduled and allocated resources
according to a chosen set of scheduling algorithms
and resource access protocols.
 The resource which implements these algorithms is
called the scheduler.
 A scheduler assigns the job to processors.
 A schedule is an assignment of all jobs in the system
on the available resources.
 By correctness of we mean the scheduler only
produce valid schedules.

51.  A valid schedule satisfies the following conditions:

52. Feasibility, Optimality and Performance
Measures
 A valid schedule is also called feasible if every job
meet its timing constraints i.e. if a valid schedule
complete by its deadline then the schedule is called
feasible schedule.
 A job can only be schedule according to the
scheduling algorithm, if the scheduler always
produces a feasible schedule.

53.  A hard real time scheduling is optimal if the
algorithm always produces a feasible schedule if the
given set of jobs has feasible schedules.
 If any optima schedule fail to find a feasible schedule
then the given set of jobs cannot feasibly scheduled
by any algorithms.
 The other performance measures are maximum and
average tardiness, lateness, response time, missed
and invalid rates.

54.  The lateness of the job is the difference between its
completion time and its deadline. Unlike tardiness, it
can be negative if it completes earlier than its
deadline and can be positive if it completes late than
deadline.
 Missed rate is the percentage of jobs that are
executed but completed too late.
 The loss rate is the percentage of jobs that are not
executed at all or discarded.
 When it is impossible to complete all the jobs on
time scheduler may choose to discard some jobs.

55. Interaction among Schedulers
 A system typically has the hierarchy of the scheduler.
 This hierarchy arise for two reasons:
 First some processors and resources used by
application are logical which need physical resources
for execution.
 Second, a job may model a server that executes on
behalf of its clients.
 The time and resources allocated to the server job
must in turn be allocated to its client jobs.