Hardware Reference
In-Depth Information
9.1.1
LOAD DEFINITIONS
In a real-time system, the definition of computational workload depends on the tempo-
ral characteristics of the computational activities. For non-real-time or soft real-time
tasks, a commonly accepted definition of workload refers to the standard queueing the-
ory, according to which a load ρ , also called traffic intensity , represents the expected
number of job arrivals per mean service time. If C is the mean service time and λ is
the average interarrival rate of the jobs, the average load can be computed as
ρ = λC.
Note that this definition does not take deadlines into account; hence, it is not particu-
larly useful to describe real-time workloads. In a hard real-time environment, a system
is overloaded when, based on worst-case assumptions, there is no feasible schedule for
the current task set, so one or more tasks will miss their deadline.
If the task set consists of n independent preemptable periodic tasks, whose relative
deadlines are equal to their period, then the system load ρ is equivalent to the processor
utilization factor:
n
C i
T i
ρ = U =
,
i =1
where C i and T i are the computation time and the period of task τ i , respectively. In
this case, a load ρ> 1 means that the total computation time requested by the periodic
activities in their hyperperiod exceeds the available time on the processor; therefore,
the task set cannot be scheduled by any algorithm.
For a generic set of real-time jobs that can be dynamically activated, the system load
varies at each job activation and it is a function of the jobs' deadlines. In general, the
load in a given interval [ t a , t b ] can be defined as
g ( t 1 ,t 2 )
t 2
ρ ( t a ,t b )=
max
t 1 ,t 2 [ t a ,t b ]
(9.1)
t 1
where g ( t 1 ,t 2 ) is the processor demand in the generic interval [ t 1 , t 2 ]. Such a def-
inition, however, is of little practical use for load calculation, since the number of
intervals in which the maximum has to be computed can be very high. Moreover, it is
not clear how large the interval [ t a , t b ] should be to estimate the overall system load.
A more practical definition that can be used to estimate the current load in dynamic
real-time systems is the instantaneous load ρ ( t ), proposed by Buttazzo and Stankovic
[BS95].
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