Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych

and the set of tasks is divided into 2 subsets [5]: T 1 =
{T 1 1 ,T 2 1 ,…,T n1 1 }, T 2 = {T 1 2 ,T 2 2 ,…,T n2 2 }, n = n1 + n2 and each
task T i 1 (i = 1,2,…,n1) requires one arbitrary processor for its
processing and its processing time is equal to t i 1 , however each
task T i 2 (i = 1,2,…,n2) requires 2 arbitrary processors simultaneously
for its processing during a period of time whose length
is equal to t i 2 ; thus, tasks T i 2 are called width-2 tasks or T 2 -
tasks. We shall assume its minimum cost and maximum operating
speed. The proposed model may be used for defining
problems for fault tolerance system. The model of a system in
this approach, typical for the theory of task scheduling, consists
of a set of operations (tasks) and existing relationships between
them (related to their order, required resources, time, readiness
and completion deadlines, priority etc.).
The management procedure contains the following
phases: identification of hardware and software resources for
task execution, defining the processing time, defining the conflict-free
task schedule and defining the level of resource cosharing
and the degree of concurrency in task performance.
A schedule is called feasible if, besides the usual conditions,
each task T i 1 is processed by one processor and each task T i
2
is processed by 2 processors at a time. A feasible schedule is
optimal, if its length is a minimum and it is implemented using
minimum resource cost. Each task is defined by a set of parameters:
resource requirements, execution time, ready time
and deadline, attribute - preemptable or nonpreemptable. The
tasks set may contain defined precedence constraints represented
by a digraph with nodes representing tasks, and directed
edges representing precedence constraints. If there is
at least one precedence constraint in a task set, we shall refer
it to as a set of dependent tasks; otherwise they are a set of
independent tasks. Let us assume that fault tolerance system
resources include universal parallel processors and other specialized
resources. As for tasks, we assume one-processor
tasks used for modeling usable preemptable/nonpreemptable
and dependent tasks, and two-processor tasks, for which we
assume time and resource. Two-processor tasks model the
system testing tasks (e.g. one processor checks the other).
Testing tasks may be dependent on the defined time moments
of readiness to perform and to complete assigned tasks. Twoprocessor
tasks may realize a defined strategy of testing
a computer system and its fault tolerance characteristics.
In fault tolerance systems an appropriate strategy of selftesting
during regular exploitation must be provided. In general,
architectures of fault tolerance computer systems are
multiprocessor ones. The objective of operating systems in
multiprocessor systems is scheduling tasks and their allocation
to system resources. For fault tolerance systems, this
means scheduling usable and testing tasks, that should detect
errors of executive modules, in particular processors. As
a result of testing, the operating system may receive the information
about incorrect operation and may locate, by the
proper analysis, a faulty module automatically. Consequently,
the operating system can make a decision about repair strategy,
for instance system reconfiguration (ignore damaged resources
for execution of tasks). The management of networks
with multiprocessors and fault tolerance consists of following
stages (Fig. 1).
So far [6] resources selection, task scheduling and task
and resources allocation have been realized independently in
sequence: in the first place resource division and tasks scheduling
next - Fig. 2.
In this paper is presented approach, in which resources
selection, task scheduling, allocation of tasks and resources,
as well as system optimization are realized coherently - Fig. 3.
In concurrent approach once the tasks have been scheduled
and allocated, the resources are reselected, changing
the ones chosen previously, in search of a satisfactory solution
meeting all the established criteria.
This concurrent approach - presented in this paper - based
on two algorithms behaving variously in different ways lets you
not only find the sub-optimal solution, but also verify this solution.
Presented algorithms let us find the solution, but at the same
time they let us evaluate the algorithms themselves. This way
we can tell which of the algorithms is faster in finding better and
better solutions, which algorithm is more tolerant to modifications
of system parameters, and also which of them enables fast adaptation
to new parameters, while the system changes dynamically.
Fig. 1. The management of system with multiprocessors and fault
tolerance
Rys. 1. Zarządzanie wieloprocesorowym systemem komputerowym
z tolerancją uszkodzeń
Fig. 2. Independent allocation resource and scheduling of task
Rys. 2. Niezależne alokacje zasobów i szeregowanie zadań
Fig. 3. Concurrent allocation resource and scheduling of task
Rys. 3. Współbieżne alokacje zasobów i szeregowanie zadań
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