Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych
Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych
Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych
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and the set of tasks is divided into 2 subsets [5]: T 1 =<br />
{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<br />
task T i 1 (i = 1,2,…,n1) requires one arbitrary processor for its<br />
processing and its processing time is equal to t i 1 , however each<br />
task T i 2 (i = 1,2,…,n2) requires 2 arbitrary processors simultaneously<br />
for its processing during a period of time whose length<br />
is equal to t i 2 ; thus, tasks T i 2 are called width-2 tasks or T 2 -<br />
tasks. We shall assume its minimum cost and maximum operating<br />
speed. The proposed model may be used for defining<br />
problems for fault tolerance system. The model of a system in<br />
this approach, typical for the theory of task scheduling, consists<br />
of a set of operations (tasks) and existing relationships between<br />
them (related to their order, required resources, time, readiness<br />
and completion deadlines, priority etc.).<br />
The management procedure contains the following<br />
phases: identification of hardware and software resources for<br />
task execution, defining the processing time, defining the conflict-free<br />
task schedule and defining the level of resource cosharing<br />
and the degree of concurrency in task performance.<br />
A schedule is called feasible if, besides the usual conditions,<br />
each task T i 1 is processed by one processor and each task T i<br />
2<br />
is processed by 2 processors at a time. A feasible schedule is<br />
optimal, if its length is a minimum and it is implemented using<br />
minimum resource cost. Each task is defined by a set of parameters:<br />
resource requirements, execution time, ready time<br />
and deadline, attribute - preemptable or nonpreemptable. The<br />
tasks set may contain defined precedence constraints represented<br />
by a digraph with nodes representing tasks, and directed<br />
edges representing precedence constraints. If there is<br />
at least one precedence constraint in a task set, we shall refer<br />
it to as a set of dependent tasks; otherwise they are a set of<br />
independent tasks. Let us assume that fault tolerance system<br />
resources include universal parallel processors and other specialized<br />
resources. As for tasks, we assume one-processor<br />
tasks used for modeling usable preemptable/nonpreemptable<br />
and dependent tasks, and two-processor tasks, for which we<br />
assume time and resource. Two-processor tasks model the<br />
system testing tasks (e.g. one processor checks the other).<br />
Testing tasks may be dependent on the defined time moments<br />
of readiness to perform and to complete assigned tasks. Twoprocessor<br />
tasks may realize a defined strategy of testing<br />
a computer system and its fault tolerance characteristics.<br />
In fault tolerance systems an appropriate strategy of selftesting<br />
during regular exploitation must be provided. In general,<br />
architectures of fault tolerance computer systems are<br />
multiprocessor ones. The objective of operating systems in<br />
multiprocessor systems is scheduling tasks and their allocation<br />
to system resources. For fault tolerance systems, this<br />
means scheduling usable and testing tasks, that should detect<br />
errors of executive modules, in particular processors. As<br />
a result of testing, the operating system may receive the information<br />
about incorrect operation and may locate, by the<br />
proper analysis, a faulty module automatically. Consequently,<br />
the operating system can make a decision about repair strategy,<br />
for instance system reconfiguration (ignore damaged resources<br />
for execution of tasks). The management of networks<br />
with multiprocessors and fault tolerance consists of following<br />
stages (Fig. 1).<br />
So far [6] resources selection, task scheduling and task<br />
and resources allocation have been realized independently in<br />
sequence: in the first place resource division and tasks scheduling<br />
next - Fig. 2.<br />
In this paper is presented approach, in which resources<br />
selection, task scheduling, allocation of tasks and resources,<br />
as well as system optimization are realized coherently - Fig. 3.<br />
In concurrent approach once the tasks have been scheduled<br />
and allocated, the resources are reselected, changing<br />
the ones chosen previously, in search of a satisfactory solution<br />
meeting all the established criteria.<br />
This concurrent approach - presented in this paper - based<br />
on two algorithms behaving variously in different ways lets you<br />
not only find the sub-optimal solution, but also verify this solution.<br />
Presented algorithms let us find the solution, but at the same<br />
time they let us evaluate the algorithms themselves. This way<br />
we can tell which of the algorithms is faster in finding better and<br />
better solutions, which algorithm is more tolerant to modifications<br />
of system parameters, and also which of them enables fast adaptation<br />
to new parameters, while the system changes dynamically.<br />
Fig. 1. The management of system with multiprocessors and fault<br />
tolerance<br />
Rys. 1. Zarządzanie wieloprocesorowym systemem komputerowym<br />
z tolerancją uszkodzeń<br />
Fig. 2. Independent allocation resource and scheduling of task<br />
Rys. 2. Niezależne alokacje zasobów i szeregowanie zadań<br />
Fig. 3. Concurrent allocation resource and scheduling of task<br />
Rys. 3. Współbieżne alokacje zasobów i szeregowanie zadań<br />
ELEKTRONIKA 11/<strong>2009</strong> 39