Analytical System Administration in Java

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istrator's taste, it is an important viewpoint in the pursuit of system administration as a scientific discipline. 11.7.1 Scales and Fluctuations Complex systems are characterized by behaviour at many levels or scales. To extract information from a complex system it is necessary to focus on the appropriate scale for that information. In physics, three scales are usually distinguished in many-component systems: the microscopic, mesoscopic and macroscopic scales. We can borrow this terminology for convenience. Microscopic behaviour details exact mechanisms at the level of atomic operations. Mesoscopic behaviour looks as small clusters of microscopic processes and examines them in isolation. Macroscopic processes concern the long-term average behaviour of the whole system.
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These three scales can also be discerned in operating systems, and they must usually be considered separately. At the microscopic level we have individual system calls and other atomic transactions (on the order of microseconds to milliseconds). At the mesoscopic level we have clusters and patterns of system calls and other process behaviour, including algorithms, procedures, possibly arising from single processes or groups of processes. Finally, there is the macroscopic level at which one views all the activities of all the users over scales at which they typically work and consume resources (minutes, hours, days, weeks). There is clearly a measure of arbitrariness in drawing these distinctions. The point is that there are typically three scales which can be usefully distinguished in a relatively stable dynamical system. 11.7.2 Principle of Superposition
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In any dynamical system where several microscopic processes can coexist, there are two possible scenarios: Every process is completely independent of every other. System resources change linearly (additively) in response to new processes. The addition of each new process affects the behaviour of the others in a non-additive (non-linear) fashion.
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The first of these is called the principle of superposition. It is a generic property of linear systems (actually this is a defining tautology). In the second case, the system is said to be non-linear because the result of adding lots of processes is not merely the sum of those processes: the processes interact and complicate matters. Owing to the complexity of interactions between subsystems in a network, it is likely that there is at least some degree of nonlinearity in the measurements we are looking for. That means that a change in one part of the system will have communicable, knock-on effects on another part of the system, with possible feedback, and so on.
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Deterministic and Stochastic Behaviour
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This is one of the things which needs to be examined, since it has a bearing on the shape of the distribution one can expect to find. Empirically one often finds, in non-linear systems, that the probability of a deviation from the expected behaviour is [102]
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for large jumps. This can be contrasted with a Gaussian measure for a random sample
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which one might normally expect. It is interesting to determine the extent of non-linearity in the behaviour of computer systems.
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11.7.3 The Idea of Convergence
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In order to converge to a stable equilibrium one needs to provide countermeasures to change which are switched off when the system has reached its desired state. For this to happen, a policy of checking-before-doing is required. This is actually a difficult issue which becomes increasingly difficult with the complexity of the task involved. Fortunately, most system configuration issues are solved by simple means (file permissions, missing files, etc.), and thus, in practice, it can be a simple matter to test whether the system is in its desired state before modifying it. In mathematics a random perturbation in time is represented by Gaussian noise, or a function whose expectation value, averaged over a representative time interval, is zero
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The simplest model of random change is the driven harmonic oscillator.
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where 5 is the state of the system and 7 is the rate at which it converges to a steady state. To make oscillations converge, they are damped by a frictional or counter force 7 (in the present case the immune system is the frictional force which will damp down unwanted changes). To have any chance of stopping the oscillations the counterforce must be able to change direction in time with the oscillations so that it is always opposing the changes at the same rate as the changes themselves. Formally, this is ensured by having the frictional force proportional to the rate of change of the system, as in the differential representation above. The solutions to this kind of motion are damped oscillations of the form
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for some frequency w and damping rate 7. In the theory of harmonic motion, three cases are distinguished: under-damped motion, damped and over-damped motion. In under-damped m o t i o n , there is never sufficient counterforce to make the oscillations converge to any
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