SYSTEM MODEL THEORY

System Model Theory and Practice

System Model Theory and Practice

Introduction

A designer obtains estimates of the utilization of different resources in the system. High utilizations are signals of scarce resources. An investment into such a resource may then be well worthwhile. The ultimate use of system models is performance predictions. For a given workload, they estimate the cycles per instruction (CPI) as a reciprocal of a throughput measure that the modelled architecture would incur.

A popular class of system models is closed queuing networks. In the basic framework, each CPU dispatches memory requests at a predetermined rate loosely corresponding to its infinite level-one cache CPI. These requests are serviced by the memory system, which is modelled to consist of queuing (e.g. cache tag and data arrays) and delay centres (e.g. the CPUs themselves) (Agarwal Horowitz and Hennessy 1999). A delay centre is a service centre with an infinite number of servers. Thus, no matter how many requests arrive at a delay centre, they are serviced concurrently. On the other hand, a queuing centre has a maximum number of requests it can service at the same time. If this number is reached, a new request must wait until one of the current services is completed. The service centres are connected via a logical network that emulates the machine's organization. A request takes a random route through the network with probabilities determined in part by the workload characteristics. Various queuing network models have been proposed. Examples include and, and references therein.

Whenever a queuing model has a product form solution, the latter can be found via the mean-value analysis, a fast iterative analytic method. Analytic models do not necessarily address second order effects such as detailed arbitration algorithms, finite queue effects, queue reordering, constant service times, and so on. Frequently, they provide enough detail for resolving many design tradeoffs. However, if more elaborate modelling is required, a more general queuing system can be constructed (Powell and Baker 2003). The solution would typically be found by simulation. At the expense of longer computation, one is able to build more general models addressing effects such as those mentioned above.

Uncertainty under a Stochastic Parameter Model

In this, we present a Bayesian approach to modelling output uncertainty. We assume that the parameter vector View the MathML source is random with distribution View the MathML source. This distribution is meant to represent our uncertainty about the actual parameters after seeing their values produced by the parameter generator as described in the introduction. Our understanding is that the actual values are close to the observed ones, but in general deviate from them usually due to technical limitations of the parameter generator. View the MathML source is then a summary of that deviation. Suppose we know View the MathML source. Since View the MathML source is a random vector and Y is a function of View the MathML source, Y is a random variable with some distribution ?(y) that is determined by distribution View the MathML source and function View the MathML ...