5 research outputs found
How to estimate a cumulative process’s rate-function
Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(·,·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I
constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstrated that this approach is favorable to a more direct method as it ensures the laws of the estimates converge weakly to a Dirac measure at I
How to estimate a cumulative process’s rate-function
Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(·,·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I
constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstrated that this approach is favorable to a more direct method as it ensures the laws of the estimates converge weakly to a Dirac measure at I
Measurement Based Resource Allocation for Multimedia Applications
Modern networks are now capable of guaranteeing a consistent Quality of Service (QoS) to multimedia traffic streams. A number of major operating system vendors are also working hard to extend these guarantees into the end-system. In both cases, however, there remains the problem of determining a service rate sufficient to ensure the desired Quality of Service. Source modelling is not a sustainable approach in the network case and it is even less feasible to model the demands of multimedia applications. The ESPRIT Measure project is successfully using online measurement and estimation to perform resource allocation for bursty traffic in ATM networks. In this paper we consider the applicability of the same theory to resource allocation in a multimedia operating system which offers QoS guarantees to its applications
Using estimated entropy in a queueing system with dynamic routing.
In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations
Most likely paths to error when estimating the mean of a reflected random walk
It is known that simulation of the mean position of a Reflected Random Walk
(RRW) exhibits non-standard behavior, even for light-tailed increment
distributions with negative drift. The Large Deviation Principle (LDP) holds
for deviations below the mean, but for deviations at the usual speed above the
mean the rate function is null. This paper takes a deeper look at this
phenomenon. Conditional on a large sample mean, a complete sample path LDP
analysis is obtained. Let denote the rate function for the one dimensional
increment process. If is coercive, then given a large simulated mean
position, under general conditions our results imply that the most likely
asymptotic behavior, , of the paths is
to be zero apart from on an interval and to satisfy the
functional equation \begin{align*} \nabla
I\left(\ddt\psi^*(t)\right)=\lambda^*(T_1-t) \quad \text{whenever } \psi(t)\neq
0. \end{align*} If is non-coercive, a similar, but slightly more involved,
result holds.
These results prove, in broad generality, that Monte Carlo estimates of the
steady-state mean position of a RRW have a high likelihood of over-estimation.
This has serious implications for the performance evaluation of queueing
systems by simulation techniques where steady state expected queue-length and
waiting time are key performance metrics. The results show that na\"ive
estimates of these quantities from simulation are highly likely to be
conservative.Comment: 23 pages, 8 figure