On two generalisations of the final value theorem : scientific relevance, first applications, and physical foundations

The present work considers two published generalisations of the Laplace-transform final value theorem (FVT) and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing. Physical sense of the irrational time functions, involved in the other generalisation, is one of the points of concern. The work strongly extends the conceptual frame of the references and outlines some new research directions for applications of the generalised theorem

Physical activity in England: Who is meeting the recommended level of participation through sports and exercise?

This article is available through the Brunel Open Access Publishing Fund. Copyright © 2012 Anokye et al.Background: Little is known about the correlates of meeting recommended levels of participation in physical activity (PA) and how this understanding informs public health policies on behaviour change. Objective: To analyse who meets the recommended level of participation in PA in males and females separately by applying ‘process’ modelling frameworks (single vs. sequential 2-step process). Methods: Using the Health Survey for England 2006, (n = 14 142; ≥16 years), gender-specific regression models were estimated using bivariate probit with selectivity correction and single probit models. A ‘sequential, 2-step process’ modelled participation and meeting the recommended level separately, whereas the ‘single process’ considered both participation and level together. Results: In females, meeting the recommended level was associated with degree holders [Marginal effect (ME) = 0.013] and age (ME = −0.001), whereas in males, age was a significant correlate (ME = −0.003 to −0.004). The order of importance of correlates was similar across genders, with ethnicity being the most important correlate in both males (ME = −0.060) and females (ME = −0.133). In females, the ‘sequential, 2-step process’ performed better (ρ = −0.364, P < 0.001) than that in males (ρ = 0.154). Conclusion: The degree to which people undertake the recommended level of PA through vigorous activity varies between males and females, and the process that best predicts such decisions, i.e. whether it is a sequential, 2-step process or a single-step choice, is also different for males and females. Understanding this should help to identify subgroups that are less likely to meet the recommended level of PA (and hence more likely to benefit from any PA promotion intervention).This study was funded by the Department of Health’s Policy Research Programme

Randomized longest-queue-first scheduling for large-scale buffered systems

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing the number of sampled buffers $d=d(n)$ to depend on the number of buffers $n$, which yields an asymptotic `decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of $n$ and $d(n)$. To our knowledge, we are the first to derive diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized longest-queue-first algorithm emulates the longest-queue-first algorithm, yet is computationally more attractive. The analysis of the system performance as a function of $d(n)$ is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized longest-queue-first scheduling algorithm

Hybrid Behaviour of Markov Population Models

We investigate the behaviour of population models written in Stochastic Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent Constraint Programming. In particular, we focus on models from which we can define a semantics of sCCP both in terms of Continuous Time Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are approximated continuously, while others are kept discrete. We will prove the correctness of the hybrid semantics from the point of view of the limiting behaviour of a sequence of models for increasing population size. More specifically, we prove that, under suitable regularity conditions, the sequence of CTMC constructed from sCCP programs for increasing population size converges to the hybrid system constructed by means of the hybrid semantics. We investigate in particular what happens for sCCP models in which some transitions are guarded by boolean predicates or in the presence of instantaneous transitions

Is there excess capacity in rural banking markets: Some empirical insights for India

According to economic theory, there are at least three indicators of excess capacity in banking: (a) low loan-to-asset ratio, (b) low profitability and (c) high per unit operating expense. If excess capacity exists, it will be easiest to identify, through these indicators, at regional rural banks. Using bank level data on regional rural banks in India for the period 1991 to 2001, the paper uncovers little evidence of excess capacity using simultaneous equation techniques; univariate analysis reinforces the findings

Scaling Size and Parameter Spaces in Variability-Aware Software Performance Models (T)

In software performance engineering, what-if scenarios, architecture optimization, capacity planning, run-time adaptation, and uncertainty management of realistic models typically require the evaluation of many instances. Effective analysis is however hindered by two orthogonal sources of complexity. The first is the infamous problem of state space explosion — the analysis of a single model becomes intractable with its size. The second is due to massive parameter spaces to be explored, but such that computations cannot be reused across model instances. In this paper, we efficiently analyze many queuing models with the distinctive feature of more accurately capturing variability and uncertainty of execution rates by incorporating general (i.e., non-exponential) distributions. Applying product-line engineering methods, we consider a family of models generated by a core that evolves into concrete instances by applying simple delta operations affecting both the topology and the model's parameters. State explosion is tackled by turning to a scalable approximation based on ordinary differential equations. The entire model space is analyzed in a family-based fashion, i.e., at once using an efficient symbolic solution of a super-model that subsumes every concrete instance. Extensive numerical tests show that this is orders of magnitude faster than a naive instance-by-instance analysis

Fluid passage-time calculation in large Markov models

Recent developments in the analysis of large Markov models facilitate the fast approximation of transient characteristics of the underlying stochastic process. So-called fluid analysis makes it possible to consider previously intractable models whose underlying discrete state space grows exponentially as model components are added. In this work, we show how fluid approximation techniques may be used to extract passage-time measures from performance models. We focus on two types of passage measure: passage-times involving individual components; as well as passage-times which capture the time taken for a population of components to evolve. Specifically, we show that for models of sufficient scale, passage-time distributions can be well approximated by a deterministic fluid-derived passage-time measure. Where models are not of sufficient scale, we are able to generate approximate bounds for the entire cumulative distribution function of these passage-time random variables, using moment-based techniques. Finally, we show that for some passage-time measures involving individual components the cumulative distribution function can be directly approximated by fluid techniques

Assessing Equilibrium Exchange Rates in CEE Acceding Countries: Can We Have DEER with BEER without FEER?

The ambition of this paper is to provide a thorough overview of equilibrium exchange rates in the acceding countries of Central and Eastern Europe. Therefore, theoretical models of equilibrium exchange rates are reviewed first and presented in a structured way. Subsequently, the existing body of the empirical literature aimed at investigating real exchange rate determination and possible misalignments is analyzed in a systematic manner. Finally, an attempt is made to sum up where we stand at the moment and what the major shortcomings of the approaches currently used in the literature are.http://deepblue.lib.umich.edu/bitstream/2027.42/40050/3/wp664.pd