Analysis of Markov-modulated infinite-server queues in the central-limit regime

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\ge 0$, in the asymptotic regime in which the arrival rates $\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\alpha$, with $\alpha \in \mathbb R^+$. The specific value of $\alpha$ has a crucial impact on the result: (i) for $\alpha>1$ the system essentially behaves as an M/M/$\infty$ queue, and in the central limit theorem the centered process has to be normalized by $\sqrt{N}$; (ii) for $\alpha<1$, the centered process has to be normalized by $N^{{1-}\alpha/2}$, with the deviation matrix appearing in the expression for the variance

Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit

This article studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates (i) by a factor N and the rates (ij) of the background process by N1+E (for some E>0), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that N tends to . In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean

A comparison of integration methods for atmospheric transport-chemistry problems

This paper is devoted to the time integration of atmospheric transport-chemistry problems. Due to the large number of species and the 3D nature off-the-shelf solvers are not feasible. This has led to the use of special techniques. Most popular is operator splitting. This paper presents a comparison between standard operator splitting, source splitting and approximate matrix factorization. All methods under consideration are comparable in costs measured step wise. The comparison is directed at real-life problems. For that purpose a regional air pollution model is used

A continuum model of lipid bilayers

We study a one-dimensional continuum model for lipid bilayers. The system consists of water and lipid molecules; lipid molecules are represented by two ‘beads’, a head bead and a tail bead, connected by a rigid rod. We derive a simplified model for such a system, in which we only take into account the effects of entropy and hydrophilic/hydrophobic interactions. We show that for this simple model membrane-like structures exist for certain choices of the parameters, and numerical calculations suggest that they are stable

Diffusive gradients in the PTS system

It has recently been conjectured that metabolic pathways with membrane-bound enzymes can give rise to concentration gradients in the cytosolic pathway components. We investigate this issue using a theoretical model for the Phosphoenolpyruvate-dependent Phosphotransferase system in {it E. coli/, for which accurate measurements of the kinetic parameters are available. We show that significant spatial gradients indeed exist, and we discuss the potential implications of this finding

Parameter estimation and determinability analysis applied to Drosophila gap gene circuits.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Mathematical modeling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to assess the quality of the parameter estimates, especially if parameter values are used to draw biological conclusions from the model. RESULTS: In this paper we describe how the quality of parameter estimates can be analyzed. We apply our methodology to assess parameter determinability for gene circuit models of the gap gene network in early Drosophila embryos. CONCLUSION: Our analysis shows that none of the parameters of the considered model can be determined individually with reasonable accuracy due to correlations between parameters. Therefore, the model cannot be used as a tool to infer quantitative regulatory weights. On the other hand, our results show that it is still possible to draw reliable qualitative conclusions on the regulatory topology of the gene network. Moreover, it improves previous analyses of the same model by allowing us to identify those interactions for which qualitative conclusions are reliable, and those for which they are ambiguous

Uncertainty propagation in neuronal dynamical systems

One of the most notorious characteristics of neuronal electrical activity is its variability, whose origin is not just instrumentation noise, but mainly the intrinsically stochastic nature of neural computations. Neuronal models based on deterministic differential equations cannot account for such variability, but they can be extended to do so by incorporating random components. However, the computational cost of this strategy and the storage requirements grow exponentially with the number of stochastic parameters, quickly exceeding the capacities of current supercomputers. This issue is critical in Neurodynamics, where mechanistic interpretation of large, complex, nonlinear systems is essential. In this paper we present accurate and computationally efficient methods to introduce and analyse variability in neurodynamic models depending on multiple uncertain parameters. Their use is illustrated with relevant example