Simulation Of Stochastic Networks Research Articles

Effects of Population Based Screening for Chlamydia Infections in The Netherlands Limited by Declining Participation Rates

BackgroundA large trial to investigate the effectiveness of population based screening for chlamydia infections was conducted in the Netherlands in 2008–2012. The trial was register based and consisted of four rounds of screening of women and men in the age groups 16–29 years in three regions in the Netherlands. Data were collected on participation rates and positivity rates per round. A modeling study was conducted to project screening effects for various screening strategies into the future.Methods and FindingsWe used a stochastic network simulation model incorporating partnership formation and dissolution, aging and a sexual life course perspective. Trends in baseline rates of chlamydia testing and treatment were used to describe the epidemiological situation before the start of the screening program. Data on participation rates was used to describe screening uptake in rural and urban areas. Simulations were used to project the effectiveness of screening on chlamydia prevalence for a time period of 10 years. In addition, we tested alternative screening strategies, such as including only women, targeting different age groups, and biennial screening. Screening reduced prevalence by about 1% in the first two screening rounds and leveled off after that. Extrapolating observed participation rates into the future indicated very low participation in the long run. Alternative strategies only marginally changed the effectiveness of screening. Higher participation rates as originally foreseen in the program would have succeeded in reducing chlamydia prevalence to very low levels in the long run.ConclusionsDecreasing participation rates over time profoundly impact the effectiveness of population based screening for chlamydia infections. Using data from several consecutive rounds of screening in a simulation model enabled us to assess the future effectiveness of screening on prevalence. If participation rates cannot be kept at a sufficient level, the effectiveness of screening on prevalence will remain limited.

Editorial foreword to special issue on Simulation of Stochastic Networks and related topics

This special issue contains a selection of papers which are based on some of the invited lectures that were given at the workshop on Simulation of Stochastic Networks which took place on June 21–23, 2010 at the Newton Institute of Mathematical Sciences in Cambridge, UK. The workshop, which was dedicated to topics related to estimation of rare events as well as other aspects including simulation of stochastic differential equations (SDEs), and steady-state simulation, was attended by over fifty active researchers and leading experts in the fields of applied probability and stochastic simulation. The special issue cuts across different areas at the intersection of applied probability and stochastic simulation and we believe that an important strength of the issue is that the contributions suggest interesting research avenues in their respective areas. We therefore hope that the readers will enjoy these contributions and feel enticed to venture into the topics that concern the papers in this special issue. The first paper in this special issue, Analysis of an interacting particle method for rare event estimation, is authored by Yi Cai and Paul Dupuis. The paper studies a class of interacting particle systems for Monte Carlo estimation of large deviations probabilities based on finding a subsolution to a certain partial differential equation (PDE). In recent years, the subsolution approach has become one of the standard methods for constructing rare event simulation estimators with suitable optimality properties. The authors extend, at least in the context of onedimensional problems, the subsolution approach for constructing suitable optimal estimators to a much broader class of particle methods. Surprisingly, they show that the PDE associated to interacting particle

A Class of Pairwise Models for Epidemic Dynamics on Weighted Networks

In this paper, we study the SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with stochastic network simulations to evaluate the impact of different weight distributions on epidemic thresholds and dynamics in general. For the SIR model, the basic reproductive ratio R0 is computed, and we show that (i) for both network models R0 is maximised if all weights are equal, and (ii) when the two models are 'equally-matched', the networks with a random weight distribution give rise to a higher R0 value. The models with different weight distributions are also used to explore the agreement between the pairwise and simulation models for different parameter combinations.

Sheet Resistance of Continuous Filament Nonwoven Fabrics

Two modeling techniques are introduced to predict the sheet resistance of electrically conductive continuous filament nonwoven fabric: a two-dimensional (2–D) discrete filament stochastic resistor network simulation, and a simple analysis using a laminate analogy. The effects of anisotropy and sample size are considered. Results are compared with experiments on a silver coated point bonded nylon nonwoven fabric. For this particular sample, experimental sheet resistance results are significantly under-predicted by the 2–D analytical and simulation approaches where perfect inter-filament bonding is assumed. The utility of the 2–D perfect bonding predictions as an ultimate lower bound on the sheet resistance that may be achieved by extremely well-bonded continuous filament networks is discussed. Simulations of 2–D filament webs with poor inter-filament bonding and moderate anisotropy are shown to agree well with the present experiments. Taken together, the present results suggest that modeling of the in-plane conduction behavior of a general continuous filament nonwoven fabric requires a 3–D structural approach to capture the effect of an appropriate number density of inter-filaments bonds.

Epidemic threshold and control in a dynamic network

In this paper we present a model describing susceptible-infected-susceptible-type epidemics spreading on a dynamic contact network with random link activation and deletion where link activation can be locally constrained. We use and adapt an improved effective degree compartmental modeling framework recently proposed by Lindquist et al. [J. Math Biol. 62, 143 (2010)] and Marceau et al. [Phys. Rev. E 82, 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically, and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network and are able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical R0 calculation for the dynamic network model and show that, depending on the relative time scales of the network evolution and disease transmission, two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks.

Morphometric analysis of three-dimensional networks of karst conduits

The main idiosyncrasy of a typical karst system is the presence of a three-dimensional network of conduits behaving as drains in the system and being responsible of both the quick response of karst springs to rainfall events and the complex distribution of solutes in the system. A morphometric analysis of the three-dimensional geometry of conduits provides quantitative measures that can be used in a range of applications. These morphometric parameters can be used as descriptors of the underground geomorphology, they provide information on speleogenesis processes, they can be correlated with karst denudation ratios, they can be used to control the simulation of realistic stochastic karst networks of conduits, and they can be correlated with hydrogeologic behaviour of the karst system. The main purpose of this paper is to define, describe and illustrate a range of morphometric indexes and morphometric functions that can be calculated nowadays because the availability of three-dimensional topographies provided by speleological work and the availability of the computational and graphical power provided by modern computers. Some of the morphometric parameters describe the existence of preferential directions of karstification, others describe the kartification along the vertical and the possible presence of inception horizons. Other indexes describe the shape complexity of the karstic network, whilst other indexes describe spatial variability of the conduit geometry, and other parameters give account of the connectivity of the three-dimensional network. The morphometric analysis is illustrated with a three-dimensional karstic network in Southern France.

Two competing orientation patterns explain experimentally observed anomalies in growing actin networks

The lamellipodium of migrating animal cells protrudes by directed polymerization of a branched actin network. The underlying mechanisms of filament growth, branching, and capping can be studied in in vitro assays. However, conflicting results have been reported for the force-velocity relation of such actin networks, namely both convex and concave shapes as well as history dependencies. Here we model branching as a reaction that is independent of the number of existing filaments, in contrast to capping, which is assumed to be proportional to the number of existing filaments. Using both stochastic network simulations and deterministic rate equations, we show that such a description naturally leads to the stability of two qualitatively different stationary states of the system, namely a +/- 35 degrees and a +70/0/-70 degrees orientation pattern. Changes in network growth velocity induce a transition between these two patterns. For sufficiently different protrusion efficiency of the two network architectures, this leads to hysteresis in the growth velocity of actin networks under force. Dependent on the history of the system, convex and concave regimes are obtained for the force-velocity relation. Thus a simple generic model can explain the experimentally observed anomalies, with far reaching consequences for cell migration.

Structured construction and simulation of nondeterministic stochastic activity networks

In this work we deal with a mechanism for process simulation called a NonDeterministic Stochastic Activity Network (NDSAN). An NDSAN consists basically of a set of activities along with precedence relations involving these activities, which determine their order of execution. Activity durations are stochastic, given by continuous, nonnegative random variables. The nondeterministic behavior of an NDSAN is based on two additional possibilities: (i) by associating choice probabilities with groups of activities, some branches of execution may not be taken; (ii) by allowing iterated executions of groups of activities according to predetermined probabilities, the number of times an activity must be executed is not determined a priori. These properties lead to a rich variety of activity networks, capable of modeling many real situations in process engineering, project design, and troubleshooting. We describe a recursive simulation algorithm for NDSANs, whose repeated execution produces a close approximation to the probability distribution of the completion time of the entire network. We also report on real-world case studies.

A rigorous framework for multiscale simulation of stochastic cellular networks

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-cell variability even in clonal populations. Stochastic biochemical networks are modeled as continuous time discrete state Markov processes whose probability density functions evolve according to a chemical master equation (CME). The CME is not solvable but for the simplest cases, and one has to resort to kinetic Monte Carlo techniques to simulate the stochastic trajectories of the biochemical network under study. A commonly used such algorithm is the stochastic simulation algorithm (SSA). Because it tracks every biochemical reaction that occurs in a given system, the SSA presents computational difficulties especially when there is a vast disparity in the timescales of the reactions or in the number of molecules involved in these reactions. This is common in cellular networks, and many approximation algorithms have evolved to alleviate the computational burdens of the SSA. Here, we present a rigorously derived modified CME framework based on the partition of a biochemically reacting system into restricted and unrestricted reactions. Although this modified CME decomposition is as analytically difficult as the original CME, it can be naturally used to generate a hierarchy of approximations at different levels of accuracy. Most importantly, some previously derived algorithms are demonstrated to be limiting cases of our formulation. We apply our methods to biologically relevant test systems to demonstrate their accuracy and efficiency.

A network approach to modeling population aggregation and genetic control of pest insects

Historically, models of the invasion and biological control of insect pests have omitted heterogeneities in the spatial structure of the targeted populations. In this study, we use stochastic network simulations to examine explicitly population heterogeneity as a function of landscape structure and insect behavior. We show that when insects are distributed non-randomly across a heterogeneous landscape, control can be significantly hindered. However, when insect populations are clustered as a result of limited dispersal, genetic control efficiency can be enhanced. In developing the model, we relax a key assumption of previous theoretical studies of genetic control: that released genetic control insects remain homogenously distributed irrespective of the spatial structure of the wild type populations. Here, this behavior (termed the ‘coverage proportion’) is parameterized and its properties are explored. We show that landscape heterogeneity and limited dispersal have little effect on the critical coverage proportion necessary for control.

Stochastic user behaviour modelling and network simulation for resource management in cooperation with mobile telecommunications and broadcast networks

The latest generations of telecommunications networks have been designed to deliver high data rates, providing flexible communication capabilities that can enable high-quality video images. However, these new generations of telecommunications networks are interference-limited, impairing their performance in cases of heavy traffic and high usage. One way to lift this constraint would be for the mobile telecommunications network operators to obtain the cooperation of a broadcast network operator so that at times when the service demand is too high, the service can be transferred to the broadcast network. This paper proposes a way for UMTS network operators to forecast the traffic associated with high-demand services intended to be deployed on the UMTS network and when demand requires to transfer it to a cooperating DVB-T network. The paper aims to justify cooperation between UMTS and DVB-T networks clearly showing how using a DVB-T network as a support to UMTS can increase the revenue generated by both networks.

Costs and Effects of Chlamydial Screening: Dynamic versus Static Modeling

The objective of this study was to assess the impact of modeling type on the economic evaluation of screening programs for asymptomatic Chlamydia trachomatis infections. We compared a stochastic network simulation model (dynamic model) with a decision analysis model (static model) for estimating the cost-effectiveness of an opportunistic screening program. The influence of the model type on the required data, the computed results, and the sensitivity of model parameters were investigated. When compared with static modeling, dynamic modeling yielded different cost-effectiveness ratios and identified other optimal screening strategies as it considers changes in the force of infection caused by screening. However, it is more complex, data- and time-demanding, and more sensitive to some parameters affecting the force of infection than static modeling. Dynamic models should be applied for the economic evaluation of prevention measures that have the potential to lower the force of infection such as large-scale chlamydial screening programs.

Effective dispersivities for a two‐dimensional periodic fracture network by a continuous time random walk analysis of single‐intersection simulations

Fracture networks are of major importance for transport problems in hydrology. Their inclusion in models requires assumptions about both the single fracture and the network structure. This paper focuses on the macroscopic effect of microscopic mixing conditions in intersections within a periodic fracture network. Mixing is characterized by the transition probabilities for particles to move from one fracture to another or to stay in the same fracture. A periodic network is used, which excludes stochastic effects and also single‐fracture dispersion. The periodic network can be solved analytically and is applicable to a variety of network structures. We find that for this type of network, effective dispersivities in the sense of asymptotic values for long times and large scales do usually exist (i.e., the asymptotic dispersion is Gaussian). For the particular case of a quadratic network, particle transition probabilities at an intersection have been obtained by microscopic lattice Boltzmann simulations of flow and transport in addition to the assumptions of complete mixing and stream routing. The resulting dispersivities show that complete mixing is not a low Péclet number limit in the presence of regions of immobile water volumes. Dispersivities depend strongly on the direction between flow and network and on the mixing model; dispersivities are large for high Péclet numbers and flow parallel to the network. Especially for these cases, we also find a scale dependence up to some orders of magnitude, which has serious implications for the interpretation of simulations and measurements. Since these results also appear in stochastic network simulations, they are therefore not specific to the periodic structure of the fracture network.

Integrated Variance Reduction Strategies for Simulation

We develop strategies for integrated use of certain well-known variance reduction techniques to estimate a mean response in a finite-horizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques of conditional expectation, correlation induction (including antithetic variates and Latin hypercube sampling), and control variates; all pairings of these techniques are examined. For each integrated strategy, we establish sufficient conditions under which that strategy will yield a smaller response variance than its constituent variance reduction techniques will yield individually. We also provide asymptotic variance comparisons between many of the methods discussed, with emphasis on integrated strategies that incorporate Latin hypercube sampling. An experimental performance evaluation reveals that in the simulation of stochastic activity networks, substantial variance reductions can be achieved with these integrated strategies. Both the theoretical and experimental results indicate that superior performance is obtained via joint application of the techniques of conditional expectation and Latin hypercube sampling.

Experimental evaluation of a simulation environment for information systems design

This article presents an experiment assessing the decision support value of a simulation environment for the information systems (IS) design process. We have implemented a prototype simulation environment that uses data flow diagrams (DFDs) augmented with the performance rates of system components to specify the structure and dynamics of IS designs. The DFD-based representation is automatically mapped to a stochastic queuing network simulation. Knowledge-based help supports formulation of simulation run parameters and interpretation of output. We measure the prototype's impact on system dynamics assessment via the accuracy of IS professionals' responses to questions about the dynamics of four IS cases. The prototype's simulation capability has a significant positive effect on accuracy scores for questions involving waiting times, system times, and queue lengths of jobs or customers. Subjects choosing to conduct more and longer simulation runs provide significantly more accurate assessments than less-active users of simulation. The findings suggest that IS professionals can make use of simulation technology within a compact time frame if the proper supports are provided; on-line help or other methods should be used to encourage users to conduct sufficiently long simulation runs; and embedding the prototype's capabilities in a computer-aided software engineering workbench would result in better designed information systems.

An algorithm for speculative parallel execution of rendezvous-synchronized simulation

This paper presents an approach for speculative parallel execution of rendezvous-synchronized simulations. Rendezvous-synchronized simulation is based on the notions of processes and gates and on the rendezvous mechanism defined in the basic process algebra of LOTOS—a standard formal specification language for temporal ordering [2] . Time is introduced via a mechanism similar to the delay behaviour annotation provided by the TOPO toolset [4-6] . The algorithm allows speculative gate activations. This increases the available parallelism while ensuring correct execution of the computation. The model is used to describe closed stochastic queueing network simulations. Analysis of their execution results suggests that the model makes available a promising degree of parallelism.

Simulation of stochastic activity networks using path control variates

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.

Parallel discrete-event simulation of FCFS stochastic queueing networks

Physical systems are inherently parallel; intuition suggests that simulations of these systems may be amenable to parallel execution. The parallel execution of a discrete-event simulation requires careful synchronization of processes in order to ensure the execution's correctness; this synchronization can degrade performance. Largely negative results were recently reported in a study which used a well-known synchronization method on queueing network simulations. In this paper we discuss a synchronization method, appointments , which has proven itself to be effective on simulations of FCFS queueing networks. The key concept behind appointments is the provision of lookahead . Lookahead is a prediction on a processor's future behavior, based on an analysis of the processor's simulation state. We show how lookahead can be computed for FCFS queueing network simulations, give performance data that demonstrates the method's effectiveness under moderate to heavy loads, and discuss performance trade-offs between the quality of lookahead, and the cost of computing lookahead.

Regenerative generalized semi-markov processes

A generalized semi-Markov process (GSMP) is the usual model for a discrete event simulation. The standard formulation assumes that the current state of the process uniquely determines the set of events that are scheduled to occur and that the state transition probabilities depend only on the current state, the next state, and the trigger event. We provide a formulation of a GSMP that avoids these restrictions, thus permitting formal specification of many non-Markovian simulation models. Using a monotone replacement property of “new better than used” distributions and sample path properties of the GSMP, we provide a criterion for recurrence in this setting and conditions under which a GSMP is a regenerative process and the time between regeneration points has finite moments. Steady state estimation methods for non-Markovian stochastic network simulations follow.

A stochastic network simulation model for production line systems†

This paper presents an application of a new network-based simulation model to a class of production line systems and compares this with a closed form procedure. The new model is capable of analysing more realistic production lines by allowing variable work element times (normal and others), parallel stations, in-process inventory, and merging subassembly lines. Furthermore, the model is capable of handling mixed model and batched assembly situations as well as the single product assembly lines. The inclusion of cost and resource options, as integral components makes the model a powerful tool of analysis. The cost option allows evaluation of alternative configurations based on the total cost of the system; whereas, the resource feature enables one to analyse the constrained resource situations. The model can be used to optimize the design of new processing lines and to balance existing lines with a fixed production requirement.