We propose a sensitivity-driven framework for constructing Dynamic Bayesian Networks (DBNs) as approximations of Ordinary Differential Equations (ODEs) models while reducing the computational cost of generating training data. The approach uses global sensitivity rankings to identify the most influential direct and indirect dynamical dependencies, which are then used to define reduced sampling supports that capture essential system interactions without exhaustive simulations. The methodology is evaluated on benchmark models of progressively higher dimensionality. A DBN built from a full training dataset serves as a reference and is compared with reduced constructions based on (i) equation sampling using only direct dependencies and (ii) sensitivity-driven supports incorporating both direct and selected indirect influences. This experimental setup allows us to assess whether equation-based sampling alone provides a sufficient approximation of the full model and to quantify the additional benefits of including indirect dynamical effects. Results show that the sensitivity-driven strategy drastically reduces the number of required simulations while maintaining the DBN’s structural and probabilistic fidelity with respect to the original ODE dynamics.

Abstract Nowadays, sustainability and energy considerations are becoming important concerns in mitigating the destructive effects of high energy consumption on the environment. In the realm of big data era, large-scale data processing systems are considered critical energy-consumption sources that exert significant impacts on the ecosystem. With the emergence of big data environments, which lead to the production of multi-structured data, numerous solutions and technologies have arisen to efficiently process vast amounts. Recently, a centralized data repository platform called Data Lake has been proposed to manage the heterogeneous data originating from diverse sources. Sustainability issues in such data management systems have received significant attention. In the dynamic environment of big data, the risk of unpredictable workloads and excessive energy usage at various phases of the data lifecycle within the data lake emphasizes the critical need for sustainable strategies. These measures aim to minimize the adverse effects of the high energy consumption during the data management procedure. In this article, we intend to design and analyze an energy-aware strategy for a green data lake framework. This strategy prioritizes ecological concerns, particularly energy consumption, by ensuring the maintenance of sufficient quality of service in terms of data availability. We present a model based on a continuous-time Markov chain (CTMC) to analyze the trade-off between energy efficiency and performance of a green data lake platform.

This paper proposes aggregation-based, three-stage algorithms to overcome the numerical problems encountered in computing stationary distributions and mean first passage times for multi-modal birth-death processes of large state space sizes. The considered birth-death processes which are defined by Chemical Master Equations are used in modeling stochastic behavior of gene regulatory networks. Computing stationary probabilities for a multi-modal distribution from Chemical Master Equations is subject to have numerical problems due to the probability values running out of the representation range of the standard programming languages with the increasing size of the state space. The aggregation is shown to provide a solution to this problem by analyzing first reduced size subsystems in isolation and then considering the transitions between these subsystems. The proposed algorithms are applied to study the bimodal behavior of the lac operon of E. coli described with a one-dimensional birth-death model. Thus, the determination of the entire parameter range of bimodality for the stochastic model of lac operon is achieved.

We present an approach to derive performance bounds of a queue under histogram-based input traffics. The results are obtained through strong stochastic bounds on the queue length and on the output traffic. The bounds provide probability inequalities on transient behaviors and on steady-state when it exists. We consider both stationary and non-stationary traffics and provide some numerical techniques in both cases. Unlike approximate methods, these bounds can be used to check if the Quality of Service constraints are satisfied or not. Our approach provides a trade-off between the accuracy of results and the computational complexity and it is much faster than the histogram-based simulation.

We consider large queueing networks for which transient and stationary probability distributions are very difficult or impossible to obtain due to the state space explosion problem. In performance analysis, we need in general to study only a part of the network (a node or a path). Thus, we propose to define bounding systems that lead to compute bounds on performance measures of the considered subsystem. The original large state space is mapped into a smaller space to overcome the state space explosion problem, and bounds both on stationary and on transient performance measures are computed from these reduced-size models. This approach provides an interesting solution for complex networks since we have a trade-off between the quality of the bounds and the state space size, thus the computational complexity. As an application, we study a general multi-server queueing network, with finite capacity queues. We define bounding systems to compute blocking probabilities. The influence of parameters on the precision of the computed bounds are studied through some numerical examples in order to give more insights into the proposed approach.

This special issue includes research papers related to a workshop held at the Royal Society on 21st of September 2010, honouring Erol Gelenbe on his 65th birthday. The workshop brought together some 40 participants including some of Erol's former and current PhD students, colleagues and friends with whom he has interacted over the years, both in Europe and the USA. The papers focus on probability models in computer science, at the core of the field of computer performance engineering, which Erol pioneered.

Abstract We propose new techniques to simplify the computation of the end‐to‐end delay for an evaluation of a Web services model. The simplification processes are associated with stochastic comparisons of random variables. Thus, the simplified models are stochastic bounds for the original ones. In this study, we consider that the Web service model can be represented by an acyclic directed graph. Thus, we propose upper and lower bounds on the response times by considering in one case special random variables for service times and in the other case we substitute the precedence graph by another one. We prove that the response times computed on the bounding models are really upper and lower bounds on the considered models. We also propose to generalize the model by considering the contention time when several executions of composite Web services are invocated. We propose in this case upper and lower bounds on response times by proposing bounding models. The response times are easier to compute on these new models. We give the corresponding proofs based on stochastic comparisons. We present several numerical results in order to show the accuracy of our bounds. Copyright © 2010 John Wiley & Sons, Ltd.

We improve the efficiency of time parallel simulation using some concepts of monotonicity of simulation models. The time parallel simulation technique partitions the simulation timespan into simulation periods which are independently executed. Such a technique relies on strong stochastic assumptions: regeneration or short influence of the initial point a on sample path. If these assumptions are not satisfied, we only obtain an approximation. We prove that if the model is monotone we can increase the parallelization of the simulations and we can prove some bounds on the result.

We propose new techniques to simplify the computation of the end to end delay for an evaluation of a Web services. These techniques allow us to simplify the model description to reduce the number of states of the underlying Markov chain. The simplification processes are associated with stochastic comparisons of random variables. Thus the simplified models are stochastic bounds for the original ones.

We use a mathematical method based on stochastic comparison of multidimensional Markov chains in order to compute packet loss rates in IP routers for MPLS networks. The key idea of this methodology is that given a complex system represented by a Markov chain which is too large to be solved, we propose to build smaller Markov chains providing performance measures bounds.

End to end QoS of communication systems is essential for users but their performance evaluation is a complex issue. The abstraction of such systems are usually given by multidimensional Markov processes whose analysis is very difficult and even intractable, if there is no specific solution form. In this study, we propose an algorithm in order to automatically derive aggregated Markov processes providing upper and lower bounds on performance measures. We applied the algorithm to the analysis of an open tandem queueing network with rejection in order to derive performance measure bounds. Parametric aggregation schemes have been proposed in order to compute bounds on loss probabilities and end to end mean delays. Therefore a tradeoff between the accuracy of the bound and the size of considered Markov chains is possible.

International audience

We study the delay characteristics of fair queueing algorithms with a stochastic comparison approach. In integrated services networks, fair queueing (FQ) policies have received much attention, because they can guarantee an end-to-end session delay bound when the burstiness of the session traffic is bounded, and they ensure the fair allocation of the bandwidth. A large class of FQ policies attempt to emulate generalized processor sharing (GPS) policy by assigning timestamps to cells. These GPS related policies have quite complex dynamic, and their exact analytical analysis is not tractable. The delay characteristics of these algorithms are evaluated by considering the worst-case, when sources have a bounded burstiness. In fact, these are deterministic delay bounds which do not always provide an insight on the underlying policies. For instance, in the case of leaky bucket constrained traffic, these bounds correspond to the case when all sessions are greedy (each session must empty the token pool in the minimum time after becoming active). We propose a methodology to analyze delay characteristics of a class of GPS-related FQ policies with general source models by providing stochastic bounds on their delay distribution. These stochastic bounds are obtained by analyzing two modified weighted round robin (WRR) policies. Clearly, since cells are scheduled periodically according to a predefined list under WRR-related policies, their models are simpler than the models of GPS-related policies.

We compare fair queuing (FQ) algorithms with a novel approach based on the majorization theory of real valued vectors. We study the temporal evolution of the received normalized service of all backlogged sessions in order to give a better insight into the performance of a FQ policy than what worst-case measures can provide. As an application of this approach, we study the effect of the eligibility criterion on the service discrepancy. We show that a FQ policy with a large eligibility set scatters the normalized service less than another FQ policy with a smaller eligible set.

Stochastic bounds are obtained on execution times of parallel programs when the number of processors is unlimited. A parallel program is considered to consist of interdependent tasks with synchronization constraints. These constraints are described by an acyclic directed graph called a task graph. The execution times of tasks are considered to be independently identically distributed (i.i.d.) random variables. The performance measure of interest is the overall execution of the considered parallel program (task graph). Stochastic bound methods are applied to obtain lower and upper bounds on this measure. Another upper bound is obtained for parallel programs having 'new better than used in expectation' (NBUE) random variables as task execution times. NBUE random variables are replaced with exponential random variables of the same mean to derive this upper bound.>