Discrete-time dynamic modeling for software and services composition as an extension of the Markov chain approach

Discrete Time Markov Chains (DTMCs) and Continuous Time Markov Chains (CTMCs) are often used to model various types of phenomena, such as, for example, the behavior of software products. In that case, Markov chains are widely used to describe possible time-varying behavior of “self-adaptive” software systems, where the transition from one state to another represents alternative choices at the software code level, taken according to a certain probability distribution. From a control-theoretical standpoint, some of these probabilities can be interpreted as control signals and others can just be observed. However, the translation between a DTMC or CTMC model and a corresponding first principle model, that can be used to design a control system is not immediate. This paper investigates a possible solution for translating a CTMC model into a dynamic system, with focus on the control of computing systems components. Notice that DTMC models can be translated as well, providing additional information

Macroscopic modelling and robust control of bi-modal multi-region urban road networks

The paper concerns the integration of a bi-modal Macroscopic Fundamental Diagram (MFD) modelling for mixed traffic in a robust control framework for congested single- and multi-region urban networks. The bi-modal MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in homogeneous (both in the spatial distribution of congestion and the spatial mode mixture) bi-modal traffic networks. We introduce the composition of traffic in the network as a parameter that affects the shape of the bi-modal MFD. A linear parameter varying model with uncertain parameter the vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multi-region cities governed by bi-modal MFDs. This model aims at designing a robust perimeter and boundary flow controller for single- and multi-region networks that guarantees robust regulation and stability, and thus smooth and efficient operations, given that vehicle composition is a slow time-varying parameter. The control gain of the robust controller is calculated off-line using convex optimisation. To evaluate the proposed scheme, an extensive simulation-based study for single- and multi-region networks is carried out. To this end, the heterogeneous network of San Francisco where buses and cars share the same infrastructure is partitioned into two homogeneous regions with different modes of composition. The proposed robust control is compared with an optimised pre-timed signal plan and a single-region perimeter control strategy. Results show that the proposed robust control can significantly: (i) reduce the overall congestion in the network; (ii) improve the traffic performance of buses in terms of travel delays and schedule reliability, and; (iii) avoid queues and gridlocks on critical paths of the network

The MDS Queue: Analysing the Latency Performance of Erasure Codes

In order to scale economically, data centers are increasingly evolving their data storage methods from the use of simple data replication to the use of more powerful erasure codes, which provide the same level of reliability as replication but at a significantly lower storage cost. In particular, it is well known that Maximum-Distance-Separable (MDS) codes, such as Reed-Solomon codes, provide the maximum storage efficiency. While the use of codes for providing improved reliability in archival storage systems, where the data is less frequently accessed (or so-called "cold data"), is well understood, the role of codes in the storage of more frequently accessed and active "hot data", where latency is the key metric, is less clear. In this paper, we study data storage systems based on MDS codes through the lens of queueing theory, and term this the "MDS queue." We analytically characterize the (average) latency performance of MDS queues, for which we present insightful scheduling policies that form upper and lower bounds to performance, and are observed to be quite tight. Extensive simulations are also provided and used to validate our theoretical analysis. We also employ the framework of the MDS queue to analyse different methods of performing so-called degraded reads (reading of partial data) in distributed data storage

A COVID-19 Recovery Strategy Based on the Health System Capacity Modeling. Implications on Citizen Self-management

Versión preprint depositada sin articulo publicado dada la actualidad del tema. *Solicitud de los autoresConfinement ends, and recovery phase should be accurate planned. Health System (HS) capacity, specially ICUs and plants capacity and availability, will remain the key stone in this new Covid-19 pandemic life cycle phase. Until massive vaccination programs will be a real option (vaccine developed, world wield production capacity and effective and efficient administration process), date that will mark recovery phase end, important decisions should be taken. Not only by authorities. Citizen self-management and organizations self-management will be crucial. This means: citizen and organizations day a day decision in order to control their own risks (infecting others and being infected). This paper proposes a management tool that is based on a ICUs and plants capacity model. Principal outputs of this tool are, by sequential order and by last best data available: (i) ICUs and plants saturation estimation data (according to incoming rate of patients), (ii) with this results new local and temporal confinement measure can be planned and also a dynamic analysis can be done to estimate maximum Ro saturation scenarios, and finally (iii) provide citizen with clear and accurate data allow them adapting their behavior to authorities’ previous recommendations. One common objective: to accelerate as much as possible socioeconomic normalization with a strict control over HS relapses risk

Propagation of epistemic uncertainty in queueing models with unreliable server using chaos expansions

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary distribution of the model, which is a function of uncertain parameters. Polynomial chaos provide an efficient alternative to more traditional Monte Carlo simulations for modelling the propagation of uncertainty arising from those parameters. Furthermore, Polynomial chaos expansion affords a natural framework for computing Sobol' indices. Such indices give reliable information on the relative importance of each uncertain entry parameters. Numerical results show the benefit of using Polynomial Chaos over standard Monte-Carlo simulations, when considering statistical moments and Sobol' indices as output quantities

Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

Stated Preference Analysis of Driver Route Choice Reaction To Variable Message Sign Information

Highway Authorities in many parts of the world have, for some years, been using variable message panels mounted above or beside the camageway to communicate short messages to motorists. Most such applications have been concerned with hazard warning and speed advice. However, their use to deliberately affect route choice is an area of great current interest. It is recognised that they have a potential role in managing demand to match the capacity available, not only to alleviate acute problems caused by roadworks and accidents, but also to contribute to satisfactory performance of networks operating close to capacity over extended periods of high, but variable, demand. The installation and operation of the panels is not cheap and there is a widespread belief that overuse, or inappropriate use, of the messages may lead to them losing their credibility with the motorists and thus ceasing to be effective. It is therefore very important to understand the likely response of motorists to various messages before displaying them and even before selecting sites for the installation of panels. A number of researchers have explored drivers' responses to traffic information and route advice offered via variable message signs (VMS). Evidence from traffic counts suggests that messages can persuade somewhere between 5% and 80% of drivers to divert. Clearly this range of estimates is far too wide to support the use of VMS for fine tuning the pattern of demand. A major contributor to the uncertainty, however, is the varying, and often unknown, proportion of drivers whose destination makes the message relevant to them. More detailed studies involving driver interviews downstream of the VM!3 site to determine the relevance of the message, as well as the response to it, include those by Kawashima (1991) and Durand-Raucher et al. (1993). These studies have produced more precise estimates of compliance but the results are obviously limited to those messages which were on display at the time the interviews were being conducted. A number of researchers have sought to overcome this restriction by examining response to a range of messages presented via a stated preference exercise (see for example Hato et al., 1995; Shao et al., 1995 and Bonsall and Whelm, 1995), via a route-choice-simulator (see for example Firmin, 1996; Bonsall and Merrall, 1995 ; Bonsall and Palmer, 1997) or via a full scale driving simulator or system mock-up (see for example Mast and Ballas, 1976 and Brocken and Van der Vlist, 1991). This research has suggested that response is highly dependent on message content, subjects' network knowledge, and on the extent of any implied diversion. We see particular value in extending this earlier work to consider a wider range of messages and to determine whether the route-choice-simulator results can be repeated and extended using a somewhat cheaper methodology - namely stated preference analysis. The objectives of the work reported in this paper were thus: to extend to our existing database on drivers' response to traffic information and route advice provided in variable message signs, to include a wider range of messages. to construct explanatory models of drivers' route choice behaviour in response to a variety of messages to explore the factors influencing this response to compare these results with previous results obtained using a variety of data collection methods to draw policy conclusions, where appropriate, on the use of variable message signs to influence drivers' route choice to draw conclusions, where appropriate, on our data collection and modelling methodology