Confluence reduction for Markov automata

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude

Complexity aided design: The FuturICT technological innovation paradigm

"In the next century, planet earth will don an electronic skin. It will use the Internet as a scaffold to support and transmit its sensations. This skin is already being stitched together. It consists of millions of embedded electronic measuring devices: thermostats, pressure gauges, pollution detectors, cameras, microphones, glucose sensors, EKGs, electroencephalographs. These will probe and monitor cities and endangered species, the atmosphere, our ships, highways and fleets of trucks, our conversations, our bodies-even our dreams ....What will the earth's new skin permit us to feel? How will we use its surges of sensation? For several years-maybe for a decade-there will be no central nervous system to manage this vast signaling network. Certainly there will be no central intelligence...some qualities of self-awareness will emerge once the Net is sensually enhanced. Sensuality is only one force pushing the Net toward intelligence”. These statements are quoted by an interview by Cherry Murray, Dean of the Harvard School of Engineering and Applied Sciences and Professor of Physics. It is interesting to outline the timeliness and highly predicting power of these statements. In particular, we would like to point to the relevance of the question "What will the earth's new skin permit us to feel?” to the work we are going to discuss in this paper. There are many additional compelling questions, as for example: "How can the electronic earth's skin be made more resilient?”; "How can the earth's electronic skin be improved to better satisfy the need of our society?”;"What can the science of complex systems contribute to this endeavour?” Graphical abstrac

Small Solar Panels Can Drastically Reduce the Carbon Footprint of Radio Access Networks

The limited power requirements of new generations of base stations (BSs) make the use of renewable energy sources, solar in particular, extremely attractive for mobile network operators. Exploiting solar energy implies a reduction of the network operation cost as well as of the carbon footprint of radio access networks, but previous research works indicate that the area of the solar panels that are necessary to power a standard macro BS is large, so large to make the solar panel deployment problematic, especially within urban areas. In this paper we use a modeling approach based on Markov reward processes to investigate the possibility of combining small area solar panels with a connection to the power grid to run a macro BS. By so doing, it is possible to increase the amount of renewable energy used to run a radio access network, while also reducing the cost incurred by the network operator to power its base stations. We assume that energy is drawn from the power grid only when needed to keep the BS operational, or during the night, that corresponds to the period with lowest electricity price. This has advantages in terms of both cost and carbon footprint. We show that solar panels of the order of 1-2 kW peak, i.e., with a surface of about 5-10 m2, combined with limited capacity energy storage (of the order of 10-15 kWh, corresponding to about 3-5 car batteries), and a smart energy management policy, can lead to an effective exploitation of renewable energy

On the Use of Small Solar Panels and Small Batteries to Reduce the RAN Carbon Footprint

The limited power requirements of new generations of base stations make the use of renewable energy sources, solar in particular, extremely attractive for mobile network operators. Exploiting solar energy implies a reduction of the network operation cost as well as of the carbon footprint of radio access networks. However, previous research works indicate that the area of the solar panels that are necessary to power a standard macro base station (BS) is large, making the solar panel deployment problematic, especially within urban areas.In this paper we use a modeling approach based on Markov reward processes to investigate the possibility of combining a connection to the power grid with small area solar panels and small batteries to run a macro base station. By so doing, it is possible to exploit a significant fraction of renewable energy to run a radio access network, while also reducing the cost incurred by the network operator to power its base stations. We assume that energy is drawn from the power grid only when needed to keep the BS operational, or during the night, which corresponds to the period with lowest electricity price. The proposed energy management policies have advantages in terms of both cost and carbon footprint. Our results show that solar panels of the order of 1-2 kW peak, i.e., with a surface of about 5-10 m2, combined with limited capacity energy storage (of the order of 1-5 kWh, corresponding to about 1-2 car batteries) and a smart energy management policy, can lead to an effective exploitation of renewable energy

The emerging energy web

There is a general need of elaborating energy-effective solutions for managing our increasingly dense interconnected world. The problem should be tackled in multiple dimensions -technology, society, economics, law, regulations, and politics- at different temporal and spatial scales. Holistic approaches will enable technological solutions to be supported by socio-economic motivations, adequate incentive regulation to foster investment in green infrastructures coherently integrated with adequate energy provisioning schemes. In this article, an attempt is made to describe such multidisciplinary challenges with a coherent set of solutions to be identified to significantly impact the way our interconnected energy world is designed and operated. Graphical abstrac

The PEPA workbench: A tool to support a process algebra-based approach to performance modelling

. In this paper we present a new technique for performance modelling and a tool supporting this approach. Performance Evaluation Process Algebra (PEPA) [1] is an algebraic language which can beused to build models of computer systems which capture information about the performance of the system. The PEPA language serves two purposes as a formal description language for computer system models. The performance-related information in the model may be used to predict the performance of the system whereas the behavioural information in the model may be exploited when reasoning about the functional behaviour of the system (e.g. when finding deadlocks or when exhibiting equivalences between sub-components). In this paper we concentrate on the performance aspects of the language. A method of reasoningaboutPEPA modelsproceedsby considering the derivation graph obtained from the model using the underlying operational semantics of the PEPA language. The derivation graph is systematically reduced ..

Analysis of Petri Net Models through Stochastic Differential Equations

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process. In this paper we apply and extend this diffusion approximation to study stochastic Petri nets. We identify a class of nets whose underlying stochastic process is a density dependent Markov chain whose indexing parameter is a multiplicative constant which identifies the population level expressed by the initial marking and we provide means to automatically construct the associated set of SDEs. Since the diffusion approximation of Kurtz considers the process only up to the time when it first exits an open interval, we extend the approximation by a machinery that mimics the behavior of the Markov chain at the boundary and allows thus to apply the approach to a wider set of problems. The resulting process is of the jump-diffusion type. We illustrate by examples that the jump-diffusion approximation which extends to bounded domains can be much more informative than that based on ODEs as it can provide accurate quantity distributions even when they are multi-modal and even for relatively small population levels. Moreover, we show that the method is faster than simulating the original Markov chain