Wireless Sensor Networks (WSNs) are often used for environment monitoring, an application which requires reliable routing of messages from source to sink nodes via multi-hop networks. Prior to installing such WSNs, engineers commonly analyse the network using discrete event simulation (DES). Whilst sophisticated simulators such as Castalia and TOSSIM take into account many low-level features of WSNs, their biggest drawback is the lack of scalability. This inhibits design-time system optimisation for large or complex networks. In this paper, we discuss how Population CTMC (PCTMC) models, used in conjunction with mean-field analysis, can be used to mitigate this problem. To illustrate the potential of PCTMC models in the WSN domain, we present a PCTMC model for a failsafe, dynamic routing protocol, which we implemented in Castalia. We show that the mean-field solution for the model yields good qualitative agreement with corresponding low-level simulations, but at a fraction of the computational cost. In particular we see good agreement for average metrics describing buffer occupancy and data flow behaviour. Moreover, our PCTMC model produces good results when packets are lost due to channel interference, an important consideration for WSNs.

Rapid and accessible performance evaluation of complex software systems requires two critical features: the ability to specify useful performance metrics easily and the capability to analyze massively distributed architectures, without recourse to large compute clusters. We present the unified stochastic probe, a performance specification mechanism for process algebra models that combines many existing ideas: state and action-based activation, location-based specification, many-probe specification, and immediate signaling. These features, between them, allow the precise and compositional construction of complex performance measurements. The paper shows how a subset of the stochastic probe language can be used to specify common response-time measures in massive process algebra models. The second contribution of the paper is to show how these response-time measures can be analyzed using so-called fluid techniques to produce rapid results. In doing this, we extend the fluid approach to incorporate immediate activities and a new type of response-time measure. Finally, we calculate various response-time measurements on a complex distributed wireless network of O(10^{129}) states in size.

BACKGROUND: Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. METHOD: Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. RESULTS: A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. CONCLUSIONS: ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting hospitals to effectively manage time and resources in clinical pathway.

Jeremy T. Bradley, Nigel Thomas, Richard A. Hayden, Anton Stefanek; Invited Response to Computer Journal Lecture by Prof. Jane Hillston, The Computer Journal, V

Capturing energy consumption directly from a stochastic behavioural model is a computationally expensive process. Using a so-called fluid analysis technique we are able to access accumulated reward measures in much larger scale stochastic systems than has been previously possible.These accumulated rewards are ideal for deriving energy and power consumption from stochastic process models. In previous work, it has been shown how to derive a set of ordinary differential equations (ODEs) whose solutions approximate the moments of component counts in a continuous-time Markov chain(CTMC) described in a stochastic process algebra. In this paper, we show how to extend the method to provide rapid access to moments of accumulated rewards in CTMCs. In addition to measuring the amount of energy used by a system, we are also interested in the time taken to reach a particular level of energy consumption. In reward terms, this is a so-called completion time. In this paper, we are able to use higher moments of rewards to give us access to completion time distributions.

Journal Article Computer Performance Evaluation: Preface Get access Jeremy T. Bradley Jeremy T. Bradley * Department of Computing, Imperial College London, London, UK *Corresponding author: [email protected] Search for other works by this author on: Oxford Academic Google Scholar The Computer Journal, Volume 54, Issue 5, May 2011, Pages 641–642, https://doi.org/10.1093/comjnl/bxq076 Published: 02 November 2010

We introduce a low-level performance modelling formalism, Shared Transaction Markov Chains (STMCs), specifically designed for the capture and analysis of massively parallel stochastic systems through fluid techniques. We introduce the notion of a shared transaction between concurrently running Markov chains which allows a multi-phase synchronisation to accurately represent complex cooperation between modelling components in a compositional manner. We demonstrate the new modelling formalism on four distinct models and show how fluid analysis may be performed, with results, where appropriate. Our contribution is that this is the first such system tailored to the fluid performance analysis of transaction-based systems as found in computing applications such as peer-to-peer networks, Web architectures and Publish-Subscribe networks. The second contribution is that STMCs permit composed phase-type distributed synchronisation which is more useful from a transaction modelling perspective.

Solution of large sparse fixed-point problems, Mline over x = over x and Mline over x + line over b = over x, may be seen as underpinning many important performance-analysis calculations. These calculations include steady-state, passage-time and transient-time calculations in discrete-time Markov chains, continuous-time Markov chains and semi-Markov chains. In recent years, much work has been done to extend the application of asynchronous iterative fixed-point solution methods to many different contexts. This work has been motivated by the potential for faster solution, more efficient use of the communication channel and/or access to memory, and simplification of task management and programming. In this paper, we present theoretical developments which allow us to extend theapplication of asynchronous iterative solution methods to solve for the key performance metrics mentioned above-such that we may employ the full breadth of Chazan and Miranker's classes of asynchronous iterations.

We introduce Performance Trees (PTs), a novel representation formalism for the specification of model-based performance queries. Traditionally, stochastic logics have been the prevalent means of performance requirement expression; however, in practice, their use amongst system designers is limited on account of their inherent complexity and restricted expressive power. PTs are a more accessible alternative, in which performance queries are represented by hierarchical tree structures. This allows for the convenient visual composition of complex performance questions, and enables not only the verification of stochastic requirements, but also the direct extraction of performance measures. In addition, PTs offer a superset of the expressiveness of Continuous Stochastic Logic (CSL) since all CSL formulae can be translated into PT form. Performance Trees can be used to represent passage time, transient, steady-state and higher order queries of varying levels of sophistication. While they are conceptually independent of the underlying stochastic modelling formalism, in many cases the tree operators we use are already backed up by good algorithmic and tool support for both stochastic verification and performance measure extraction. We do not therefore perceive major barriers to the integration of PTs into existing stochastic model checking tools. Indeed, we illustrate how semi-Markov passage time computation algorithms, based on numerical Laplace transform inversion, can be directly applied to the resolution of a case study PT query.