Marcel C. Guenther

Higher moment analysis of a spatial stochastic process algebra

We introduce a spatial stochastic process algebra called MASSPA, which provides a formal behavioural description of Markovian Agent Models, a spatial stochastic modelling framework. We provide a translation to a master equation which governs the underlying transition behaviour. This provides a means of simulation and thus comparison of numerical results with simulation that was previously not available. On the theoretical side, we develop a higher moment analysis to allow quantities such as variance to be produced for spatial stochastic models in performance analysis for the first time. We compare the simulation results against resulting ODEs for both mean and standard deviations of model component counts and finish by analysing a distributed wireless sensor network model.

Journey Data Based Arrival Forecasting for Bicycle Hire Schemes

The global emergence of city bicycle hire schemes has recently received a lot of attention in the performance and modelling research community. A particularly important challenge is the accurate forecast of future bicycle migration trends, as these assist service providers to ensure availability of bicycles and parking spaces at docking stations, which is vital to match customer expectations. This study looks at how historic information about individual journeys could be used to improve interval arrival forecasts for small groups of docking stations. Specifically, we compare the performance of small area arrival predictions for two types of models, a mean-field analysable time-inhomogeneous population CTMC model (IPCTMC) and a multiple linear regression model with ARIMA error (LRA). The models are validated using historical rush hour journey data from the London Barclays Cycle Hire scheme, which is used to train the models and to test their prediction accuracy.

Moment closures for performance models with highly non-linear rates

Fluid analysis of Population CTMCs with non-linear evolution rates requires moment closures to transform a linear system with infinitely many ordinary differential equations (ODEs) into a non-linear one with a finite number of ODEs. Due to the ubiquity of kinetics with quadratic rates in physical processes, various closure techniques have been discussed in the context of systems biology and performance analysis. However, little research effort has been put into moment closures for higher-order moments of models with piecewise linear and higher-order polynomial evolution rates. In this paper, we investigate moment closure techniques applied to such models. In particular we look at moment closures based on normal and log-normal distributions. We compare the accuracy of the moment approximating ODEs with the exact results obtained from simulations. We confirm that by incorporating higher-order moment ODEs, the moment closure techniques give accurate approximations to the standard deviation of populations. Moreover, they often improve the accuracy of mean approximations over the traditional mean-field techniques.

PCTMC models of wireless sensor network protocols

Wireless Sensor Networks (WSNs) consist of a large number of spatially distributed embedded devices (nodes), which communicate with one another via radio. Over the last decade improvements in hardware and a steady decrease in cost have encouraged the application of WSNs in areas such as industrial control, security and environmental monitoring. However, despite increasing popularity, the design of end-to-end software for WSNs is still an expert task since the choice of middleware protocols heavily influences the performance of resource-constrained WSNs. As a consequence, WSN designers resort to discrete event simulation prior to deploying networks. While such simulations are reasonably accurate, they tend to be computationally expensive to run, especially for large networks. This particularly limits the number of distinct protocol configurations that engineers can test in advance of construction and hence their final setup may be suboptimal. To mitigate this effect we discuss how highly efficient mean-field techniques can be brought to bear on models of wireless sensor networks. In particular, we consider the practical modelling issues involved in constructing appropriately realistic Population CTMC (PCTMC) models of WSN protocols.

Mean-field analysis of data flows in wireless sensor networks

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.

On Performance of Gossip Communication in a Crowd-Sensing Scenario

Many applications associated with the smart city experience rely on spatio-temporal data. Specific use-cases include location-dependent real-time traffic, weather and pollution reports. Data is traditionally sampled using stationary sensors, however, in densely populated areas one could envisage crowd-sensing data collection schemes where cars, bikes and pedestrians collect information in transit and transmit it to a service provider through one of either a fast mobile network such as LTE(4G) or by Wifi/Gossip communication. While mobile sensors reduce the need for expensive infrastructure, the downside is that performance characteristics of data coverage and transmission are less reliable and harder to predict. In this paper we present a generic model to investigate the robustness and efficiency of LTE/Gossip hybrid data transmission strategies for crowd-sensing networks that are not amenable to mean-field analysis. To illustrate our model’s scalability, we fit it to journey data from the London Cycle Hire scheme.

Passage-time computation and aggregation strategies for large semi-Markov processes

High-level semi-Markov modelling paradigms such as semi-Markov stochastic Petri nets and process algebras are used to capture realistic performance models of computer and communication systems but often have the drawback of generating huge underlying semi-Markov processes. Extraction of performance measures such as steady-state probabilities and passage-time distributions therefore relies on sparse matrix-vector operations involving very large transition matrices. Previous studies have shown that exact state-by-state aggregation of semi-Markov processes can be applied to reduce the number of states. This can, however, lead to a dramatic increase in matrix density caused by the creation of additional transitions between remaining states. Our paper addresses this issue by presenting the concept of state space partitioning for aggregation. We present a new deterministic partitioning method which we term barrier partitioning. We show that barrier partitioning is capable of splitting very large semi-Markov models into a number of partitions such that first passage-time analysis can be performed more quickly and using up to 99% less memory than existing algorithms.