Passage time distributions in large Markov chains

Accepted versio

Stochastic Modelling and Optimisation of Internet Auction Processes

AbstractInternet auctions are an attractive mechanism for the exchange of goods at a non-fixed price point. The operation of these auctions can be run under a variety of parameters. In this paper, we provide a theoretical analysis of fixed time forward auctions in cases where a single bid or multiple bids are accepted in a single auction. A comparison of the economic benefits and the corresponding buyer and seller surpluses between the auctions where a single bid is accepted and the auctions where multiple bids are accepted is made. These models are verified through systematic simulation experiments, based on a series of operational assumptions, which characterise the arrival rate of bids, as well as the distribution from which the private values of buyers are sampled. Decision rules for optimising surplus under different auction fee structures are also given

Distributed Response Time Analysis of GSPN Models with MapReduce

widely used in the performance analysis of computer and communications systems. Response time densities and quantiles are often key outputs of such analysis. These can be extracted from a GSPN’s underlying semi-Markov process using a method based on numerical Laplace transform inversion. This method typically requires the solution of thousands of systems of complex linear equations, each of rank n, where n is the number of states in the model. For large models substantial processing power is needed and the computation must therefore be distributed. This paper describes the implementation of a Response Time Analysis module for the Platform Independent Petri net Editor (PIPE2) which interfaces with Hadoop, an open source implementation of Google’s MapReduce distributed programming environment, to provide distributed calculation of response time densities in GSPN models. The software is validated with analytically calculated results as well as simulated ones for larger models. Excellent scalability is shown. I

Automated Customer-Centric Performance Analysis of Generalised Stochastic Petri Nets Using Tagged Tokens

Since tokens in Generalised Stochastic Petri Net (GSPN) models are indistinguishable, it is not always possible to reason about customer-centric performance measures. To remedy this, we propose tagged tokens - a variant of the tagged customer technique used in the analysis of queueing networks. Under this scheme, one token in a structurally restricted net is tagged and its position tracked as it moves around the net. Performance queries can then be phrased in terms of the position of the tagged token. To date, the tagging of customers or tokens has been a time-consuming, manual and model-specific process. By contrast, we present here a completely automated methodology for the tagged token analysis of GSPNs. We first describe an intuitive graphical means of specifying the desired tagging configuration, along with the constraints on GSPN structure which must be observed for tagged tokens to be incorporated. We then present the mappings required for automatically converting a GSPN with a user-specified tagging structure into a Coloured GSPN (CGSPN), and thence into an unfolded GSPN which can be analysed for performance measures of interest by existing tools. We further show how our methodology integrates with Performance Trees, a formalism for the specification of performance queries. We have implemented our approach in the open source PIPE Petri net tool, and use this to illustrate the extra expressibility granted by tagged tokens through the analysis of a GSPN model of a hospitals Accident and Emergency department. © 2009 Elsevier B.V. All rights reserved

Uncle Traps: Harvesting Rewards in a Queue-based Ethereum Mining Pool

Mining pools in Proof-of-Work cryptocurrencies allow miners to pool their computational resources as a means of reducing payout variance. In Ethereum, uncle blocks are valid Proof-of-Work solutions which do not become the head of the blockchain, yet yield rewards if later referenced by main chain blocks. Mining pool operators are faced with the non-trivial task of fairly distributing rewards for both block types among pool participants. Inspired by empirical observations, we formally reconstruct a Sybil attack exploiting the uncle block distribution policy in a queue-based mining pool. To ensure fairness of the queue-based payout scheme, we propose a mitigation. We examine the effectiveness of the attack strategy under the current and the proposed policy via a discrete-event simulation. Our findings show that the observed attack can indeed be obviated by altering the current reward scheme

Flux: Revisiting Near Blocks for Proof-of-Work Blockchains

The term near or weak blocks describes Bitcoin blocks whose PoW does not meet the required target difficulty to be considered valid under the regular consensus rules of the protocol. Near blocks are generally associated with protocol improvement proposals striving towards shorter transaction confirmation times. Existing proposals assume miners will act rationally based solely on intrinsic incentives arising from the adoption of these changes, such as earlier detection of blockchain forks. In this paper we present Flux, a protocol extension for proof-of-work blockchains that leverages on near blocks, a new block reward distribution mechanism, and an improved branch selection policy to incentivize honest participation of miners. Our protocol reduces mining variance, improves the responsiveness of the underlying blockchain in terms of transaction processing, and can be deployed without conflicting modifications to the underlying base protocol as a velvet fork. We perform an initial analysis of selfish mining which suggests Flux not only provides security guarantees similar to pure Nakamoto consensus, but potentially renders selfish mining strategies less profitable

Modelling infection spread using location tracking.

The precision of location tracking technology has improved greatly over the last few decades. We aim to show that by tracking the locations of individuals in a closed environment, it is now possible to record the nature and frequency of interactions between them. Further, that it is possible to use such data to predict the way in which an infection will spread throughout such a population, given parameters such as transmission and recovery rates. We accordingly present a software package that is capable of recording and then replaying location data provided by a high-precision location tracking system. The software then employs a combination of SIR modelling and the epidemiological technique of contact tracing in order to predict the spread of an ..