The Manchester Centre for Interdisciplinary Computational and Dynamical Analysis Seminars 2011/12

• Tuesday 31 January
  2012Elastic Systems: Challenges in Capturing their Dynamic Behaviour
  Prof Alex Yakovlev (University of Newcastle)
  
  3.00 pm Alan Turing building, Frank Adams 1
  Abstract (click to view)

  Elastic systems are an interesting behavioural paradigm that has evolved in the area of digital electronics where computing and communication actions are coordinated in time by causal relations between the actions, such as precedence, rather than by the signalling events from a global clock generator. This distinction of elastic systems from (globally) synchronous, i.e. those based on rigid synchronisation with the global clock, places them into the class of systems that are "discrete by level but continuous by time". Some of the advantages of making systems elastic involve their inherent robustness to variations in their component delays, power supply levels and environmental conditions. In this talk we look at elastic systems in the domain of electronic circuits, and present a number of formal techniques to capture their behaviour. Discrete event modelling formalisms, such as Petri nets, reflect the elasticity property well when the system operates within certain bounds of deterministic behaviour (the property of confluence). However, in some situations, such as those where the system has to decide on the order of occurrence between two or more independent actions, the modelling has to be more detailed than what is possible within the discrete-event scope, and takes us into the area of dynamical systems with continuous models, such as ODEs. The talk will present examples of elastic circuits that are confluent and non-deterministic. Practical applications for such circuits include control logic in processors and interfaces, synchronization and arbitration in complex multi-core processors, analogue-to-digital and time-to-digital conversion.

• Tuesday 14 February
  2012Beyond the Steady State: Response Time and Transient Analysis of Markov Chains
  Dr Nick Dingle (University of Manchester)
  
  3.00 pm Alan Turing building, Frank Adams 1
  Abstract (click to view)

  It is important to ensure that complex computer and communication systems meet their performance requirements before they enter service. This can be achieved through the modelling and analysis of the system in question, and is usually conducted by capturing the behaviour of the system with a formal model. When the choice of the next state depends only on the current state and state sojourn times are random numbers sampled from the negative exponential distribution, we have a continuous-time Markov chain. When state sojourn times are drawn from general distributions, we have a semi-Markov chain. From a steady-state probability distribution we can obtain standard resource-based performance measures, such as mean buffer occupancy, system availability and throughput, and expected values of various sojourn times. Such analysis allows us to answer questions such as: "What is the probability that the system will be in a failure state in the long run?" and "What is the average utilisation of this resource?". Such analysis does not, however, tell us everything we might need to know about the performance of a system. In this talk I will focus on the harder problem of calculating transient probability and response time distributions in very large Markov models and semi-Markov models. Addressing this is vital if we are to answer questions involving quantiles of performance metrics rather than just mean values. I will describe the techniques we have derived for conducting such analysis, and discuss how these have been implemented on a range of computer architectures including HPC clusters and GPUs.

Further information

For further information please contact the Seminar organiser.