Research Priorities

• Control of telecommunications networks - how do we assign service effort in order to minimise the expected delay under cost constraints?
• Population processes - can ensemble behaviour be deduced from models for individual behaviour?

Researchers

• Chief Investigator: Phil Pollett
• Research Fellow: Ross McVinish
• PhD student : Fionnuala Buckley
• PhD student : Dejan Jovanovic
• PhD student : Andrew Smith
• Honours student: Alex Ridley

Research Projects

• Stochastic models for ecological networks

  Project leader: Phil Pollett (UQ)
  Researchers: Fionnuala Buckley (UQ), Ross McVinish (UQ) and Andrew Smith (UQ)

  We are studying populations that occupy several geographically separated habitat patches. Although the individual patches may become extinct locally, they may be recolonized through migration from other patches. We are developing models that account for the persistence of these populations and which provide an effective means of studying their long-term behaviour. We have given particular attention to populations for which extinction and colonization happens in distinct phases, often at different stages in the organism's life cycle. By incorporating a simple device to account for the colonization potential of occupied patches, we have developed deterministic and distributional approximation methods to analyse these models. We are also developing models for spatially structured populations, exploiting recent developments in stochastic network theory and adapting methods that were developed originally for the study of telecommunications systems. By recording the numbers of individuals in the various patches, we are able to incorporate local patch dynamics, spatial structure and migration patterns.

  Research outputs

  • Buckley, F.M. and P.K. Pollett (2009) Analytical methods for a stochastic mainland-island metapopulation model. In (Eds. Anderssen, R.S., Braddock, R.D. and Newham, L.T.H.) Proceedings of the 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation, July 2009, pp. 1767-1773.
  • Pollett, P.K. (2009) Ensemble behaviour in population processes with applications to ecological systems. Environmental Modeling & Assessment 14, 545-553.
• Optimal capacity assignment in queueing networks

  Project leader and researcher: Phil Pollett (UQ)

  How do we best to assign the service effort in a queueing network in order to minimise the expected delay under a cost constraint? This question is addressed for systems with several types of customers, general service time distributions, stochastic or deterministic routing, and a variety of service regimes. For such networks there are typically no analytical formulae for the waiting time distributions. Thus, the optimal allocation problem is approached using approximation techniques, in particular, the residual-life approximation for the distribution of queueing times. This work generalises results of Leonard Kleinrock, who studied networks with exponentially distributed service times. These results are illustrated with reference to data networks.

  Research outputs

  • Pollett, P.K. (2009) Optimal capacity assignment in general queueing networks. In (Eds Charles Pearce and Emma Hunt) Optimization: Structure and Applications, Springer Optimization and its Applications Series, Vol. 32, pp. 261-272.

Awards and Achievements

• Honours student Alex Ridley was awarded the Kate McNaughton of Roma Scholarship.
• Research Fellow Ross McVinish was awarded a grant of $11,910 under the UQ New Staff Research Start-up Fund Scheme for a project titled "Bayesian nonparametric methods for system identification"