Our primary research is focused on the analysis of probability distributions and stochastic systems, in particular systems arising in queueing theory. Our work is supported by grants from various institutions. The research includes work on stochastic analysis, characterisations of probability distributions and scheduling control of stochastic systems. More specifically, current areas of interest include: load balancing in distributed stochastic systems, approximations and stability of stochastic differential equations with applications in various areas, statistical inference for stochastic processes, probabilistic moment problems, non-linear Markov chains and their ergodicity, independence/dependence structure of random variables and processes, achievable region approach to stochastic optimisation, Gittins indexation and queueing control.
Current collaborative projects include joint work with: Academia Sinica, Taiwan; Latvian University of Technology, Riga; Fordham University, New York; Hokkaido University, Sapporo; Universitat Pompeu Fabra, Barcelona. Of great importance is our long-standing and continuing collaboration with Professor Kevin Glazebrook (Lancaster University) and Professor Isi Mitrani of Computing Science at Newcastle.
P.S. Ansell, K.D. Glazebrook, C. Kirkbride (2003). Generalised 'job the shortest queue' policies for the dynamic routing of jobs to multiclass queues. Journal of Operational Research Society 57, 379-389.
P.S. Ansell, K.D. Glazebrook, J. Nino-Mora, M. O'Keeffe (2003). Whittle's index policy for a multi-class queueing system with convex holding costs. Mathematical Methods of Operational Research 57, 21-39.
K.D. Glazebrook, P.S. Ansell, R.T. Dunn, R.R. Lumley (2005). On the optimal allocation of service to impatient tasks. Journal of Applied Probability 41, 51-72.
K.D. Glazebrook, H.M. Mitchell, P.S. Ansell (2005). Index policies for the maintenance of a collection of machines by a set of repairmen. European Journal of Operational Research 165, 267-284.
C.S. Gillespie, E. Renshaw (2005). The evolution of a batch-immigration process subject to counts. Proceedings of the Royal Society of London Series A 461, 1563-1581.
J. Stoyanov (2004). Stieltjes classes for moment-indeterminate probability distributions. Journal of Applied Probability 41, 281-294.
J. Stoyanov, L. Tolmatz (2005). Method for constructing Stieltjes classes for M-indeterminate probability distributions. Applied Mathematics and Computation 165, 669-685.
J. Stoyanov, L. Tolmatz (2004). New Stieltjes classes involving generalized gamma distributions. Statistics & Probability Letters 69, 213-219.
J. Stoyanov, M. Al-Sadi (2004). Properties of classes of life distributions based on the conditional variance. Journal of Applied Probability 41, 954-960.