Institute of Mathematics and Statistics
University of Kent
Canterbury, CT2 7NF, UK
office hours (E227) for autumn term 2009: Tuesday 14.30 and Thursday 11.00
e-mail: L.Breuer@kent.ac.uk
Course Material on Stochastic Processes:
Selected Publications
Queueing theory
The Periodic BMAP/PH/c Queue, Queueing Systems 38 (2001), pp.67-76.
Operator-Geometric Solutions for the M/G/k Queue and its Variants, presented at the INFORMS conference in New York, July 2001.
The Inhomogeneous BMAP/G/infinity Queue, in: B. Haverkort (ed.): ''Proceedings of the 11th GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communication Systems'', VDE Verlag, Germany, pp.209-223.
A Retrial BMAP/PH/N System, Queueing Systems 40 (2002), pp.431--455.
On the MAP/G/1 Queue with Lebesgue--dominated Service Time Distribution and LCFS Preeemptive Repeat Service Discipline, Stochastic Models 18 (2002), pp.589--595
Two Examples for Computationally Tractable Periodic Queues, International Journal of Simulation 3 (2003), pp.15--24
Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution, Queueing Systems 45 (2003), pp.47-57
"An Introduction to Queueing Theory and Matrix-Analytic Methods", Springer, November 2005
"Threshold Policies for Controlled Retrial Queues with Heterogeneous Servers", Annals of Operations Research 141 (2006), pp.151-176
"Applying Foster´s criteria to a GI/PH/1 queueing system", Cybernetics and Systems Analysis 42(3), pp.433-439, 2006
Continuity of the M/G/c queue, Queueing Systems 58:321-331, 2008
Spatial queues
Spatial Queues, PhD Thesis, University of Trier, 2000.
Markovian Spatial Queues with Periodic Arrival and Service Rates , Proceedings of the 10th MMB Conference in Trier, Germany, Report No. 99-17 of the University of Trier, Dept. of Mathematics and Computer Science, 1999, pp.97-102
A Planning Tool for Mobile Communication Networks , presented at the Dagstuhl Seminar on Advanced Stochastic Modelling in Telecommunications, April 2000.
A Stochastic Model for Mobile Communication Networks, presented at the ASMT conference in Prague, June 2001, published in: E. Kerckhoffs, M. Snorek (eds.): ''Modeling and Simulation 2001. 15th European Simulation Multiconference'', SCS Publication, Netherlands, pp.813--817.
"From Markov jump processes to spatial queues", Kluwer Academic Publishers, 2003
Statistics
An EM algorithm for Batch Markovian Arrival Processes and its comparison to a simpler estimation procedure, Annals of Operations Research 112 (2002), pp.123--138
"An EM algorithm for platoon arrival processes in discrete time", Operations Research Letters 33, pp.535-543, 2005
An EM algorithm for Markovian arrival processes observed at discrete times, Stochastic Models, submitted
Risk theory and fluid queues
"Risk processes analyzed as fluid queues", Scandinavian Actuarial Journal 2005(2), pp.127-141
"Phase-type approximations to finite-time ruin probabilities in the Sparre Andersen and stationary renewal risk models", ASTIN Bulletin 35(1), pp.131-144, 2005
"The surplus prior to ruin and the deficit at ruin for a correlated risk process", Scandinavian Actuarial Journal 2005(6), pp.433-445
"Fluid queues to solve jump processes", Performance Evaluation 62, pp.132-146, 2005
"The use of vector-valued martingales in risk theory", Blatter der DGVFM 29(1):1-12, 2008
The distribution of the total dividends in a Markov-additive risk model under a barrier strategy, submitted
A generalised Gerber-Shiu function for Markov-additive risk processes, submitted
Miscellaneous
On Markov-Additive Jump Processes, Queueing Systems 40 (2002), pp.75--91.
A piecewise-deterministic Model for Brownian Motion, Theory of Stochastic Processes 8(24), N1-2, pp.40-46
First passage times for Markov-additive processes with positive jumps of phase-type, J. Appl. Prob. 45(3):779-799, 2008
A quintuple law for Markov-additive processes with phase-type jumps, submitted