The University of Queensland

Distributed fault detection using consensus of Markov chains

Jovanović, Degan P. and Pollett, Philip K. (2014). Distributed fault detection using consensus of Markov chains. Optimization and control methods in industrial engineering and construction. (pp. 85-105) edited by Honglei Xu and Xiangyu Wang. Dordrecht, The Netherlands: Springer. doi: 10.1007/978-94-017-8044-5_6

Optimal capacity assignment in general queueing networks

Pollett, P. K. (2009). Optimal capacity assignment in general queueing networks. Optimization: structure and applications. (pp. 261-272) edited by Charles Pearce and Emma Hunt. New York, United States: Springer. doi: 10.1007/978-0-387-98096-6_14

Identifying Q-processes with a given finite m-invariant measure

Pollett, P. K. (2002). Identifying Q-processes with a given finite m-invariant measure. Markov Processes and Controlled Markov Chains. (pp. 41-55) edited by Z. Hou, J.A. Filar and A. Chen. The Netherlands: Kluwer. doi: 10.1007/978-1-4613-0265-0_3

A model for cell proliferation in a developing organism

Pollett, Philip K., Tafakori, Laleh and Taylor, Peter G. (2022). A model for cell proliferation in a developing organism. Journal of Mathematical Biology, 84 (7) 63, 1-22. doi: 10.1007/s00285-022-01769-5

Quasi-stationary distributions for queueing and other models

Pollett, Phil (2022). Quasi-stationary distributions for queueing and other models. Queueing Systems, 100 (3-4), 241-243. doi: 10.1007/s11134-022-09750-1

Normal approximations for discrete-time occupancy processes

Hodgkinson, Liam, McVinish, Ross and Pollett, Philip K. (2020). Normal approximations for discrete-time occupancy processes. Stochastic Processes and their Applications, 130 (10), 6414-6444. doi: 10.1016/j.spa.2020.05.016

Local approximation of a metapopulation's equilibrium

Barbour, A. D., McVinish, R. and Pollett, P. K. (2018). Local approximation of a metapopulation's equilibrium. Journal of Mathematical Biology, 77 (3), 1-29. doi: 10.1007/s00285-018-1231-0

A metapopulation model with Markovian landscape dynamics

McVinish, R., Pollett, P. K. and Chan, Y. S. (2016). A metapopulation model with Markovian landscape dynamics. Theoretical Population Biology, 112, 80-96. doi: 10.1016/j.tpb.2016.08.005

Limiting the spread of disease through altered migration patterns

McVinish, R., Pollett, P. K. and Shausan, A. (2016). Limiting the spread of disease through altered migration patterns. Journal of Theoretical Biology, 393, 60-66. doi: 10.1016/j.jtbi.2015.12.019

Connecting deterministic and stochastic metapopulation models

Barbour, A.D, McVinish, Ross and Pollett, Philip K (2015). Connecting deterministic and stochastic metapopulation models. Journal of Mathematical Biology, 71 (6), 1481-1504. doi: 10.1007/s00285-015-0865-4

Indirect detection of genetic dispersal (movement and breeding events) through pedigree analysis of dugong populations in southern Queensland, Australia

Cope R. C., Pollett, P. K., Lanyon, J. M. and Seddon, J. M. (2015). Indirect detection of genetic dispersal (movement and breeding events) through pedigree analysis of dugong populations in southern Queensland, Australia. Biological Conservation, 181, 91-101. doi: 10.1016/j.biocon.2014.11.011

Development and testing of a genetic marker-based pedigree reconstruction system 'PR-genie' incorporating size-class data

Cope, Robert C., Lanyon, Janet M., Seddon, Jennifer M. and Pollett, Philip K. (2014). Development and testing of a genetic marker-based pedigree reconstruction system 'PR-genie' incorporating size-class data. Molecular Ecology Resources, 14 (4), 857-870. doi: 10.1111/1755-0998.12219

A closing scheme for finding almost-invariant sets in open dynamical systems

Froyland, Gary, Pollett, Philip K. and Stewart, Robyn M. (2014). A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 1 (1), 135-162. doi: 10.3934/jcd.2014.1.135

Binomial autoregressive processes with density-dependent thinning

Weiss, Christian H. and Pollett, Philip K. (2014). Binomial autoregressive processes with density-dependent thinning. Journal of Time Series Analysis, 35 (2), 115-132. doi: 10.1002/jtsa.12054

A model for a spatially structured metapopulation accounting for within patch dynamics

Smith, Andrew G., McVinish, Ross and Pollett, Philip K. (2014). A model for a spatially structured metapopulation accounting for within patch dynamics. Mathematical Biosciences, 247 (1), 69-79. doi: 10.1016/j.mbs.2013.11.001

The limiting behaviour of Hanski's incidence function metapopulation model

McVinish, R. and Pollett, P. K. (2014). The limiting behaviour of Hanski's incidence function metapopulation model. Journal of Applied Probability, 51 (2), 297-316. doi: 10.1239/jap/1402578626

Quasi-stationary distributions for discrete-state models

van Doorn, Erik A. and Pollett, Philip K. (2013). Quasi-stationary distributions for discrete-state models. European Journal of Operational Research, 230 (1), 1-14. doi: 10.1016/j.ejor.2013.01.032

The limiting behaviour of a stochastic patch occupancy model

McVinish, R. and Pollett, P. K. (2013). The limiting behaviour of a stochastic patch occupancy model. Journal of Mathematical Biology, 67 (3), 693-716. doi: 10.1007/s00285-012-0568-z

Optimal design of experimental epidemics

Pagendam, D. E. and Pollett, P. K. (2013). Optimal design of experimental epidemics. Journal of Statistical Planning and Inference, 143 (3), 563-572. doi: 10.1016/j.jspi.2012.09.011

Special issue: modelling for decision making in ecological systems - preface

Bean, N. G., Pollett, P. K., Ross, J. V. and Taylor, P. G. (2013). Special issue: modelling for decision making in ecological systems - preface. Ecological Modelling, 249, 1-2. doi: 10.1016/j.ecolmodel.2012.07.034

Interaction between habitat quality and an Allee-like effect in metapopulations

McVinish, R. and Pollett, P. K. (2013). Interaction between habitat quality and an Allee-like effect in metapopulations. Ecological Modelling, 249, 84-89. doi: 10.1016/j.ecolmodel.2012.07.001

The deterministic limit of a stochastic logistic model with individual variation

McVinish, R. and Pollett, P. K. (2013). The deterministic limit of a stochastic logistic model with individual variation. Mathematical Biosciences, 241 (1), 109-114. doi: 10.1016/j.mbs.2012.10.001

Total variation approximation for quasi-equilibrium distributions, II

Barbour, A. D. and Pollett, P. K. (2012). Total variation approximation for quasi-equilibrium distributions, II. Stochastic Processes and Their Applications, 122 (11), 3740-3756. doi: 10.1016/j.spa.2012.07.004

Chain binomial models and binomial autoregressive processes

Weiss, Christian H. and Pollett, Philip K. (2012). Chain binomial models and binomial autoregressive processes. Biometrics, 68 (3), 815-824. doi: 10.1111/j.1541-0420.2011.01716.x

A central limit theorem for a discrete-time SIS model with individual variation

McVinish, R. and Pollett, P.K. (2012). A central limit theorem for a discrete-time SIS model with individual variation. Journal of Applied Probability, 49 (2), 521-530. doi: 10.1239/jap/1339878802

The limiting behaviour of a mainland-island metapopulation

McVinish, R. and Pollett, P. K. (2012). The limiting behaviour of a mainland-island metapopulation. Journal of Mathematical Biology, 64 (5), 775-801. doi: 10.1007/s00285-011-0429-1

Hodges-Lehmann scale estimator for Cauchy distribution

Kravchuk, O.Y. and Pollett, P.K. (2012). Hodges-Lehmann scale estimator for Cauchy distribution. Communications in Statistics-Theory and Methods, 41 (20), 3621-3632. doi: 10.1080/03610926.2011.563016

Limits of large metapopulations with patch-dependent extinction probabilities

McVinish, R. and Pollett, P. K. (2010). Limits of large metapopulations with patch-dependent extinction probabilities. Advances in Applied Probability, 42 (4), 1172-1186. doi: 10.1239/aap/1293113156

Total variation approximation for quasi-stationary distributions

Barbour, A. D. and Pollett, P. K. (2010). Total variation approximation for quasi-stationary distributions. Journal of Applied Probability, 47 (4), 934-946. doi: 10.1239/jap/1294170510

Locally optimal designs for the simple death process

Pagendam, D. E. and Pollett, P. K. (2010). Locally optimal designs for the simple death process. Journal of Statistical Planning and Inference, 140 (11), 3096-3105. doi: 10.1016/j.jspi.2010.04.017

Analytical methods for a stochastic mainland-island metapopulation model

Buckley, F. M. and Pollett, P. K. (2010). Analytical methods for a stochastic mainland-island metapopulation model. Ecological Modelling, 221 (21), 2526-2530. doi: 10.1016/j.ecolmodel.2010.02.017

Preface to the selected papers on modelling and control of metapopulation networks

Buckley, F. M., Nicol, S. and Pollett, P. K. (2010). Preface to the selected papers on modelling and control of metapopulation networks. Ecological Modelling, 221 (21), 2512-2514. doi: 10.1016/j.ecolmodel.2010.05.017

Robust optimal observation of a metapopulation

Pagendam, D. E. and Pollett, P. K. (2010). Robust optimal observation of a metapopulation. Ecological Modelling, 221 (21), 2521-2525. doi: 10.1016/j.ecolmodel.2010.02.018

Simple rules for ranking and optimally managing metapopulations

Ross, J. V. and Pollett, P. K. (2010). Simple rules for ranking and optimally managing metapopulations. Ecological Modelling, 221 (21), 2515-2520. doi: 10.1016/j.ecolmodel.2010.02.016

Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction

Chen, AY, Pollett, P, Li, JP and Zhang, HJ (2010). Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction. Methodology And Computing In Applied Probability, 12 (3), 511-531. doi: 10.1007/s11009-009-9121-y

Markovian bulk-arrival and bulk-service queues with state-dependent control

Chen, Anyue, Pollett, Phil, Li, Junping and Zhang, Hanjun (2010). Markovian bulk-arrival and bulk-service queues with state-dependent control. Queueing Systems, 64 (3), 267-304. doi: 10.1007/s11134-009-9162-5

Modelling population processes with random initial conditions

Pollett, P. K., Dooley, A. H. and Ross, J. V. (2010). Modelling population processes with random initial conditions. Mathematical Biosciences, 223 (2), 142-150. doi: 10.1016/j.mbs.2009.11.008

Limit theorems for discrete-time metapopulation models

Buckley, Fionnuala M. and Pollett, Philip K. (2010). Limit theorems for discrete-time metapopulation models. Probability Surveys, 7 (1), 53-83. doi: 10.1214/10-PS158

Optimal sampling and problematic likelihood functions in a simple population model

Pagendam, D. E. and Pollett, P. K. (2009). Optimal sampling and problematic likelihood functions in a simple population model. Environmental Modeling and Assessment, 14 (6), 759-767. doi: 10.1007/s10666-008-9159-1

Ensemble behaviour in population processes with applications to ecological systems

Pollett, P. K. (2009). Ensemble behaviour in population processes with applications to ecological systems. Environmental Modeling and Assessment, 14 (5), 545-553. doi: 10.1007/s10666-008-9165-3

On parameter estimation in population models II: Multi-dimensional processes and transient dynamics

Ross, J. V., Pagendam, D. E. and Pollett, P. K. (2009). On parameter estimation in population models II: Multi-dimensional processes and transient dynamics. Theoretical Population Biology, 75 (2-3), 123-132. doi: 10.1016/j.tpb.2008.12.002

Quantitative Risk Stratification in Markov Chains with Limiting Conditional Distributions

Chan, D. C., Pollett, P. K. and Weinstein, M. C. (2009). Quantitative Risk Stratification in Markov Chains with Limiting Conditional Distributions. Medical Decision Making, 29 (4), 532-540. doi: 10.1177/0272989X08330121

Quasi-Stationary Distributions for Reducible Absorbing Markov Chains in Discrete Time

van Doorn, E. A. and Pollett, P. K. (2009). Quasi-Stationary Distributions for Reducible Absorbing Markov Chains in Discrete Time. Markov Processes and Related Fields, 15 (2), 191-204.

Ehrenfest model for condensation and evaporation processes in degrading aggregates with multiple bonds

Flegg, M. B., Pollett, P. K. and Gramotnev, D. K. (2008). Ehrenfest model for condensation and evaporation processes in degrading aggregates with multiple bonds. Physical Review E, 78 (3) 031117, Article Number: 031117 Pt.1. doi: 10.1103/PhysRevE.78.031117

A note on the existence and uniqueness of a bounded mean-reverting process

Lesmono, D., Pollett, P. K., Tonkes, E. J. and Burrage, K. (2008). A note on the existence and uniqueness of a bounded mean-reverting process. Journal of the Indonesian Mathematical Society, 14 (2), 83-93.

Metapopulation persistence in a dynamic landscape: more habitat or better stewardship?

Ross, J. V., Sirl, D. J., Pollett, P. K. and Possingham, H. P. (2008). Metapopulation persistence in a dynamic landscape: more habitat or better stewardship?. Ecological Applications, 18 (3), 590-598. doi: 10.1890/07-1094.1

Survival in a quasi-death process

Van Doorn, E. A. and Pollett, P. K. (2008). Survival in a quasi-death process. Linear Algebra and its Applications, 429 (4), 776-791. doi: 10.1016/j.laa.2008.04.004

Management, control and decision making for ecological systems

Pollett, Philip K. and Ross, Joshua V. (2007). Management, control and decision making for ecological systems. Ecological Modelling, 201 (1), 1-1. doi: 10.1016/j.ecolmodel.2006.07.020

A note on extinction times for the general birth, death and catastrophe process

Pollett, Phil K., Zhang, Hanjun J. and Cairns, Benjamin J. (2007). A note on extinction times for the general birth, death and catastrophe process. Journal of Applied Probability, 44 (2), 566-569. doi: 10.1239/jap/1183667423

A remark on the uniqueness of weighted Markov branching processes

Chen, A. Y., Pollett, P. K., Li, J. P. and Zhang, H. J. (2007). A remark on the uniqueness of weighted Markov branching processes. Journal of Applied Probability, 44 (1), 279-283. doi: 10.1239/jap/1175267178

Computable bounds for the decay parameter of a birth-death process

Sirl, D., Zhang, H. J. and Pollett, P. K. (2007). Computable bounds for the decay parameter of a birth-death process. Journal of Applied Probability, 44 (2), 476-491. doi: 10.1239/jap/1183667415

Estimation for queues from queue length data

Ross, J. V., Taimre, T. and Pollett, P. K. (2007). Estimation for queues from queue length data. Queueing Systems, 55 (2), 131-138. doi: 10.1007/s11134-006-9009-2

On costs and decisions in population management

Ross, J. V. and Pollett, P. K. (2007). On costs and decisions in population management. Ecological Modelling, 201 (1), 60-66. doi: 10.1016/j.ecolmodel.2006.07.021

Stochastic models for the spread of HIV in a mobile heterosexual population

Sani, A., Kroese, D. P. and Pollett, P. K. (2007). Stochastic models for the spread of HIV in a mobile heterosexual population. Mathematical Biosciences, 208 (1), 98-124. doi: 10.1016/j.mbs.2006.09.024

On parameter estimation in population models

Ross, J. V., Taimre, T. and Pollett, P. K. (2006). On parameter estimation in population models. Theoretical Population Biology, 70 (4), 498-510. doi: 10.1016/j.tpb.2006.08.001

Extinction times for a birth-death process with two phases

Ross, JV and Pollett, PK (2006). Extinction times for a birth-death process with two phases. Mathematical Biosciences, 202 (2), 310-322. doi: 10.1016/j.mbs.2006.02.004

Approximating persistence in a general class of population processes

Cairns, BJ and Pollett, F (2005). Approximating persistence in a general class of population processes. Theoretical Population Biology, 68 (-), 77-90. doi: 10.1016/j.tpb.2005.02.002

On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure

Gray, B, Pollett, P and Zhang, HJ (2005). On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure. Journal of Applied Probability, 42 (3), 713-725. doi: 10.1239/jap/1127322022

Uniqueness criteria for continuous-time Markov chains with general transition structures

Chen, AY, Pollett, P, Zhang, HJ and Cairns, B (2005). Uniqueness criteria for continuous-time Markov chains with general transition structures. Advances In Applied Probability, 37 (4), 1056-1074. doi: 10.1239/aap/1134587753

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Pollett, P. and Zhang, H. J. (2004). Existence and uniqueness of Q-processes with a given finite μ-invariant measure. Australian & New Zealand Journal of Statistics, 46 (1), 113-120. doi: 10.1111/j.1467-842X.2004.00317.x

Foreword: Festschrift in honour of Daryl Daley

Pollett, Phil and Taylor, Peter (2004). Foreword: Festschrift in honour of Daryl Daley. Australian and New Zealand Journal of Statistics, 46 (1), 3-3. doi: 10.1111/j.1467-842X.2004.00305.x

A reduced load approximation accounting for link interactions in a loss network

Thompson, M.R. and Pollett, P. K. (2004). A reduced load approximation accounting for link interactions in a loss network. Journal of Applied Mathematics and Decision Sciences, 7 (4), 229-248. doi: 10.1155/S1173912603000191

Extinction times for a general birth, death and catastrophe process

Cairns, Ben and Pollett, P. K. (2004). Extinction times for a general birth, death and catastrophe process. Journal of Applied Probability, 41 (4), 1211-1218. doi: 10.1239/jap/1101840567

The collision branching process

Chen, A., Pollett, P., Zhang, H. and Li, J. (2004). The collision branching process. Journal of Applied Probability, 41 (4), 1033-1048. doi: 10.1239/jap/1101840549

A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Pollett, PK and Thompson, MR (2003). A new method for analysing the equilibrium and time-dependent behaviour of Markovian models. Mathematical And Computer Modelling, 38 (11-13), 1409-1418. doi: 10.1016/S0895-7177(03)90144-0

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

Clancy, D and Pollett, PK (2003). A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic. Journal of Applied Probability, 40 (3), 821-825. doi: 10.1239/jap/1059060909

Product form approximations for highly linear loss networks with trunk reservation

Bebbington, M., Pollett, P. and Ziedins, I. (2003). Product form approximations for highly linear loss networks with trunk reservation. Mathematical And Computer Modelling, 38 (11-13), 1147-1156. doi: 10.1016/S0895-7177(03)90115-4

Path integrals for continuous-time Markov chains

Pollett, P. K. and Stefanov, V. T. (2002). Path integrals for continuous-time Markov chains. Journal of Applied Probability, 39 (4), 901-904. doi: 10.1239/jap/1037816029

Integrals for continuous-time Markov chains

Pollett, P. K. (2002). Integrals for continuous-time Markov chains. Mathematical Biosciences, 182 (2), 213-225. doi: 10.1016/S0025-5564(02)00161-X

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Bebbington, M., Pollett, P. and Ziedins, I. (2002). Two-link approximation schemes for loss networks with linear structure and trunk reservation. Telecommunication Systems, 19 (2), 187-207. doi: 10.1023/A:1013394009996

Approximations for the long-term behaviour of an open-population epidemic model

Clancy, D., O'Neill, P. D. and Pollett, P. K. (2001). Approximations for the long-term behaviour of an open-population epidemic model. Methodology and Computing in Applied Probability, 3 (1), 75-95. doi: 10.1023/a:1011418208496

Quasi-stationarity in populations that are subject to large-scale mortality or emigration

Pollett, P. K. (2001). Quasi-stationarity in populations that are subject to large-scale mortality or emigration. Environment International, 27 (2-3), 231-236. doi: 10.1016/S0160-4120(01)00092-7

Similar Markov chains

Pollett, P. K. (2001). Similar Markov chains. Journal of Applied Probability, 38A (A), 53-65. doi: 10.1239/jap/1085496591

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

Elmes, S., Pollett, P. K. and Walker, D. M. (2000). Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains. Mathematical and Computer Modelling, 31 (10-12), 107-113. doi: 10.1016/S0895-7177(00)00077-7

Quasistationarity of continuous-time Markov chains with positive drift

Coolen-Schrijner, P., Hart, A. and Pollett, P (2000). Quasistationarity of continuous-time Markov chains with positive drift. Journal of The Australian Mathematical Society Series B-applied Mathematics, 41 (4), 423-441. doi: 10.1017/S0334270000011735

Modelling congestion in closed queueing networks

Pollett, P. K. (2000). Modelling congestion in closed queueing networks. International Transactions in Operational Research, 7 (4-5), 319-330. doi: 10.1111/j.1475-3995.2000.tb00202.x

New methods for determining quasi-stationary distributions for Markov chains

Hart, A. G. and Pollett, P. K. (2000). New methods for determining quasi-stationary distributions for Markov chains. Mathematical And Computer Modelling, 31 (10-12), 143-150. doi: 10.1016/S0895-7177(00)00081-9

Quasistationarity in continuous-time Markov chains where absorption is not certain

Darlington, SJ and Pollett, PK (2000). Quasistationarity in continuous-time Markov chains where absorption is not certain. Journal of Applied Probability, 37 (2), 598-600. doi: 10.1239/jap/1014842561

Quasistationary distributions for level-dependent quasi-birth-and-death processes

Bean, N. G., Pollett, P. K. and Taylor, P. (2000). Quasistationary distributions for level-dependent quasi-birth-and-death processes. Communications in Statistics-Stochastic Models, 16 (5), 511-541. doi: 10.1080/15326340008807602

Modelling quasi-stationary behaviour in metapopulations

Pollett, PK (1999). Modelling quasi-stationary behaviour in metapopulations. Mathematics and Computers in Simulation, 48 (4-6), 393-405. doi: 10.1016/S0378-4754(99)00019-1

Quasi-stationarity of discrete-time Markov chains with drift to infinity

Coolen-Schrijner, P. and Pollett, P. K. (1999). Quasi-stationarity of discrete-time Markov chains with drift to infinity. Methodology and Computing in Applied Probability, 1 (1), 81-96. doi: 10.1023/a:1010018406356

Quasistationary distributions for continuous time Markov chains when absorption is not certain

Pollett, PK (1999). Quasistationary distributions for continuous time Markov chains when absorption is not certain. Journal of Applied Probability, 36 (1), 268-272. doi: 10.1017/S0021900200017022

Quasistationary distributions for continuous time Markov chains when absorption is not certain

Pollett, P. K. (1999). Quasistationary distributions for continuous time Markov chains when absorption is not certain. Journal of Applied Probability, 36 (1), 268-272. doi: 10.1239/jap/1032374247

Non-explosivity of limits of conditioned birth and death processes

Roberts, GO, Jacka, SD and Pollett, PK (1997). Non-explosivity of limits of conditioned birth and death processes. Journal of Applied Probability, 34 (1), 35-45. doi: 10.2307/3215172

THE QUASI-STATIONARY BEHAVIOR OF QUASI-BIRTH-AND-DEATH PROCESSES

Bean, N. G., Bright, L., Latouche, G., Pearce, C. E. M., Pollett, P. K. and Taylor, P. G. (1997). THE QUASI-STATIONARY BEHAVIOR OF QUASI-BIRTH-AND-DEATH PROCESSES. Annals of Applied Probability, 7 (1), 134-155. doi: 10.1214/aoap/1034625256

Limiting conditional distributions for birth-death processes

Kijima, M, Nair, MG, Pollett, PK and VanDoorn, EA (1997). Limiting conditional distributions for birth-death processes. Advances In Applied Probability, 29 (1), 185-204. doi: 10.2307/1427866

Modelling the long-term behaviour of evanescent ecological systems

Pollett, PK (1996). Modelling the long-term behaviour of evanescent ecological systems. Ecological Modelling, 86 (2-3), 135-139. doi: 10.1016/0304-3800(95)00040-2

The Determination of Quasi-Stationary Distributions Directly From the Transition Rates of An Absorbing Markov-Chain

Pollett, PK (1995). The Determination of Quasi-Stationary Distributions Directly From the Transition Rates of An Absorbing Markov-Chain. Mathematical and Computer Modelling, 22 (10-12), 279-287. doi: 10.1016/0895-7177(95)00205-G

On the Identification of Continuous-Time Markov-Chains with a Given Invariant Measure

Pollett, PK (1994). On the Identification of Continuous-Time Markov-Chains with a Given Invariant Measure. Journal of Applied Probability, 31 (4), 897-910. doi: 10.2307/3215315

Poisson Approximations for Telecommunications Networks (Vol 32, Pg 348, 1991)

Brown, TC and Pollett, PK (1994). Poisson Approximations for Telecommunications Networks (Vol 32, Pg 348, 1991). Journal of the Australian Mathematical Society Series B-Applied Mathematics, 36 (01), 132-132. doi: 10.1017/S0334270000010298

An Efficient Procedure for Computing Quasi-Stationary Distributions of Markov-Chains with Sparse Transition Structure

Pollett, PK and Stewart, DE (1994). An Efficient Procedure for Computing Quasi-Stationary Distributions of Markov-Chains with Sparse Transition Structure. Advances in Applied Probability, 26 (1), 68-79. doi: 10.2307/1427580

On the Relationship Between Mu-Invariant Measures and Quasi-Stationary Distributions for Continuous-Time Markov-Chains (Vol 25, Pg 82, 1993)

Nair, MG and Pollett, PK (1993). On the Relationship Between Mu-Invariant Measures and Quasi-Stationary Distributions for Continuous-Time Markov-Chains (Vol 25, Pg 82, 1993). Advances in Applied Probability, 25 (3), 717-719.

On the Relationship Between Mu-Invariant Measures and Quasi-Stationary Distributions for Continuous-Time Markov-Chains

Nair, MG and Pollett, PK (1993). On the Relationship Between Mu-Invariant Measures and Quasi-Stationary Distributions for Continuous-Time Markov-Chains. Advances in Applied Probability, 25 (1), 82-102. doi: 10.2307/1427497

On the problem of establishing the existence of stationary distributions for continuous-time markov chains

Pollett, P. K. and Taylor, P. G. (1993). On the problem of establishing the existence of stationary distributions for continuous-time markov chains. Probability in the Engineering and Informational Sciences, 7 (4), 529-543. doi: 10.1017/S0269964800003119

Connecting Internally Balanced Quasi-Reversible Markov-Processes

Henderson, W, Pearce, Cem, Pollett, PK and Taylor, PG (1992). Connecting Internally Balanced Quasi-Reversible Markov-Processes. Advances in Applied Probability, 24 (4), 934-959. doi: 10.2307/1427720

Diffusion Approximations for Some Simple Chemical-Reaction Schemes

Pollett, PK and Vassallo, A (1992). Diffusion Approximations for Some Simple Chemical-Reaction Schemes. Advances in Applied Probability, 24 (4), 875-893. doi: 10.2307/1427717

A NOTE ON EVANESCENT PROCESSES

Pollett, P. K. and Jones, D. Vere (1992). A NOTE ON EVANESCENT PROCESSES. Australian Journal of Statistics, 34 (3), 531-536. doi: 10.1111/j.1467-842X.1992.tb01067.x

Invariant-Measures for Q-Processes When Q Is Not Regular

Pollett, PK (1991). Invariant-Measures for Q-Processes When Q Is Not Regular. Advances in Applied Probability, 23 (2), 277-292. doi: 10.2307/1427748

On the Construction Problem for Single-Exit Markov-Chains

Pollett, PK (1991). On the Construction Problem for Single-Exit Markov-Chains. Bulletin of the Australian Mathematical Society, 43 (3), 439-450.

Diffusion Approximations for a Circuit Switching Network with Random Alternative Routing

Pollett, PK (1991). Diffusion Approximations for a Circuit Switching Network with Random Alternative Routing. Australian Telecommunication Research, 25 (2), 45-51.

On the construction problem for single-exit Markov chains

Pollett, P. K. (1991). On the construction problem for single-exit Markov chains. Bulletin of the Australian Mathematical Society, 43 (3), 439-450. doi: 10.1017/S0004972700029282

Poisson Approximations for Telecommunications Networks

Brown, TC and Pollett, PK (1991). Poisson Approximations for Telecommunications Networks. Journal of the Australian Mathematical Society Series B-Applied Mathematics, 32 (3), 348-364. doi: 10.1017/S0334270000006913

On a Model for Interference Between Searching Insect Parasites

Pollett, PK (1990). On a Model for Interference Between Searching Insect Parasites. Journal of the Australian Mathematical Society Series B-Applied Mathematics, 32 (02), 133-150. doi: 10.1017/S0334270000008390

A Note On the Classification of Q-Processes When Q Is Not Regular

Pollett, PK (1990). A Note On the Classification of Q-Processes When Q Is Not Regular. Journal of Applied Probability, 27 (2), 278-290. doi: 10.2307/3214647

A Description of the Long-Term Behavior of Absorbing Continuous-Time Markov-Chains Using a Center Manifold

Pollett, PK and Roberts, AJ (1990). A Description of the Long-Term Behavior of Absorbing Continuous-Time Markov-Chains Using a Center Manifold. Advances in Applied Probability, 22 (1), 111-128. doi: 10.2307/1427600

The Generalized Kolmogorov Criterion

Pollett, PK (1989). The Generalized Kolmogorov Criterion. Stochastic Processes and Their Applications, 33 (1), 29-44. doi: 10.1016/0304-4149(89)90064-1

The Supercritical Birth, Death and Catastrophe Process - Limit-Theorems On the Set of Extinction

Pakes, AG and Pollett, PK (1989). The Supercritical Birth, Death and Catastrophe Process - Limit-Theorems On the Set of Extinction. Stochastic Processes and Their Applications, 32 (1), 161-170. doi: 10.1016/0304-4149(89)90060-4

On the Problem of Evaluating Quasistationary Distributions for Open Reaction Schemes

Pollett, PK (1988). On the Problem of Evaluating Quasistationary Distributions for Open Reaction Schemes. Journal of Statistical Physics, 53 (5-6), 1207-1215. doi: 10.1007/BF01023864

Reversibility, Invariance and Mu-Invariance

Pollett, PK (1988). Reversibility, Invariance and Mu-Invariance. Advances in Applied Probability, 20 (3), 600-621. doi: 10.2307/1427037

A Method Involving Antithetic Sampling for Estimating Blocking Probabilities in a Circuit-Switched Network

Pollett, PK (1988). A Method Involving Antithetic Sampling for Estimating Blocking Probabilities in a Circuit-Switched Network. Australian Telecommunication Research, 22 (2), 39-44.

Preserving Partial Balance in Continuous-Time Markov-Chains

Pollett, PK (1987). Preserving Partial Balance in Continuous-Time Markov-Chains. Advances in Applied Probability, 19 (2), 431-453. doi: 10.2307/1427426

Quasi-Stationary Distributions for Autocatalytic Reactions

Parsons, RW and Pollett, PK (1987). Quasi-Stationary Distributions for Autocatalytic Reactions. Journal of Statistical Physics, 46 (1-2), 249-254. doi: 10.1007/BF01010344

Connecting Reversible Markov-Processes

Pollett, PK (1986). Connecting Reversible Markov-Processes. Advances in Applied Probability, 18 (4), 880-900. doi: 10.2307/1427254

On the Equivalence of Mu-Invariant Measures for the Minimal Process and its Q-Matrix

Pollett, PK (1986). On the Equivalence of Mu-Invariant Measures for the Minimal Process and its Q-Matrix. Stochastic Processes and Their Applications, 22 (2), 203-221. doi: 10.1016/0304-4149(86)90002-5

Stochastic-Models of Computer-Communication Systems - Response-Time Problems in Communication-Networks - Scheduling and Characterization Problems for Stochastic Networks - Discussion

Kingman, J, Biggins, JD, Hordijk, A, Ackroyd, MH, Pollett, PK, Gibbens, RJ, Bather, JA, Key, PB, Macphee, IM, Donnelly, PJ, Bernerslee, C, Stidham, S and Zachary, S (1985). Stochastic-Models of Computer-Communication Systems - Response-Time Problems in Communication-Networks - Scheduling and Characterization Problems for Stochastic Networks - Discussion. Journal of the Royal Statistical Society Series B-Methodological, 47 (3), 415-428.

Distributional Approximations for Networks of Quasireversible Queues

Pollett, PK (1984). Distributional Approximations for Networks of Quasireversible Queues. Lecture Notes in Mathematics, 1095, 108-129.

Sojourn Times in Closed Queuing-Networks

Kelly, FP and Pollett, PK (1983). Sojourn Times in Closed Queuing-Networks. Advances in Applied Probability, 15 (3), 638-656. doi: 10.2307/1426623

Some Distributional Approximations in Markovian Queuing-Networks

Brown, TC and Pollett, PK (1982). Some Distributional Approximations in Markovian Queuing-Networks. Advances in Applied Probability, 14 (3), 654-671. doi: 10.2307/1426679

Fault diagnosis using consensus of Markov chains

Jovanovic, Dejan P. and Pollett, Philip K. (2011). Fault diagnosis using consensus of Markov chains. 3rd International Workshop on Dependable Control of Discrete Systems, Saarbrucken, Germany, 15-17 June 2011. Piscataway, NJ, United States: IEEE. doi: 10.1109/DCDS.2011.5970320

Fault modelling using a mixture of conditional Gaussian transitions

Jovanovic, Dejan P., McVinish, Ross S. and Pollett, Philip K. (2011). Fault modelling using a mixture of conditional Gaussian transitions. 19th Mediterranean Conference on Control and Automation, Corfu, Greece, 20-23 June 2011. Piscataway, NJ, United States: IEEE. doi: 10.1109/MED.2011.5983194

Interaction between habitat quality and an Allee-like effect in metapopulations

McVinish, R. and Pollett, P. K. (2011). Interaction between habitat quality and an Allee-like effect in metapopulations. 19th International Congress on Modelling and Simulation (MODSIM2011), Perth, Australia, 12-16 December 2011. Perth, Australia: Modelling and Simulation Society of Australia and New Zealand.

Analytical methods for a stochastic mainland-island metapopulation model

Buckley, F. M. and Pollett, P. K. (2009). Analytical methods for a stochastic mainland-island metapopulation model.

Analytical methods for a stochastic mainland-island metapopulation model

Buckley, F. M. and Pollett, P. K. (2009). Analytical methods for a stochastic mainland-island metapopulation model. 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 13-17 July, 2009. Canberra, Australia: Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation.

Robust optimal observation of a metapopulation

Pagendam, D. E. and Pollett, P. K. (2009). Robust optimal observation of a metapopulation. 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 13-17 July, 2009. Canberra, Australia: Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation.

Rules of thumb for metapopulation management

Ross, J. V. and Pollett, P. K. (2009). Rules of thumb for metapopulation management. 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 13-17 July, 2009. Canberra, Australia: Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation.

Ensemble behaviour in population processes with applications to ecological systems

Pollett, P. K. (2007). Ensemble behaviour in population processes with applications to ecological systems. 17th Biennial Congress on Modelling and Simulation (MODSIM07), Christchurch, New Zealand, 10-13 December, 2007. Christchurch, New Zealand: Modelling and Simulation Society of Australia and New Zealand.

Optimal sampling and problematic likelihood functions in a simple population model

Pagendam, D. E. and Pollett, P. K. (2007). Optimal sampling and problematic likelihood functions in a simple population model. 17th Biennial Congress on Modelling and Simulation (MODSIM07), Christchurch, New Zealand, 10-13 December, 2007. Christchurch, New Zealand: Modelling and Simulation Society of Australia and New Zealand.

Costs and decisions in population management: Koalas on Kangaroo Island

Pollett, P. K. and Ross, J.V. (2005). Costs and decisions in population management: Koalas on Kangaroo Island. 16th Biennial Congress on Modelling and Simulation MODSIM05, University of Melbourne, 12 - 15 December 2005. Canberra, Australia: Modelling and Simulation Society of Australia and New Zealand.

Product Form Approximations for Highly Linear Loss Networks with Trunk Reservation

Bebbington, M., Pollett, P. and Ziedins, I. (2003). Product Form Approximations for Highly Linear Loss Networks with Trunk Reservation.

A method for evaluating the distribution of the total cost of a random process over its lifetime

Pollett, P. K. and Stefanov, V.T. (2003). A method for evaluating the distribution of the total cost of a random process over its lifetime. International Congress on Modelling and Simulation, Townsville, Australia, 14-17 July 2003. Townsville, Australia: Modelling and Simulation Society of Australia and New Zealand.

Evaluating persistence times in populations that are subject to local catastrophes

Cairns, B. J. and Pollett, P. K. (2003). Evaluating persistence times in populations that are subject to local catastrophes. International Congress on Modelling and Simulation, Townsville, Australia, 14-17 July 2003. Townsvile, Australia: Modelling and Simulation Society of Australia and New Zealand.

A reduced load approximation accounting for link interactions in a loss network

Thompson, M. and Pollett, P. K. (2001). A reduced load approximation accounting for link interactions in a loss network. 16th National Conf. of the Aust.Soc. for Operations Research, McLarens On the Lake, McLaren Vale, Sth. Australia, 23 - 26 September 2001. Adelaide, South Australia: DSTO (Defence Science and Technology Organisation).

Diffusion approximations for ecological models

Pollett, P. K. (2001). Diffusion approximations for ecological models. International Congress on Modelling and Simulation, Australian National University, Canberra, 10-13/12/01. Canberra, Australia: Modelling and Simulation Society of Australia and New Zealand.

Resource allocation in general queueing networks with applications to data networks

Pollett, P. K. (2001). Resource allocation in general queueing networks with applications to data networks. 16th National Conf. of the Aust.Soc. for Operations Research, McLarens On the Lake, McLaren Vale, Sth. Australia, 27th September 2001. Adelaide, South Australia: DSTO (Defence Science and Technology Organisation).

Resource allocation in general queueing networks

Pollett, P. K. (2000). Resource allocation in general queueing networks. Putting OR/Ms Theory into Real Life, Kito Nijyo Club, Sapporo, Japan, 26-28 June 2000. Sapporo, Japan: Operations Research Society of Japan, Hokkaido Chapter.

Bottlenecks in Markovian queueing networks

Pollett, P. K. (1999). Bottlenecks in Markovian queueing networks. 15th National Conference of the Australian Society for Operations Research, Gold Coast, Aust., 4-7 July, 1999. Brisbane: Aust. Society for Operations Res..

Product form approximations for highly linear loss networks with trunk reservation

Bebbington, M. S., Pollett, P. K. and Ziedins, I. (1999). Product form approximations for highly linear loss networks with trunk reservation. Christchurch, NZ, 23-25 Sept, 1999. Brisbane: Cen. for Statistics, Univ. of Qld.

Quasistationarity in populations that are subject to large-scale mortality or emigration

Pollett, P. K. (1999). Quasistationarity in populations that are subject to large-scale mortality or emigration. MODSIM 99 - International Congress on Modelling & Simulation, Hamilton, NZ, 6-9 December 1999. Hamilton, NZ: Modelling and Simulation Society of Aust. and NZ.

The analysis of continuous-time Markovian models using expected rates

Pollett, P. K. and Thompson, M. (1999). The analysis of continuous-time Markovian models using expected rates. 1st West.Pacific & 34d Aust.-Japan Workshop on Stochastic Models in Engin. Technology & Management, Christchurch, NZ, 23-25 September 1999. Brisbane: Cen. for Statistics, Univ. of Qld.