NEW STOCHASTIC MODELS FOR SCIENCE, ECONOMICS, SOCIAL SCIENCE AND ENGINEERING

A Model for Cell Proliferation in a Developing Organism

Philip K Pollett, Laleh Tafakori, Peter G Taylor

2022-06-01

In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models go..

Parameter estimation in branching processes with almost sure extinction

Peter Braunsteins, Sophie Hautphenne, Carmen Minuesa

2022-02-01

We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these..

Extinction probabilities in branching processes with countably many types: a general framework

Daniela Bertacchi, Peter Braunsteins, Sophie Hautphenne, Fabio Zucca

2022-01-01

We consider Galton–Watson branching processes with countable typeset X. We study the vectors (Formula Presented) recording the con..

Optimal market thickness

Simon Loertscher, Ellen Muir, Peter G Taylor

2021-11-18

Traders that arrive over time give rise to a dynamic tradeoff between the benefits of increasing gains from trade by accumulating ..

Strategic customer behavior in an M/M/1 feedback queue

Mark Fackrell, Peter Taylor, Jiesen Wang

2021-03-20

We investigate the behavior of equilibria in an M/M/1 feedback queue where price- and time-sensitive customers are homogeneous wit..

A Restless Bandit Model for Resource Allocation, Competition, and Reservation

Jing Fu, Bill Moran, Peter G Taylor

2021-03-12

We study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. I..

Antibody Dynamics for Plasmodium vivax Malaria: A Mathematical Model.

Somya Mehra, James M McCaw, Mark B Flegg, Peter G Taylor, Jennifer A Flegg

2021-01-02

Malaria is a mosquito-borne disease that, despite intensive control and mitigation initiatives, continues to pose an enormous publ..

Resource competition in virtual network embedding

Jing Fu, Bill Moran, Peter G Taylor, Chenchen Xing

2020-12-09

We consider a virtual network (VN) embedding problem on a large-scale substrate physical network. We permit varying capacities and..

Local limit theorems for occupancy models

AD Barbour, Peter Braunsteins, Nathan Ross

2020-09-27

We present a rather general method for proving local limit theorems, with a good rate of convergence, for sums of dependent random..

THE PROBABILITIES OF EXTINCTION IN A BRANCHING RANDOM WALK ON A STRIP

Peter Braunsteins, Sophie Hautphenne

2020-09-01

We consider a class of multitype Galton-Watson branching processes with a countably infinite type set whose mean progeny matrices ..

Modeling and analysis of block arrival times in the Bitcoin blockchain

R Bowden, HP Keeler, AE Krzesinski, PG Taylor

2020-07-18

In the original Bitcoin paper and other research papers since, it is assumed that Bitcoin blocks are mined at the instants of a ho..

Energy-efficient job-assignment policy with asymptotically guaranteed performance deviation

J Fu, B Moran

2020-06-01

We study a job-assignment problem in a large-scale server farm system with geographically deployed servers as abstracted computer ..

A paradox for expected hitting times

M Holmes, PG Taylor

2020-03-06

We prove a counterintuitive result concerning the expected hitting/absorption time for a class of Markov chains. The “paradox” alr..

An Activation-Clearance Model for Plasmodium vivax Malaria

Somya Mehra, James M McCaw, Mark B Flegg, Peter G Taylor, Jennifer A Flegg

2020-02-12

Malaria is an infectious disease with an immense global health burden. Plasmodium vivax is the most geographically widespread spec..

The value of communication and cooperation when servers are strategic

M Fackrell, C Li, PG Taylor, J Wang

2019-10-01

In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In th..

Networks of interacting stochastic fluid models with infinite and finite buffers

Nikki Sonenberg, Peter G Taylor

2019-08-01

Stochastic fluid models have been widely used to model the level of a resource that changes over time, where the rate of variation..

The time-dependent expected reward and deviation matrix of a finite QBD process

Sarah Dendievel, Sophie Hautphenne, Guy Latouche, Peter G Taylor

2019-06-01

Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of it..

Bounds for the solution to the single-period inventory model with compound renewal process input: An application to setting credit card limits

JK Budd, PG Taylor

2019-05-01

Motivated by a desire to calculate the optimal credit limit for a credit card account in terms of the card-holder’s purchasing beh..

Towards Q-learning the Whittle Index for Restless Bandits

Jing Fu, Yoni Nazarathy, Sarat Moka, Peter G Taylor

2019-01-01

We consider the multi-armed restless bandit problem (RMABP) with an infinite horizon average cost objective. Each arm of the RMABP..

Why is Kemeny's constant a constant?

Dario Bini, Jeffrey J Hunter, Guy Latouche, Beatrice Meini, Peter Taylor

2018-12-01

In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum ha..

A sequential stochastic mixed integer programming model for tactical master surgery scheduling

Ashwani Kumar, Alysson M Costa, Mark Fackrell, Peter G Taylor

2018-10-16

In this paper, we develop a stochastic mixed integer programming model to optimise the tactical master surgery schedule (MSS) in o..

A lightning-caused wildfire ignition forecasting model for operational use

Nicholas Read, Thomas J Duff, Peter G Taylor

2018-05-01

Lightning-caused wildfires are responsible for substantial losses of lives and property worldwide. Convective storms can create la..

Energy-Efficient Priority-Based Scheduling for Wireless Network Slicing

Qing Wang, Jing Fu, Jingjin Wu, Bill Moran, Moshe Zukerman

2018-01-01

Wireless network slicing is a promising technology for next-generation networks to provide tailored on-demand services to mobile u..

How old is this bird? The age distribution under some phase sampling schemes

Sophie Hautphenne, Melanie Massaro, Peter Taylor

2017-12-01

In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual’s lifetime. Unde..

The spatial distribution of rainfall extremes and the influence of El Nino Southern Oscillation

Kate Saunders, Alec G Stephenson, Peter G Taylor, David Karoly

2017-12-01

Extreme rainfall does not occur in spatial isolation. Rainfall occurs in a region, and within that region nearby locations are lik..

Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies

Na Li, David A Stanford, Peter Taylor, Ilze Ziedins

2017-11-01

In 1964, Kleinrock proposed a queueing discipline for a single-server queue in which customers from different classes accumulate p..

The Markov-modulated Erlang loss system

M Mandjes, PG Taylor, K De Turck

2017-11-01

This paper focuses on a loss system in which both the arrival rate and the per-customer service rate vary according to the state o..

A general noncentral hypergeometric distribution

S Loertscher, EV Muir, PG Taylor

2017-01-01

We construct a general non-central hypergeometric distribution, which models biased sampling without replacement. Our distribution..

Allocation in a Vertical Rotary Car Park

M Fackrell, P Taylor

2017-01-01

We consider a vertical rotary car park consisting of l levels with c parking spaces per level. Cars arrive at the car park accordi..

Approximating the equilibrium quantity traded and welfare in large markets

Ellen V Muir, Konstantin Borovkov

2017-01-01

We consider the efficient outcome of a canonical economic market model involving buyers and sellers with independent and identical..

Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay

J Goebel, HP Keeler, AE Krzesinski, PG Taylor

2016-10-01

In the context of the ‘selfish-mine’ strategy proposed by Eyal and Sirer, we study the effect of communication delay on the evolut..

Modelling modal gating of ion channels with hierarchical Markov models

Ivo Siekmann, Mark Fackrell, Edmund J Crampin, Peter Taylor

2016-08-01

Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has bee..

The roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues

Peter Braunsteins, Sophie Hautphenne, Peter G Taylor

2016-06-01

In an M/M/1/C queue, customers are lost when they arrive to find C customers already present. Assuming that each arriving customer..

Lyapunov Exponents for Branching Processes in a Random Environment: The Effect of Information

Sophie Hautphenne, Guy Latouche

2016-04-01

We consider multitype branching processes evolving in a Markovian random environment. To determine whether or not the branching pr..

THE RUNNING MAXIMUM OF A LEVEL-DEPENDENT QUASI-BIRTH-DEATH PROCESS

Michel Mandjes, Peter Taylor

2016-04-01

The objective of this note is to study the distribution of the running maximum of the level in a level-dependent quasi-birth-death..

QUEUES WITH ADVANCED RESERVATIONS: AN INFINITE-SERVER PROXY FOR THE BOOKINGS DIARY

RJ Maillardet, PG Taylor

2016-03-01

Queues with advanced reservations are endemic in the real world. In such a queue, the 'arrival' process is an incoming stream of c..

A queueing model for the capacity planning of a multi-phase human services process

N Sonenberg, G Au, PG Taylor

2015-07-03

The increasing availability of data concerning service demand and service provision has enabled the application of queueing models..

A Structured Markov Chain Approach to Branching Processes

Sophie Hautphenne

2015-07-03

Algorithmic methods developed for structured Markov chains are extended to solve questions about a class of continuous-time branch..

The intercept term of the asymptotic variance curve for some queueing output processes

Sophie Hautphenne, Yoav Kerner, Yoni Nazarathy, Peter Taylor

2015-04-16

We consider the output processes of some elementary queueing models such as the M/M/1/K queue and the M/G/1 queue. An important pe..

Discussion on "On the Laplace Transform of the Aggregate Discounted Claims with Markovian Arrivals," by Jiandong Ren, Volume 12(2)

H Keeler, P Taylor

2015-01-01

Waiting time distributions in the accumulating priority queue

David A Stanford, Peter Taylor, Ilze Ziedins

2014-07-01

We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets ar..

A multi-class multi-server accumulating priority queue with application to health care

AB Sharif, DA Stanford, P Taylor, I Ziedins

2014-06-01

We consider the accumulating priority queue (APQ), a priority queue where customer priorities are a function of their waiting time..

Renfrey Burnard Potts 1925-2005

LH Campbell, PG Taylor

2014-01-01

Ren Potts was an Australian applied mathematician whose early work in statistical mechanics later became influential: the ‘Potts M..