• Markov modelling: Queueing processes and evolutionary dynamics
  • Pedagogy: Active learning approaches
  • Game Theory: Strategic behaviour in queues and the Iterated Prisoner's dilemma
  • Healthcare: Applied modelling of patient flow


  1. 2018: Determining patient outcomes from patient letters: A comparison of text analysis approaches: Jennifer Morgan, Paul Harper, Vincent Knight, Andrew Nelson, Andreas Artemiou, Alex Carney - Journal of the Operational Research Society
  2. 2018: Nashpy: a Python library for the computation of Nash equilibria: Vincent Knight, James Campbell - Submitted to Journal of Open Source Software
  3. 2017: Modelling deadlock in open restricted queueing networks: Geraint Palmer, Paul Harper, Vincent Knight - European Journal of Operational Research
  4. 2017: Predicting Adolescent Social Networks to Stop Smoking in Secondary Schools: Angelico Fetta, Vincent Knight, Paul Harper, Janet Williams - European Journal of Operational Research
  5. 2017: Ciw: An open source discrete event simulation library: Geraint Palmer, Vincent Knight, Paul Harper, Asyl Hawa - Journal of Simulation - (Preprint)
  6. 2017: Reinforcement Learning Produces Dominant Strategies for the Iterated Prisoner's Dilemma: Marc Harper, Vincent Knight, Martin Jones, Georgios Koutsovoulos, Nikoleta Glynatsi, Owen Campbell - PLOS One - (Preprint)
  7. 2017: An Evolutionary Game Theoretic Model of Rhino Horn Devaluation: Nikoleta Glynatsi, Vincent Knight, Tamsin Lee - Arxiv pre print
  8. 2017: Evolution Reinforces Cooperation with the Emergence of Self-Recognition Mechanisms: an empirical study of the Moran process for the iterated Prisoner's dilemma : Vincent Knight, Marc Harper, Nikoleta Glynatsi, Owen Campbell - Arxiv pre print
  9. 2016: Time-dependent stochastic methods for managing and scheduling Emergency Medical Services: Julie Vile, Jon Gillard, Paul Harper, Vincent Knight - Operations Research for Health Care.
  10. 2016: Editorial: Health Systems ESI XXXI — OR applied to Health in a Modern World.: Roberto Aringhieri, Vincent Knight, Honora Smith - Operations Research for Health Care, 5, 3.
  11. 2016: Measuring the Price of Anarchy in Critical Care Unit Interactions.: Vincent Knight, Izabela Komenda, Jeff Griffiths - The journal of the operational research society
  12. 2016: An Open Framework for the Reproducible Study of the Iterated Prisoner’s Dilemma.: Vincent Knight, Owen Campbell, Marc Harper, Karol Langner, James Campbell, Thomas Campbell, Alex Carney, Martin Chorley, Cameron Davidson-Pilon, Kristian Glass, Nikoleta Glynatsi, Tomáš Ehrlich, Martin Jones, Georgios Koutsovoulos, Holly Tibble, Jochen Müller, Geraint Palmer, Piotr Petunov, Paul Slavin, Timothy Standen, Luis Visintini, Karl Molden. - Journal of open research software - (Preprint)
  13. 2016: Editorial: Operations Research for Health Care ESI XXXI — OR applied to Health in a Modern World.: Roberto Aringhieri, Vincent Knight, Honora Smith - Operations Research for Health Care, 8, 22–23.
  14. 2016: Ambulance Allocations for Maximising Survival within a Heterogeneous Population using a Heterogeneous Fleet.: Leanne Smith, Paul Harper, Vincent Knight - Submitted to the journal of the operational research society
  15. 2015: Compliance with National Guidelines for Stroke in Radiology.: Izabela Komenda, Hannah Williams, Vincent Knight - Operations Research for Health Care.
  16. 2015: Rostering staff at a mathematics support service using a finite-source queueing model: Jon Gillard, Vincent Knight, Julie Vile, Rob Wilson - IMA Journal of Management Mathematics. 27 (2)
  17. 2015: Modelling of psoriasis patient flows for the reconfiguration of secondary care services and treatments: Kayne Putman, Alex Anstey, Paul Harper, Vincent Knight - Health Systems.
  18. 2015: Playing games: a case study in active learning applied to Game Theory.: Vincent Knight - Connections
  19. 2015: Containment of socially optimal policies in multiple-facility Markovian queueing systems.: Rob Shone, Vincent Knight, Paul Harper, Janet Williams, John Minty - Journal of the Operational Research Society.
  20. 2014: Tweeting the Terror: Modelling the Social Media Reaction to the Woolwich Terrorist Attack: Peter Burnap, Matthew Williams, Luke Sloan, Omer Rana, Will Housley, Adam Edwards, Vincent Knight, Rob Procter, Alex Voss - Social Network Analysis and Mining
  21. 2014: Operational research ambassadors in schools: Noel-Ann Bradshaw, Paul Harper, Vincent Knight, Louise Orpin - Proceedings of the HEA STEM, Edinburgh 2014
  22. 2014: Mathematical modelling of patient flows to predict critical care capacity required following the merger of two district general hospitals into one.: James Williams, Steve Dumont, Jack Parry-Jones, Izabela Komenda, Jeff Griffiths, Vincent Knight - Anaesthesia. 70 (1)
  23. 2013: Selfish routing in public services.: Vincent Knight, Paul Harper - European Journal of Operational Research. 230 (1) 122-132
  24. 2013: Comparisons between observable and unobservable M/M/1 queues with respect to optimal customer behavior: Rob Shone, Vincent Knight, Janet Williams - European Journal of Operational Research
  25. 2013: Using Singular Spectrum Analysis to Obtain Staffing Level Requirements in Healthcare.: Vincent Knight, Jon Gillard - Journal of the Operational Research Society
  26. 2012: Ambulance Allocation for Maximal Survival with Heterogeneous Outcome Measures.: Vincent Knight, Paul Harper, Leanne Smith - OMEGA - The International Journal of Management Science. 40 (6) 918--926
  27. 2012: Discrete Conditional Phase-Type Models Utilising Classification Trees: Application to Modelling Health Service Capacities.: Paul Harper, Vincent Knight, Adele Marshall - European Journal of Operational Research. 219 (3) 522--530
  28. 2012: Modelling Emergency Medical Services with Phase Type Distributions.: Vincent Knight, Paul Harper - Health Systems. 1 53-68
  29. 2012: How Efficient can an Emergency Unit be? A Perfect World Model.: Kesh Baboolal, Jeff Griffiths, Vincent Knight, Andrew Nelson, Cheryl Voake, Janet Williams - Emergency Medicine Journal.
  30. 2011: Cost-Effective Workforce Planning: Optimising the Dental Team Skill-Mix for England.: Paul Harper, E Kleinman, Jenny Gallagher, Vincent Knight - Journal of Enterprise Information Management
  31. 2011: Bed Management in a Critical Care Unit.: Jeff Griffiths, Vincent Knight, Izabela Komenda - IMA Journal of Management Mathematics.
  32. 2011: On the Peter Principle: An Agent Based Investigation into the Consequential Effects of Social Networks and Behavioural Factors.: Angelico Fetta, Paul Harper, Vincent Knight, Janet Williams, Israel Vieira - Physica A: Statistical Mechanics and its Applications.
  33. 2011: Modelling Patient Choice in Healthcare Systems: Development and Application of a Discrete Event Simulation with Agent-Based Functionality.: Vincent Knight, Janet Williams, Iain Reynolds - Journal of Simulation.
  34. 2011: Operational Research Informing National Health Policy: Paul Harper, Vincent Knight, Israel Vieira, Janet Williams - Cardiff University. ISBN: 978-0-9569158-0-1
  35. 2011: Forecasting Welsh Ambulance Demand using Singular Spectrum Analysis.: Janet Williams, Jon Gillard, Paul Harper, Vincent Knight - In Journal of the Operational Research Society
  36. 2010: Forecasting Welsh Ambulance Demand using Singular Spectrum Analysis.: Janet Williams, Jon Gillard, Paul Harper, Vincent Knight - In Proceedings of the XXXVI International ORAHS Conference
  37. 2008: Higher Spin Alternating Sign Matrices: Roger Behrend, Vincent Knight - Electronic Journal of Combinatorics.~14(1): R83, 38pp.


  1. Ben Black (MSc): Empirical investigation of the Ohtsuki-Nowak approximation (2018 - 2018)
  2. Solomon Keedle-Isack (Summer): Further evolutionary game theoretic modelling of Rhino poaching (2018 - 2018)
  3. Henry Wilde (PhD): Costs in healthcare (2017 - present)
  4. Mansour Hakem (Nuffield Research Placement): Investigating Axelrod's second tournament (2017 - 2017)
  5. Toby Devlin (BSc): Machine learning for optimisation of move sequence (2017 - 2017)
  6. Will Guo (Nuffield Research Placement): Investigating Axelrod's second tournament (2017 - 2017)
  7. Thomas Rodwell (PhD): Diary planner for healthcare ward (2017 - present)
  8. Lewis Parsons (Summer): Building a framework for research excellence framework submission coordination (2017 - 2017)
  9. James Campbell (BSc): Fingerprinting prisoner's Dilemma strategies (2016 - 2016)
  10. Cindy Huang (Nuffield Research Placement): Investigating deadlock in queues with vacation and baulking (2016 - 2016)
  11. Nikoleta Glynatsi (PhD): Machine learning and the Prisoner's Dilemma (2016 - present)
  12. Rhys Ward (Summer): Building Game Theoretical Software in a Research Environment (2015 - 2015)
  13. Tobenna Peter Igwe (Google Summer of Code): Extending Game Theory in Sage (2015 - 2015)
  14. Ffinian Sullivan (Nuffield Research Placement): Understanding mixed behaviour in queue balking threshold policies (2015 - 2015)
  15. James Campbell (Summer): Building Game Theoretical Software in a Research Environment (2015 - 2015)
  16. Hannah Lorrimore (Summer): Building Game Theoretical Software in a Research Environment (2015 - 2015)
  17. James Campbell (Summer): Building Game Theoretical Software in a Research Environment (2014 - 2014)
  18. Geraint Palmer (PhD): Jackson networks and healthcare (2014 - present)
  19. Imogen Dunne (BSc.): The Effect of Personality Traits on Academic Achievement in Flipped versus Traditional Learning Environments (2014 - 2015)
  20. Rhys Jones (BSc.): Modelling Rugby Lineout Strategies Using Game Theory (2013 - 2014)
  21. Jason Young (MMath): Markov Decision Processes for the study a system of two queues in series. (2013 - 2014)
  22. Ceri Morse (BSc.): Modelling Lineout Strategies using Game Theory (2012 - 2013)
  23. Jason Young (Summer): Understanding the effect of selfish behaviour in a series of 2 queues (2012 - 2012)
  24. Chappman Sin (BSc.): Mathematical modelling of Risk (the board game) (2011 - 2012)
  25. Iain Reynolds (Summer): Modelling patient choice in healthcare systems development and application of a discrete event simulation with agent-based functionality (2011 - 2011)
  26. Rob Shone (PhD): Individually and Socially Optimal Policies in Queueing Systems with Multiple Heterogeneous Facilities (2011 - 2014)
  27. Angelico Fetta (PhD): Agent Based Simulation for Complex Health Systems Interventions (2011 - 2014)
  28. Izabela Komenda (PhD): Bed management in a critical care unit (2010 - 2013)
  29. Stuart MacGregor (BSc.): A study into two player hide and seek games verifying results from game theory using monte carlo simulation, with a particular application to anti-submarine warfare (2010 - 2011)
  30. Catherine Fortune (BSc.): Game Theory and the Lemke-Howson algorithm (2010 - 2011)
  31. Tatjana Timofejeva (BSc.): Impact of unscheduled care Modelling time varying activities at a Hospital (2010 - 2011)
  32. Julie Vile (PhD): Time-dependent stochastic modelling for predicting demand and scheduling of emergency medical services (2009 - 2012)
  33. Fern Gould (BSc.): Game Theory and the Iterated Prisoner's Dilemma (2009 - 2010)
  34. Tamsin Griffiths (BSc.): Troops to Task Tool and Refugee Estimation (2009 - 2010)
  35. Leanne Smith (PhD): Modelling emergency medical vehicle services (2008 - 2013)


  1. Cardiff University CUROP Award: Further game theoretic dynamics of Rhino poaching, £2100, (2018 - 2018)
  2. EPSRC: Identifying and modelling victim, business regulatory and malware behaviours in a changing cyberthreat landscape, £101659, (2013 - 2016)
  3. Aneurin Bevan Health Board: Creation of a Mathematical/OR Modelling Unit to Support the Aneurin Bevan Health Board, £319944, (2013 - 2015)
  4. Sustainable software institute: Fellowship, £3000, (2013 - ongoing)
  5. Cardiff and Vale University Health Board: Operational Research Modelling to Support Cardiff and Vale UHB, £371427, (2013 - 2018)
  6. ESRC: Hate speech? Understanding the modelling of social media identity formation and behaviour through the Cardiff Online Social Media Observatory (COSMOS), £7015, (2013 - 2016)
  7. Health Foundation and Cardiff and Vale University Health Board: Estimating quality improvement and cost reduction for the patient and local health economy of transferring ENT/audiology services into a community setting, £61237, (2013 - 2014)
  8. Cardiff University CUROP Award: Developing and Evaluating Mathematical Teaching Resources through Open Source Software, £2200, (2012 - 2012)
  9. LANCS (EPSRC): Post-Doctoral Training Scheme Grant: Investigating the Effects of Individual Behaviour on Hierarchical queueing Systems, £5000, (2012 - 2012)
  10. LANCS (EPSRC): Post-Doctoral Training Scheme Grant: Choice and Healthcare Investigation Project, £2500, (2010 - 2011)
  11. Cardiff University CUROP Award: Patient Choice: A Discrete Event Simulation, £2500, (2010 - 2012)



  • Axelrod: A Python library/github project that replicates Axelrod's tournament.
  • Ciw: A Python library for simulation queueing networks
  • Conference Scheduler: A Python library to schedule conferences using integer linear programming
  • Game Theory in Sage: A collection of code to continue the integration of Game Theoretic capabilities in to Sage.
  • Nashpy: A Python library to find equilibria in 2 player normal form games
  • Virtual Microscope: A web application to display and annotate scanned slides.
  • ghtalks: Organise and share talks with gh-pages
  • sklDj: A Django web app interface to machine learning algorithms



Outreach activities

  • Monmouth Science initiative.
  • Speaking at the British Science festival 2015.
  • STEM live: a university wide event.
  • Regular workshops at the School of Mathematics.

Media appearances

  1. 2018-06-07: Pythagoras' trousers - Mathematics behind modelling jet stream as a traffic jam
  2. 2017-03-23: Talk Python to Me Podcast - Game Theory and the Axelrod library
  3. 2017-03-17: Cardiff University YouTube Channel - PyCon Namibia and the Phoenix project
  4. 2017-01-09: Pythagoras' trousers - Mathematics in animation
  5. 2017-01-02: Pythagoras' trousers - Alpha Go
  6. 2016-09-26: Pythagoras' trousers - Election polling
  7. 2016-01-27: Namibia broadcasting company - Discussing PyCon Namibia
  8. 2015-06-16: BBC Radio Wales - Game Theory and Nash Equilibrium
  9. 2015-04-16: Sci screen screening - The Imitation Game
  10. 2014-05-05: 2014 Pythagoras Lecture - Mathematics and Healthcare Management
  11. 2014-03-19: BBC Parliament - Voice of the Future 2014