Simulation and Stochastic Modelling

Simulation and Stochastic Modelling are very flexible modelling approaches, and are capable of incorporating uncertainty. Therefore, they are among the most widely used techniques in Operational Research and Management Science.

To gain insight into the behaviour of complex systems, and thereby improve decision-making, we can model individual components of the system, often incorporating randomness via probability distributions. Discrete event simulation, agent-based simulation and system dynamics link the components together in different ways to build models of the whole system. The overall behaviour of the system then emerges from the interactions between the elements, as the sum becomes more than its parts.

For some systems, insights can be gained through direct mathematical analysis without the need to resort to simulation, for example by using stochastic modelling techniques such as queueing theory, renewal theory, asymptotic analysis, Markov chains and Markov processes, or through exact computation using stochastic dynamic programming.  

The interplay between the modelling approaches is also very important. The development of simulation models can be guided by insights derived from stochastic models and the generality of stochastic models can be tested against simulated test cases. They can also  be used in combination in multi-fidelity modelling, where a simulation model is often the high-fidelity but computationally expensive and stochastic modelling provides a less expensive low-fidelity model. 

At present, the group consists of Dr Dave Worthington, Dr Roger Brooks, Dr Catherine Cleophas, Dr Richard Williams, Dr Amjad Fayoumi, Dr Peter Jacko and Emeritus Professor Mike Pidd. The group also benefits from the appointment of Professor Barry Nelson as a Distinguished Visiting Scholar in the department.

Current research areas include:

  • Conceptual modelling in discrete, continuous, and agent-based simulations.
  • Validation and calibration of simulation models on empirical data
  • Simulations as a tool to evaluate planning solutions and algorithms
  • Simulations as a tool to further develop our understanding of complex dynamical systems
  • Behaviour of time-dependent queues
  • Queueing networks, especially as applied to health care.
  • Infinite-server queues, and their application in health care
  • Using simulation to support information systems design
  • Simulation optimisation
  • Multi-fidelity modelling
  • Agent-based simulation methodology and applications
  • Analysis and simulation of Bayesian designs of clinical trials
  • Stochastic scheduling, routing/dispatching, search, and resource allocation
  • Design and performance evaluation of communications networks

If you would like to apply for a PhD, please see our departmental PhD admissions page. 

Some recent and current PhD projects are part of the STOR-i Doctoral Training Centre which is a joint venture between the Department of Mathematics and Statistics, and the Department of Management Science. These projects usually have supervisors in both departments and/or an industrial partner.

Previous and ongoing PhD projects include: 

  • Queue Modelling for Call Centre Management – Efi Chassioti (2005)
  • Empirical Investigation of Conceptual Modelling and the Modelling Process – Wang Wang (2007)
  • Determining the range of predictions for calibrated agent-based simulation models - DongFang Shi (2008)
  • On queues with time varying demand  - Navid Izady (2010)
  • Generic simulation modelling of Accident and Emergency patient flows in acute hospitals in England – Adrian Fletcher (2012)
  • Combining forecasting and queueing models for call centre staffing – Xi Chen (2014)
  • An Agent-Based Model of the IL-1 Stimulated Nuclear Factor-kappa B Signalling Pathway – Richard Williams, University of York (2015)
  • The development and application of an analytical healthcare model for understanding and improving hospital performance – Dan Suen (2016)
  • Methods for enhancing system dynamics modelling: state-space models, data-driven structural validation & discrete-event simulation – Mark Bell (2017)
  • Online Discrete Event Simulation for the Management of Inpatient Beds (ongoing
  • Uncertainty Quantification and Simulation Arrival Processes (ongoing)
  • Symbiotic Simulation in an Airline Operations Environment (ongoing)
  • Agent-based simulation of financial markets (ongoing)
  • Agent-based simulation of classroom interactions (ongoing)
  • Simulation optimisation in forest land allocation between forest-dependent wildlife habitat conservation and other competitive uses (ongoing)
  • Bayesian Bandit Models for the Optimal Design of Clinical Trials – Faye Williamson (ongoing)
  • Optimal Search Accounting for Speed and Detection Capability – Jake Clarkson (ongoing)
  • Dynamic allocation of assets subject to failure or depletion – Stephen Ford (ongoing)
  • Robust and Stochastic Optimisation Approaches to Network Capacity Expansion and QoS Improvement – Francis Garuba (ongoing)
  • Simulation and Optimization of Scheduling Policies in Dynamic Stochastic Resource-Constrained Multi-Project Environments – Ugur Satic (ongoing)

Recent MSc projects include:

  • Developing a generic simulation model for NHS England to better understand hospital bed occupancy by time of day and its impact on A&E performance.
  • Prostate cancer pathway modelling for Calderdale and Huddersfield NHS Foundation Trust
  • Discrete Event Simulation of patient pathways for multi-drug resistant tuberculosis (MDR-TB) treatment for Liverpool School of Tropical Medicine
  • Input Model Uncertainty Assessment: A Study Within the Automotive Industry - for Ford Motor Company
  • Developing a Queueing Model for Vehicles Required in Police Districts
  • Modelling the emergency response service in Blackpool Division for North West Ambulance Service
  • Using system dynamics to measure the impact of uncertainty in construction projects
  • Using system dynamics to understand the impact of emergent information systems on enterprise agility
  • Simulating the annual LUMS Triathlon event to compare options for competitor scheduling
  • Evaluating the effect of golf ball technology on player performance using simulation