There is a strong Cardiff OR tradition in the study of queueing systems, with applications of queueing theory, simulation and probability theory to practical problems. A typical research project involves both analytical insights from queueing theory and the use of computer simulation, and a number of PhD students are working in this area with particular applications to healthcare, transportation and telecommunications problems.
Queueing studies have focussed on bulk service queues and time-dependent queueing models, including research projects at Gatwick Airport, the Severn Bridge, the Channel Tunnel, and healthcare services (including the intensive care unit, operating theatres and ambulance services). Recent theoretical has made significant progress with the transient solution of queueing systems with a variety of service mechanisms (Prof. Jeff Griffiths and Dr Janet Williams) and a number of research projects have been awarded, dating back as far as 1975, to contracts and consultancies from Transport Research Laboratory, Suez Canal Authority, BP Oil Ltd, Department of Transport, Research Councils, etc. Projects have been undertaken relating to delays to pedestrians and vehicles at pedestrian crossings, accident analyses within computer controlled signal networks, facilities provided at motorway roadworks, toll systems, advantages of flared junctions at traffic signals, etc.
Research and application in simulation has involved discrete-event, system dynamics, agent-based, Monte Carlo and hybrid methods. Novel research has focussed on the use of simulation models incorporating small-world theory for modelling of disease propagation (Dr Israel Vieira), modelling consumer choice (Dr Vince Knight) and incorporating human behaviour (Prof. Paul Harper). Applications include NHS patient choice, HIV/AIDS, ambulance services, breast cancer, A&E department and critical care. Novel work on hybrid methods is exploring the feasibility and benefits of combined methodologies (such as DES and SD) and work with Social Scientists.
Probabilistic methods are being applied to modelling of telecommunication systems and opportunistic networks (Dr Dafydd Evans) which consist of mobile nodes equipped with short range wireless communications devices. Information is dispersed both by wireless transmission between the participating nodes and the movement of the nodes themselves. For example, a source node located at a railway station transmits a message to people passing nearby, who then disseminate the message across the local area. Fixed nodes are strategically placed throughout the area to act as message repositories. Dr Evans is developing probabilistic models of opportunistic networks, and using these to derive theoretical performance bounds for this type of network. Network performance statistics can involve concepts at the network level (e.g number of connected components), at the neighbourhood level (e.g. number of nodes within transmission range) or at the node level (e.g. number of messages waiting to be relayed).
Vieira IT, Cheng RCH, Harper PR and de Senna V (2010), Small World Network Models of the Dynamics of HIV Infection”. Annals of Operational Research. 178: 173-200.Allen SM,
Griffiths J D (2006), Cascades of Queues. J. of the Operational Research Society, 2006, 711-717, 57 (6).
Griffiths JD, Leonenko G and Williams JE (2006), The transient solution to M/Ek/1 queue. Operations Research Letters, 2006, 349-354, 34 (3).
Griffiths JD, Price-Lloyd N, Smithies M and Williams JE (2006), A Queueing Model of Activities in an Intensive Care Unit. IMA J. of Management Mathematics, 2006, 277-288, 17 (3).
Evans D, Hurley S and Whitaker, RM. 2002 Optimisation in the design of mobile ad-hoc networks with steerable directional antennae. Proc. Ad-Hoc Networks and Wireless Conference.
Evans D, Jones, AJ and Schmidt WM (2002), Asymptotic moments of near neighbour distance distributions, Proc. R. Soc. A, 458 (2028), 2839-2849.