Scheduling Customers in Queueing Systems in the Presence of Random Arrivals

Speaker: Wathsala Karunarathne, OPTIMA

Synopsis: The optimal control of arrivals to a service system is an area of research with applications in many industries, for example, manufacturing systems, call centres, hospitals, retail and computer systems. Scheduling is a well-known solution to the problem of controlling arrivals, and a proper scheduling approach can hugely increase a system’s efficiency. Many real-world scenarios such as medical clinics, barbershops, motor mechanics and restaurants accept randomly arriving customers and customers by appointment. However, the problem of scheduling customers in an environment where random arrivals occur has not been addressed widely. We consider a complicated system with added uncertainty brought by randomly arriving customers on top of the uncertainty of stochastic service times, and we assume the system prioritises scheduled customers over random customers. This problem aims to determine the optimum schedule for a fixed number of customers so that the total expected cost of customers’ waiting and that of the server being idle is minimised, whilst the system’s expected revenue is maximised. We show the efficiency of considering random customers in scheduling when the system accepts random customers.

Bio: Wathsala Karunarathne is a PhD candidate at the School of Mathematics and Statistics, The University of Melbourne and a member of OPTIMA. Her research interests are Stochastic modelling, optimisation, game theory, and data-driven queueing problems.

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