Optimisation of single-queue service delivery systems using a Markovian approach

Service delivery systems, such as banks and airport checking terminals, are faced with the daunting task of processing an increasing demand of customers. At the same time, customers have to make accept, reject or reprocess decisions for the service being offered (when given a choice). Singleserver systems are simple and can be utilised as preliminary models, but most organisations generally use multi-server service delivery systems, which require more complex modelling. Modelling of the systems state using Markovian and queuing models provides a more robust approach to better understand the dynamics of the service delivery system, thereby enabling improved services based on anticipated demand variations. In addition, it provides a means to ensure an effective cost minimisation and an increased profit for the service delivery organisation. Therefore, this research proposes a Markovian-based conceptual model to optimise general service delivery systems. To illustrate the model, a numerical example for both single- and multi-server service delivery systems to determine the optimum system parameters is presented and solved. The results obtained showed that the net profit is very sensitive to both the service and arrival rates, among other parameters.