Queieuing: a behavioural Approach
Larsen E. R.
Van Ackere A.
This research is part of a broader attempt to understand the behavioural aspects of queuing theory. Traditionally, work in the queuing area has focused on the design, running and performance of the facility, with relatively little emphasis on the customers, the users of this facility. We are interested in what happens to queues when customers become more "intelligent", i.e. they do not simply arrive at the facility according to some random process. To do so we must provide at least two extensions to traditional queuing models: (i) we have to provide some information about the performance of the facility to the customer and (ii) we need to provide the customer with enough computational capability to enable him to react to this information. Given these elements, the customer can decide whether or not it is worthwhile using the facility.As we use nonlinear models, we cannot find closed form solutions and thus resort to simulation and numerical analysis to gain understanding of model behaviour. In the first stage we use aggregated information flows as feedback to provide information to the customers about the current expected waiting time. This expectation will then determine whether they choose to use the facility again and/or how frequently they will be using it. Two determining factors for how this affects the behaviour of the system are (i) the time lag involved in customers adjusting their perceptions and (ii) the speed at which they react to their updated perceptions. Model complexity is further increased by allowing the manager of the facility to form his own perception of the required capacity and adjust it accordingly, again with a time delay. In this way we get simultaneous adjustment, i.e. both customers and management adjust continuously to an evolving situation. In the second stage we use agent modelling to capture the experience of individual customers using the facility, thus we simulate individual experiences for each customer. This allows us to model heterogeneous customers who may have different sensitivities regarding the cost of waiting as well as different ways in which to form their own perception of the efficiency of the facility. Using agent modelling enables us to characterise not only the facility, but also the population of users of the facility, thus creating a better understanding of how customers might co-evolve with the facility that serves them, something which cannot be done within the traditional queuing framework.