Queues occur frequently in many areas of nature and technology, for example in transport modelling, but much current use of queues is made in modelling communications networks.
Whilst probabilistic results have been derived from queueing models, there has been limited research about the optimal measurement times in order to make inference about the parameters which determine the queues' behaviour. In particular, in some applications (e.g. communications networks) measuring queues can require adding customers to the queue to act as survey customers. This has the effect of altering the future behaviour of the queue, and potentially changing the optimal measurement pattern of the queues: observations interfere with the experiment. We look in some detail at this interesting interfering case.
We examine the optimal design of measurements on queues with particular reference to the M/M/1 queue. Using the statistical theory of design of experiments, we find optimal times to measure the queue when the parameters of the queue are unknown. We present some guidelines on how to extend for other probabilistic models (differential equation models and more general Markov chain models).