A multi-server queueing model with locking

In this paper we analyse a multi-server queueing model with locking. The model is motivated by a situation we encountered at a maintenance facility for trains. Maintenance is done at parallel tracks, where each track offers space to two trains. Trains can enter and leave the tracks from one and the same side only. This gives rise to locking of the front train: in order to leave the maintenance track the front train has to wait till maintenance of the back train (if there is one) has also been completed. Hence, part of the maintenance (or track) capacity is lost. The queueing model is used to investigate the loss of capacity and its effect on sojourn times. The performance of this system is also compared with other designs. A surprising result is that in light traffic it is better to use only half of the track capacity by allowing no more than one train at a maintenance track.