As demand for travel increases, providing for it fully in infrastructure is considered both impractical and environmentally harmful. Emphasis is shifting from new building to maximising performance of existing facilities.Indeed, congestion is often seen less as evidence of failure of a transport system than evidence of its utility for travellers, who are prepared tobear the cost in order to acquire a benefit. Reliability, or predictability of journey times, is thought to be achievable at relatively low cost, by managing the network more effectively. Congestion commonly results from transient excess of demand over capacity. Queues arise not only from bottlenecks and unpredictable incidents, but also random sources whose statistics are theoretically predictable. Queues usually develop at junctions and points where capacity is constricted. Observations confirm that they can exhibit large day-to-day variation. The classic probabilistic queues are the M/M/1 and M/D/1: Markovian (random) or Deterministic (uniform) arrivals and service with one server. The effect of randomness on mean queues can be included in time-dependent closed form models, but these do not describevariability. Empirical relationships relating queue variance to peak shape have been derived by calibrating from simulation, but cannot deal with all possible peak shapes. This paper develops a more general time-dependentformula for queue variance, which not only enables a profile of variance to be calculated, but can also reveal errors in the mean queue model. The improved model developed is able to predict the development of mean queue size and variance for arbitrary time-sliced demand profiles. Although the sheared queue formula is necessarily approximate, it has some desirable properties so is worth retaining as far possible. Work remains to be done, because the effect of initial utilisation is not embodied in the queue growth model. As with queue decay, an exponential relaxation process may work,but acting on a much shorter time scale. For the model as a whole, simplicity and computational efficiency are as important criteria as accuracy, to ensure it is practical to incorporate it in existing traffic models. Forthe covering abstract see ITRD E137145.
Samenvatting