A Queueing Theory Model of Nonstationary Traffic Flow

Abstract

T he queueing-theoretical model for stationary traffic flow developed in a former paper is extended and modified for nonstationary flow. In particular it is shown how speed-flowdensity relationships under nonstationary conditions may deviate from those obtained for stationary conditions. It is shown how the wide scatter which is often observed with empirical speed-flow-density data can be explained by nonstationarity. Furthermore, hysteresis loops, which may show up in speed-flow-density relationships, are interpreted by means of nonstationarity.

Estimating probability distributions of dynamic queues

“…We believe that the only necessary condition on the arrival and service processes is that they be temporally and mutually uncorrelated, and on this basis, the theory and methods to be described are applicable to M/G/1 and even G/G/1 processes. Heidemann (2001) shows that there is a parallel between random queuing and both steady-state and dynamic flow-density relationships in a channel of finite capacity such as a motorway segment. He identifies degree of saturation with the ratio of actual density to jam density, while accepting there are issues with using an M/M/1 model because it is inconsistent with the observed relatively narrow range of desired travel speeds, so some form of M/G/1 process may be more appropriate.…”

Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes

“…In fact, queues in random environments are well suited for modeling the influence of incidents like accidents and defect cars on congestions of vehicles [44,45].…”

Dynamic network loading: A stochastic differentiable model that derives link state distributions

“…However, accounting for the transients of traffic is necessary to capture in greater detail the build-up and dissipation of spillbacks, and more generally, that of queues. To the best of our knowledge, the work in [36] is the first queueing theory approach to analyze traffic under a transient regime. Stationary performance measures are compared to their transient counterparts, their differences are illustrated, and the importance of accounting for traffic dynamics is demonstrated.…”

“…It also indicates that nonstationary models can partially explain the scatter of empirical data, as well as hysteresis loops. Given the complexity of transient analysis, the model in [36] is a classical inifinite capacity queue (M/M/1).…”