Two time-varying and state-dependent fluid queuing models for traffic circulation systems

Accurately modeling dynamic traffic circulation systems, such as roads for vehicles and corridors for pedestrians, is of great importance for the planning, design, operation and management of circulation systems. The traffic demand of circulation systems is time-varying and congestion-dependent, the service ability is state-dependent (i.e., it drops sharply once congestion occurs), and inherent randomness exists in circulation systems at the same time. In this paper, we first develop a loss queuing model that simultaneously takes the above characteristics into account by using the existing pointwise stationary fluid flow approximation (PSFFA). Then, on the basis of the loss model, we develop a feedback queuing model by integrating the PSFFA and the generalized expansion methods (GEM). The computational complexities of the algorithms are only a linear function of the number of time slices. Simulation experiments show that the proposed models and algorithms perform well regardless of variations in traffic intensity. The obtained dynamic performance may capture the queue accumulation and dissipation at any time slice and reveal the after-effects of a time slice with large traffic intensity. We derive the asymptotic behavior as traffic demand grows and show that excessive traffic demand will downgrade system throughput and lead to a vicious circle of road congestion, i.e., the circulation system will gradually become a bottleneck with increasingly lower throughput. Numerical experiments based on the commuting data of KunShan City reveal some interesting findings.