01558263

Component

Modeling queuing behavior is central to the analysis of transportation and other service systems. To date, several queuing models been developed, but analytical insights on their global properties are hard to obtain. This is because in most cases, queuing dynamics are formulated as differential or difference equations, with possible discontinuities in their solutions. making most conventional analytical tools inadequate. As a result, simulations are often used to study these models, and if not properly treated, negative flows could arise from the simulation near certain discontinuities. In this paper, the authors propose a continuous-time queuing model that captures generalized queuing dynamics, where bottleneck capacity and demand can vary simultaneously. The authors provide insights on the global properties of this model, upon deriving its closed-form variational solutions. Rather than resorting to the usual Hamilton-Jacobi theory, the derivations are built on an intrinsic periodicity property of the general queuing dynamics combined with measure-theoretic analysis. This treatment allows the authors to obtain results with more complex boundary conditions and make further extensions. The authors demonstrate its applications and show its solution properties in queuing simulation and performance bounding. In particular, the authors provide graphical, iterative and linearized solution schemes, which are all devoid of the well-known negative flow issue associated with numerical solutions to the point queue model.

This paper was sponsored by TRB committee AHB45 Traffic Flow Theory and Characteristics.

01550057

15-5412

English

17p

2015

Transportation Research Board 94th Annual Meeting

Digital/other

Figures; References

Bottlenecks; Highway capacity; Queuing theory; Simulation; Traffic queuing

Highways; Planning and Forecasting; I72: Traffic and Transport Planning

Transportation Research Board Annual Meeting 2015 Paper #15-5412

TRIS, TRB, ATRI

Dec 30 2014 1:49PM