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This paper presents a modelling framework to evaluate travel delay of all vehicles influenced by moving bottlenecks on highways. During the derivation of analytical formulas, the arrival of slow vehicles was approximated by a Poisson process based on the assumption that they occupied a constant low proportion of the traffic stream. The mathematical analysis process was developed from moving bottlenecks with the same velocity to those with multiple different velocities, and the closed-form expression of expected average travel delay was obtained by utilizing kinematic-wave moving bottleneck theory, gap acceptance theory, probability theory and renewal theory. Model validation and parameters sensitive analysis were conducted by simulation relying on the open source database of US highway 10. The maximum passing rate and the macroscopic parameters of initial traffic state with maximum delay could be found by means of approximate formulas. The proposed modeling framework can be applied for evaluating impacts of slow vehicles on highway operation quantifiably, based on which traffic managements like truck prohibited period decision and speed or lane restriction could be made more scientifically.

In this article, by a concept of Stepanov type µ-pseudo almost automorphic functions developed recently, we investigate some new existence results on bounded solutions to a semilinear integro-differential equation in Banach spaces. We first establish a new composition theorem of such functions, and then we prove the main results via ergodicity and composition theorems of Stepanov type µpseudo almost automorphic functions combined with theories of uniformly exponentially stable and strongly continuous family of operators. These bounded solutions can cover (weighted) pseudo almost automorphic solutions with a Stepanov type forcing term as special cases. 2010 AMS Mathematics subject classification. Primary 34K14, 35B15, 45N05, 58D25. Keywords and phrases.Stepanov type µ-pseudo almost automorphic functions, Integro-differential equations, bounded solutions, fixed point theorems.

As a countermeasure to urban exhaust pollution and traffic congestion, traffic restriction based on the last digit of license plate numbers has been widely introduced throughout the world. However, the effect of traffic restriction is weakened as it causes the long-distance detour of restricted travel modes and induces travel demand to shift to unrestricted travel modes. To consider detour and shift of traffic demand caused by traffic restriction, we propose a stochastic user equilibrium model under traffic rationing based on mode shifting rate and the corresponding solution algorithm. A case study is conducted to verify the effectiveness of proposed model and algorithm. Main findings of numerical experiments include: (1) Compared with traditional stochastic user equilibrium model, the temporary traffic demand shift caused by long-distance detour are well considered in proposed model. (2) Sensitivity analysis of the consumption parameters used in the proposed model shows that, the involved cost parameters have different effectiveness on the mode shifting rate. This study provides a reasonable relaxation of the intensively used assumption, that all restricted vehicles outside the restricted district will detour in traffic rationing research, and provides a reasonable approach to evaluate the change of link flow and the beneficial effectiveness on the sustainability of traffic environment after implementation of traffic restriction policy.