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This paper proposes a simultaneous route and departure time choice (SRDTC) problem with fixed demand in a degradable transport network. In this network, travelers face with stochastic travel times. Their selection of routes and departure times follows the UE principle in terms of the mean generalized route cost, which is defined as the probabilistic dynamic user optimal (PDUO) principle. The proposed PDUO-SRDTC problem is formulated as a variational inequality (VI) problem. As a special case of PDUO-SRDTC problem, the PDUO route choice (PDUO-RC) problem is also proposed and formulated as a VI problem. Network degradation is defined on the degradation of the outflow capacity of each link. A Monte Carlo-based stochastic link transmission model (MC-SLTM) is developed to capture the effect of physical queues and the random evolution of traffic states during flow propagation to estimate mean generalized route costs. Both the extragradient algorithm and the route-swapping method with a variable sample size scheme are developed to solve the proposed VI problems. Numerical examples are developed to illustrate the paradoxical phenomena of the problems and the effectiveness of the solution methods. Numerical results show that constructing a new road, enhancing link outflow capacity, or reducing outflow capacity degradation can lead to poor network performance and it is important to consider both network degradation and queue spillback when making transportation policies aimed at improving network performance. The results also demonstrate that the variable sample size scheme can give a quicker and better solution than the traditional fixed sample size scheme. [ABSTRACT FROM AUTHOR]

Dynamic user optimal simultaneous route and departure time choice(DUO-SRDTC) problems are usually formulated as variational inequality (VI) problems whose solution algorithms generally require continuous and monotone route travel cost functions to guarantee convergence. However, the monotonicity of the route travel cost functions can not be ensured even if the route travel time functions are monotone. In contrast to traditional formulations, this paper formulates a DUO-SRDT C problem (that can have fixed or elastic demand) as a system of nonlinear equations. The system of nonlinear equations is a function of generalized origin-destination (OD) travel costs rather than route flows and includes a dynamic user optimal (DUO) route choice subproblem with perfectly elastic demand and a quadratic programming (QP) subproblem under certain assumptions. This study also proposes a solution method based on the backtracking inexact Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, the extra gradient algorithm, and the Frank-Wolf e algorithm The BFGS method, the extra gradient algorithm, and the Frank-Wolf e algorithm are used to solve the system of nonlinear equations, the DUO route choice subproblem, and the QP subproblem, respectively. The proposed formulation and solution method can avoid the requirement of monotonicity of the route travel cost functions to obtain a convergent solution and provide a new approach with which to solve DUO-SRDTC problems. Finally, numeric examples are used to demonstrate the performance of the proposed solution method. [ABSTRACT FROM AUTHOR]