  This study investigates the efficiency and effectiveness of an area-based
tradable credit scheme (TCS) using the trip-based Macroscopic Fundamental
Diagram model for the morning commute problem. In the proposed TCS, the
regulator distributes initial credits to all travelers and designs a
time-varying and trip length specific credit tariff. Credits are traded between
travelers and the regulator via a credit market, and the credit price is
determined by the demand and supply of credits. The heterogeneity of travelers
is considered in terms of desired arrival time, trip length and departure-time
choice preferences. The TCS is incorporated into a day-to-day modelling
framework to examine the travelers' learning process, the evolution of network,
and the properties of the credit market. The existence of an equilibrium
solution and the uniqueness of the credit price at the equilibrium state are
established analytically. Furthermore, an open-source simulation framework is
developed to validate the analytical properties of the proposed TCS and compare
it with alternative control strategies in terms of mobility, network
performance, and social welfare. Bayesian optimization is then adopted to
optimize the credit toll scheme. The numerical results demonstrate that the
proposed TCS outperforms the no-control case and matches the performance of the
time-of-day pricing strategy, while maintaining revenue-neutral nature.
