This study focuses on a tradable credit scheme (TCS)-based multi-period equilibrium modeling framework to address the planning problem of a central authority which seeks to minimize the vehicular emissions in a traffic network over a planning horizon (PH). In this context, the multi-period TCS (MPTCS) equilibrium conditions consist of traffic and market equilibrium conditions. To develop an effective TCS design in practice, this study factors the heterogeneity in travelers' value of time (VOT) to enable realism in capturing the traffic equilibrium conditions, and the interest rate to reflect market realism. The VOT is an important factor in the route choice process as travelers tradeoff the credit consumption and travel time costs of each route. Further, travelers decide between selling or transferring unused credits across periods based on the dynamic interest rates over the PH as they can accrue interest by selling credits in the market. The study investigates the existence and uniqueness of multi-period equilibrium credit prices, aggregate link flows and travel demand rates. Then, the equilibrium credit prices under the MPTCS are analyzed and it is demonstrated that while credit price volatility increases with increasing interest rates, it can be dampened by the ability of travelers to transfer credits under the MPTCS. Finally, a system optimal (SO) MPTCS is designed to determine the TCS parameters (credit allocation and charging schemes) that minimize vehicular emissions in a traffic network over the PH. The study insights suggest that the SO design of MPTCS provides a capability to manage network vehicular emissions over the PH. Further, they suggest that if VOT is not factored, the TCS would be socially inequitable, and ignoring interest rates creates inefficiencies in achieving desired emissions levels.
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