Personal mobility carbon allowance (PMCA) schemes are designed to reduce carbon consumption from transportation networks. PMCA schemes influence the travel decision process of users and accordingly impact the system metrics including travel time and greenhouse gas (GHG) emissions. We develop a multi-user class dynamic user equilibrium model to evaluate the transportation system performance when PMCA scheme is implemented. The results using Sioux-Falls test network indicate that PMCA schemes can achieve the emissions reduction goals for transportation networks. Further, users characterized by high value of travel time are found to be less sensitive to carbon budget in the context of work trips. Results also show that PMCA scheme can lead to higher emissions for a path compared with the case without PMCA because of flow redistribution. The developed network equilibrium model allows to examine the change in system states at different carbon allocation levels and to design parameters of PMCA schemes accounting for population heterogeneity.