<p>New technologies such as electric vehicles, Autonomous vehicles and transportation platforms are changing the way humanity move in a dramatic way and cities around the world need to adjust to this rapid change brought by technology. One of the aspects more challenging for urban planners is the parking problem as the new increase or desire for these private technologies may increase traffic congestion and change the parking requirements across the city. For example, Electric vehicles will need parking places for both parking and charging and Autonomous vehicles could increase the congestion by making longer trips in order to search better parking alternatives. Thus, it becomes essential to have clear, precise and practical models for transportation engineers in order to better represent present and future scenarios including normal vehicles, autonomous vehicles and electric vehicles in the context of parking and traffic alike. Classical network model such as traffic assignment have been frequently used for this purpose although they do not take into account essential aspects of parking such as fixed capacities, variety of users and autonomous vehicles. In this work a new methodology for modelling parking for multi class traffic assignment is proposed including autonomous vehicles and hard capacity constraints. The proposed model is presented in the classical Cournot Game formulation based on path flows and in a new link-node formulation which states the traffic assignment problem in terms of link flows instead of path flows. This proposed model allows for the creation of a new algorithm which is more flexible to model requirements such as linear constrains among different players flows and take advantage of fast convergence of Linear programs in the literature and in practice. Also, this link node formulation is used to redefine the network capacity problem as a linear program making it more tractable and easier to calculate. Numerical examples are presented across this work to better exemplify its implications and characteristics. The present work will allow planners to have a clear methodology for modelling parking and traffic in the context of multiusers which can represent diverse characteristics as parking time or type of vehicles. This model will be modified to take into account AV and the necessary assumptions and discussion will be provided.</p>