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to HONEY... the wind beneath my wings... Preface Traffic assignment is the process of allocating a given set of traffic movements to a specific traffic system. The purposes of traffic assignment include the assigning of estimated future trips to the existing traffic system in order to assess the deficiencies of the system, to evaluate the effects of possible improvements in the traffic system and to test possible alternate routes for the traffic system. One of the most popular principles used in the study of traffic assignment models is the Wardrop user equilibrium principle which states that users of the traffic network will choose the route having the minimum cost between each OD pair, and through this process, the routes that are used will have equal costs; moreover, routes with costs higher than the minimum will have no flow. Moreover, the traffic equilibrium problem (TEP) is to find a vector pair of route flows and minimum route costs such that the Wardrop user equilibrium principle, together with the nonnegativity condition imposed on the travel demand function, are satisfied