An alternative definition of dynamic user optimum on signalised road networks Y. E. Ge 1 * and Xizhao Zhou 2 1 School of Transportation and Logistics, Faculty of Infrastructure Engineering, Dalian University of Technology, Liaoning 116024, China 2 School of Economics and Management, Shanghai Maritime University, Shanghai 200135, China SUMMARY In the literature on dynamic traffic assignment (DTA), dynamic user optimum (DUO) and dynamic user equilibrium (DUE) are interchangeable and refer to a stable state on a road network in which, under the assumption of perfect information on traffic conditions and the assumption that every traveller chooses the least costly path to travel, no one can reduce his or her travel cost by changing his or her path unilaterally. This paper proposes an alternative definition of DUO on signalised road networks; in such a DUO state, the travel times or costs of used paths between the same origin–destination pair can be different because of the existence of signalised junctions. Usually, on signalised road networks, a DUE solution is sought to approximate such a DUO solution by assuming that the capacity of each approach at a signalised junction is equal to the saturation flow rate of the approach times the corresponding split. By comparing the DUE and DUO solutions of a DTA problem on a small signalised road network, this paper discusses advantages and disadvantages of this approximation and shows that such a DUE solution would not be a good approximation to a DUO solution. Copyright © 2012 John Wiley & Sons, Ltd. KEY WORDS: dynamic traffic assignment; dynamic user optimum; dynamic user equilibrium; signalised road network 1. INTRODUCTION In defining the conventional concept of dynamic user equilibrium (DUE), it is assumed that every traveller has perfect information on traffic conditions and chooses the least costly path to travel. Once such an equilibrium state is achieved, no one can reduce his or her travel cost by changing his or her path unilaterally. Dynamic user optimum (DUO) is conventionally interchangeable with DUE in the literature on dynamic traffic assignment (DTA). It has been shown that the continuity of travel times at time t of each link on a road network in terms of the number of vehicles travelling on the link at the time is a sufficient condition of the existence of a DUE state [1,2]. Zhu and Marcotte [3] discussed further about a number of different definitions of continuity under which a path-choice DUE state exists. This implies that the discontinuity of path travel times or costs can cause no existence of DUE. Typically, that a signalised junction makes link/path travel times discontinuous can lead to no DUE state on a road network. But if all travellers would not mind or could accept a small difference in travel costs between used paths of an origin–destination (OD) pair, a tolerance-based DUO state can be defined [4,5]. In tolerance-based DUO, the travel costs of all used paths between an OD pair are not greater than the achieved minimum travel cost between the OD pair plus an acceptable tolerance, which is a *Correspondence to: Ying-En Ge, School of Transportation and Logistics, Faculty of Infrastructure Engineering, Dalian Uni- versity of Technology, 2 Linggong Road, Ganjingzi District, Dalian, Liaoning 116024, China. E-mail: Y.E.Ge@dlut.edu.cn Copyright © 2012 John Wiley & Sons, Ltd. JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2012; 46:236–253 Published online 6 March 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/atr.207