To estimate travel times through road networks, in this study, we assume a stochastic demand and formulate a stochastic network equilibrium model whose travel times, flows, and demands are stochastic. This model enables us to examine network reliability under stochastic circumstances and to evaluate the effect of providing traffic information on travel times. For traffic information, we focus on travel time information and propose methods to evaluate the effect of providing that information. To examine the feasibility and validity of the proposed model and methods, we apply them to a simple network and the real road network of Kanazawa, Japan. The results indicate that providing ambulance drivers in Kanazawa with travel time information leads to an average reduction in travel time of approximately three minutes.
Keywords:stochastic network equilibrium, emergency vehicles, travel time information provision stochastic route choice, and developed a second-order stochastic network equilibrium with stochastic flows.A main cause of network uncertainty is variation in travel demand; thus, stochastic demand should be incorporated into network equilibrium models. Shao et al. (2006) and Siu & Lo (2008) introduced stochastic demands into network equilibrium models and explicitly considered stochastic flows. Lam et al. (2008) and Sumalee et al. (2010) considered network flow under stochastic supply and demand, and examined the impacts of adverse weather conditions. Zhang et al. (2011), who similarly considered stochastic supply and demand, introduced the expected residual minimization into stochastic-flow network equilibrium. Nakayama & Watling (2014) proposed stochastic network equilibrium models with stochastic flows, in which stochastic travel time, network flow, and demand are treated consistently. However, they assumed that the stochastic travel demands are independent among origin-destination (OD) pairs.In this study, we improve upon the model of Nakayama & Watling (2014), alleviating the independent demand and other assumptions, and formulate a stochastic network equilibrium model under stochastic demands. Using the proposed stochastic network equilibrium model, we develop methods to evaluate the effect of providing travel time information. Then, we apply the model and methods to a simple network and the real road network of Kanazawa, Japan, and examine their applicability and validity.
Assumptions for Drivers and NotationThe notation used in this study is as follows: I = the number of OD pairs A = the total number of links J i = the number of routes between OD pair i J = the total number of all routes (= J 1 + J 2 +⋅⋅⋅+ J I ) K = the total number of latent drivers δ a,ij = link route incidence variable (δ a,ij = 1 if link a is part of route j between OD pair i; 0 otherwise) σ σ σ J J J J J J J J J J