Passive transit-signal priority (TSP) is an effective approach to improve the operational efficiency of transit systems on arterial roads. This paper presents an integrated TSP model that benefits both transit vehicles and other road users. The proposed model uses the random arrival characteristics of transit vehicles related to their stochastic dwell times at near-side stops. Thus, it enables not only two-way bandwidth maximization within subsystems but also the combined optimization of adjacent subsystems. To minimize any negative impact on side-street traffic, this study, unlike previous research, considers the influential area by the introduction of TSP. Case studies on 15 intersections in Sejong, Korea, verify the superior performance of the proposed model for both transit and general vehicles.