## 3 Signal Control Method  
### Signal Phase Sequence  
Since integrated waiting areas aim to ease congestion at intersections where traffic demand is high, adaptive control does not have many advantages over fixed-time controls [27]. As shown in Figure 1, two stop lines are installed on the intersection approach with the first one located at the front of the integrated waiting area and the second stop line downstream at the end of the integrated waiting area. The control method of the signalized intersection with integrated waiting area is different from the conventional intersection without integrated waiting area. An intersection with integrated waiting area can be operated by two pre-timed signal controllers: one for the pre-signals on the approach with integrated waiting area and the other for the main intersection. A set of pre-signal lights group is added at the pre-stop line of the waiting area. In addition, all the traffic flow from each direction is controlled by the pre-signal lights to enter the waiting area safely and orderly [28]. The signal timing plan can be divided into two sub-plans, which are integrated. One is the plan for the main intersection signals, and the other is for the pre-signals. These two signal timing plans share an identical cycle length, so an intersection with integrated waiting areas can be operated continuously. Figure 3: Typical layout of the partial integrated waiting areas. (**a**) With exclusive lanes for through and right-turn; (**b**) With exclusive lanes for left and right-turn; (**c**) With exclusive lanes for through, left and right-turn; (**d**) With an exclusive lane for right-turn. Two phases are employed for pre-signals with the first phase for through vehicles and the second for left-turn vehicles. The signal timing strategies for the main intersection is also illustrated in Figure 4. Left-turn indication for approaches follows a through indication. During the first phase, the upstream pre-signals provide a green indication for the through movement at NS and EW approaches. Through movement vehicles proceed downstream distributing to all available lanes in the integrated waiting areas. Meanwhile, right-turn vehicles proceed to the rightmost lane in the integrated waiting areas as shown in Figure 2b. Then the right-turn vehicles will pass through the intersection under the give-way rules. The reason for providing a green indication for the EW through movement when the main signal provides the green indication for the NS through movement is to leave more time for vehicles to enter the integrated waiting areas. The downstream signal at the main intersection, afterwards, provides a green indication for the through movement of all available lanes at the WB and EB approaches. During this phase, left-turn vehicles are held upstream by the pre-signal for those lanes. Phase 2 for pre-signal is for left-turn movements. Through movement vehicles are held at the pre-signal while left-turn vehicles distribute to all available lanes and right-turn vehicles proceed to the rightmost lane in the integrated areas at the WB and EB approaches, where the left-turn vehicles receive a circular green indication at the downstream signal to pass through the intersection and right-turn vehicles pass through the intersection under the give-way rules. Each phase requires an all-red time that is long enough to clear the integrated waiting areas. Accordingly, it is important to understand how to coordinate between the pre-signal and main signal at the intersection. The main and pre-signal coordinated control method should be adopted for the intersection with integrated waiting areas. Figure 4 displays the phase and sequence of the signal at a typical cross intersection with integrated waiting areas. Residual vehicles in the integrated waiting areas pose potential safety concerns.