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This manuscript investigated coordinated intersection signal design problem for mixed traffic flow of Human-Driven Vehicles (HDVs) and Connected and Autonomous Vehicles (CAVs). Two main macroscopic impact of the mixed flow on signal setting are considered: saturation flow rate and the platoon dispersion. In order to capture the traffic flow operational characteristics on coordinated intersections, three locations, namely entrance location where the loop detector was located at, and upstream intersection and downstream intersection were defined. Two types of vehicle cumulative curves, namely cumulative arrival profile and cumulative departure profile were constructed. The mixed-flow traffic dynamics were analyzed, and the arrival-departure curves relationship was derived using a combination of Newell car-following and Akçelik acceleration model. A mixed-flow platoon dispersion model was proposed to describe the vehicle's progression between two locations. Due to the nonlinear nature of the problem, a particle swarm optimization (PSO) method was employed to obtain the optimal signal parameters, including the cycle length, green duration, and optimal offset. The algorithm was implemented and validated in a case study involving two intersections, with the demand formulated and simulated by the Markov chain. The results showed that the proposed model could effectively decrease delays when compared with current signal control methods. INDEX TERMS Coordinated signal control, connected and autonomous vehicles, cumulative curves, platoon dispersion, traffic flow modeling.

the dispatcher (or fleet operator) dictates which taxi picks up a given customer, and sometimes which route is to be used if dispatching is based on a geographic information system. Therefore, a taxi driver's personal routing objective usually is not put into effect in a dispatch market. In a cab stand and street hail market, taxi drivers are autonomous decision makers and decide where to go and which routes to take.The routing objectives of a taxi driver vary depending on the taxi's occupancy. If a taxi is occupied by customers, then a leastcost path is usually sought. Several paradigms in the literature are directly related to such a routing objective (2, 5-7). What is not well understood is a taxi driver's route choice behavior when a taxi is vacant, in which case the driver's behavior is likely to be driven by an objective different from minimal travel time. It is intuitive to assume that an occupied taxi driver seeks to arrive at the destination in the least amount of time or distance as expected or required by the customer. (This study does not consider customers who hail a taxi for sightseeing or drivers who seek to increase a fare by traveling the long way to the destination.) If a taxi is vacant, the usual objective is to minimize the elapsed time until the next customer is picked up (search time), and the decision to be made is which downstream link to run at each intersection. If a taxi starts from a link where the driver is aware of the low probability of getting customers (e.g., the taxi drops off a customer at a location where returning, or ongoing, customers are few at the time), the driver will intend to make his way to a location where he knows the customer arrival rate may be high. The driver knows the general direction to go in but is still making local route choice decisions and remaining on the lookout for customers while moving toward that high-probability area.It is assumed that (a) a taxi driver wants to maximize her chance of reaching a customer when she makes a turning decision at an intersection, (b) the outcomes of past trials form the driver's experiences and belief about customer availability for specific geographic areas at given time periods, (c) such an experience or a belief affects the routing decision, and (d) the experience or belief will be updated regularly by outcomes of new trials. The presented research proposes a probabilistic dynamic programming model for routing vacant taxis that is based on these behavior propositions.Both analytical derivation and numerical analysis are conducted on a hypothetical network inspired by the traffic network structure in the city of Taipei, Taiwan. The outcome of this study shows that the proposed methods offer a promising modeling framework for capturing the routing behavior of drivers of vacant taxis. The study sheds light on modeling of routing decisions of taxi drivers, which is critical for developing strategies such as path-based traffic simulation and origin-destination estimation in a region with a high percentage of taxi traffic....