# A Framework to Determine the Utilization of Vacant Taxis on HOV Lanes with the Optimal Deployment
## 1 Introduction  
Taxis play a significant role in traffic systems since many travelers are willing to choose taxi mode due to the speediness, convenience, scarcity of parking, pricing, and door-to-door 24 h service. Numerous countries have regulated their own taxi market. For example, Belgium, Denmark, Germany, Japan, etc., have fare regulations, and Switzerland, Italy, Korea, and Romania have entry regulations in their own taxi markets for the benefits of this industry. Some studies have conducted research on regulatory policies to explore the effects [1; 2; 3]. However, little attention has been paid to the regulation that vacant taxis use HOV lanes. On one hand, vacant taxis belong to transit, which means they are qualified to enter HOV lanes. On the other hand, vacant taxis account for congestion externalities like regular vehicles, which implies that they are supposed to be forbidden from using HOV lanes. In recent years, taxi demand has become increasingly higher, with non-negligible impacts on traffic systems. Therefore, exploring the effects of the scheme that vacant taxis use HOV lanes is necessary. Abundant studies have been conducted in the field of the taxi market. In terms of an aggregated model, [PERSON] first dealt with taxi studies by modeling the taxicab market with scheduled fares and free entry [4]. [PERSON] proposed a model taking into account the travel and waiting time as physical variables for the optimization of taxi fleet size [5]. [PERSON] built the first structure model considering a uniform customer demand distribution and demonstrated the shadow cost of taxis, concluding that subsidization is necessary under the idea of the decentralization of the social optimum [6]. During the years from 1997 to 2010, [PERSON] and [PERSON] finished a series of work on the equilibrium of the taxi market. For instance, they provided a model to describe how vacant and occupied taxis cruise and serve customers at the urban level [7]. [PERSON] et al. considered traffic congestion and elastic demand in the model and proposed a method to calculate the waiting time [8]. [PERSON] et al. detected the consequences of externalities in different markets [9]. They concluded that in the competitive market the second-best solution brings a more efficient taxi utilization in the condition of high demand with a smaller fleet and higher fare [10]. [PERSON] et al. proposed a non-linear fare structure to explore the impacts on the taxi market [11]. This series of work widely extended the equilibrium model of the taxi market. In addition, [PERSON] et al. analyzed the economics of equilibrium properties of the taxi market, taking both bilateral taxi-customer search frictions and congestion externalities into consideration [12], and [PERSON] et al. detected the specific area design for taxi service [13]. With technological development, some studies detected the impacts from new technologies or new markets formed by new technologies on the taxi market. [PERSON] et al. proposed a model to describe the taxi market in the presence of an e-hailing application through a smartphone [14]. [PERSON] et al. evaluated the pricing scheme of an e-hailing platform [15]. [PERSON] proposed an empirical study of the impacts from the ride-sourcing market on the taxi market by collecting real data from Shenzhen city [16]. There is a tide of ride-sourcing market research caused by new technologies. Since the 1990s, HOV lanes have been implemented in many places around the world, such as the United States, Germany, Norway, Australia, and China, for the purpose of the alleviation of traffic congestion. Abundant studies have emerged investigating the impacts of HOV lanes on the efficiency, emission, and safety performance of traffic networks as well as the optimal design of HOV lanes. The results show that HOV lanes bring different effects in various situations. On one hand, HOV lanes show positive performance on routes and whole traffic networks [17; 18]. For example, [PERSON] et al.