Rises in the number of transit buses, bus routes, and overall traffic volume in China’s cities, coupled with interference from other transport modes, such as taxis loading and unloading passengers nearby, have led to increasing traffic delays at bus stops, which is considered one of the factors degrading service levels and traffic operations on urban roadways. This paper studies traffic characteristics at bus stops, investigates variations in delay from different types or designs of bus stops, and analyzes the impact of it on traffic capacity, the purpose of which is to propose a solution to predicting the feasibility of an integrated design of bus stops and taxi stands with the help of mathematical models and based on the objectives of optimal traffic operations and passenger transfer.

Transit buses and taxis are an integral part of the urban public transport system. Bus transport is characterized by its high passenger capacity, high efficiency, low per-passenger road use, and low environmental impact and is seen as an important measure for alleviating urban traffic congestions. Taxis convey passengers between locations of their choice, offering convenience, speed, and more flexible services. This differs from other modes of public transport where the pick-up and drop-off locations are determined by the service provider and is favored by short-distance passengers [

Taxis pulling over and picking up passengers is one of the main causes of delay on urban roadways with high traffic volume, especially in sections near bus stops where passenger transfers occur [

Many researchers have been conducted on the planning and designing of transit bus stops; however, the same cannot be said about taxi stands. Taxi transport has no fixed routes and it follows a random pattern of vehicle arrival, making it very difficult to plan and design taxi stands that are applicable universally or over a large area. In addition, as transit bus transport often put the greatest emphasis over other modes of public transport when it comes to developing a city-wide public transport system, the conventional approach is so that services like taxis should not affect bus operations, which suggests that a taxi stand should be positioned near a bus stop rather than between two adjacent bus stops on the same route, which would lead to more blockages and longer delays for buses [

An integrated design of bus stop and taxi stand, which will be referred to as “a bus and taxi stop” hereon, can help introduce more ways to regulate taxi service, reduce delays to buses, and also provide a better transfer experience for passengers.

The flow of traffic is a complex process influenced by a number of random factors. The arrival of vehicles is a random process. There are two ways of describing vehicle arrival in probability: (1) discrete distributions, which are used to study the volatility of traffic in a certain time period, and (2) continuous distributions, with focus on traffic characteristics such as speed, time, and distance.

Transit buses and taxis are different from other modes of transport in that changes in traffic volume are not significant between peak and off-peak hours, and the vehicle arrival is a random process. Therefore, we can use the Poisson distribution to describe the number of buses and taxis arriving in a given time interval [

The basic formula for the Poisson distribution is as follows:

The bus arrivals obey the Poisson distribution with arrival rate

In an integrated bus and taxi stop design, buses and taxis arrive at the stop according to Poisson distribution [

The general queuing service system (Figure

The queuing service system.

The queuing system for standing vehicles belongs to the

the probability of zero vehicles waiting in the system

the probability of

the average number of vehicles in the system

the average queuing length

the average consumption during the queuing time

the average waiting time in the queue

If the integrated stop can accommodate more than one parked vehicle at the a time, allowing multiple service channels, then the queuing system is called a “multichannel service” system, also known as an

A single line in a multichannel service or

the probability of zero vehicles in the system

the probability of

the average number of vehicles in the system

the average queue length

the average consumption during the queuing time

the average waiting time in the queue

We can tell whether the integrated stop is valid based on the number of vehicles and the length of the queue in the system, which requires the number of queuing vehicles (standard vehicles) to be no more than

In this case, it is convenient for passengers to transfer and will not cause interference to bus operations.

If the probability is high because there are more than

Distance between bus stop and taxi stand.

Both the bus stop and the taxi stand need to “shelter” the parked vehicles (Figure

Lengths of the stop.

A single vehicle’s parking length

As there is no fixed schedule for taxi operations, taxis should have only a short parking time at the stop. Therefore, the length of the taxi stand should be only long enough to serve just one taxi at a time, which is about 4 m.

The length calculated by the above formula agrees with actual lengths at taxi stands.

We studied the section of People’s Road between Chongqing Road and Beian Road in the city of Changchun China, which is a 306 m long two-way road with eight lanes. Being one of the main traffic ways in a central business district, it is crowded with pedestrians and taxi operations, both of which lead to significant delays to buses. There are 12 bus routes operating from the south to the north, 8 of which load and unload passengers in this section of road.

The arrival rate for buses is 62 pcu/h in this direction and 12 for taxis, both following Poisson distributions. In one hour, we observed 242 people boarding buses and 302 people alighting. The numbers are 28 ad 36 for taxis. We assume it takes 7 seconds on average for a person to board or alight a bus and 15 seconds to board or alight a taxi.

Assuming that the traffic remains the same for the integrated stop, the arrival rate of the system is

The stop can accommodate three buses (six standard vehicles) at a time, making the service intensity

Here, we assume that the integrated stop can accommodate eight standard vehicles at most at any moment. The probability of their being more than eight standard cars can be calculated as follows:

Thus,

This calculation shows that the probability of their being more than eight standard vehicles queuing is high. Thus, the taxis have a greater impact on the operations of the buses, and we cannot merge the taxi stand into the bus stop directly. Instead, we need to set up a taxi stand around 50 m ahead of the bus stop.

This paper introduced a model-based approach to study the feasibility of having an integrated design to reduce delays to buses from taxi transport by determining whether an integrated single stop design is plausible to serve both buses and taxis at the same time and used vehicle arrival, probability distributions, and queuing theory to look into the traffic characteristics at bus stops. We first analyzed the current traffic operations and then described bus and taxi traffic characteristics according to the appropriate traffic flow models. This paper agrees that the arrival of buses and taxis can be described with Poisson distribution and it abstracts the process of vehicles getting into the stop as a queuing model system. In doing so, the probability of queuing vehicles in the system can be calculated. Finally we applied the models on a real road and discussed the potential traffic conditions of redesigning the bus stops along that road. In future follow-up studies, the authors would like to look into more types of arrivals and a variety of queuing service systems with hopes to future improve the method and models.

The authors declare that there is no conflict of interests regarding the publication of this paper.