Flexible transit services, which bring together the characteristics of fixed-route transit and demand-responsive transit, have been proven to be cost-efficient in low-density residential areas. In this paper, a methodology is proposed to assist planners in making better decisions when choosing between route deviation policy and point deviation policy, which are two promising types of flexible transit services. A user cost function is developed to measure the service quality of the transit systems, and analytical models are constructed to compare the system performance under both expected and unexpected demand levels. Based on the experiments for various scenarios over a real-life transit example, the critical demands, which represent the switching point between the two competing service policies, have been derived. Our findings show that point deviation policy is more efficient at low-demand levels, while route deviation policy is a better choice at low-to-moderate demand levels. At unexpectedly high demand levels, route deviation policy is better able to accommodate rejected passengers than point deviation policy.
With the acceleration of urbanization in recent decades, an increasing number of suburban areas with low population density have arisen. The increasing dispersion of population results in a low degree of resource sharing for traditional fixed-route transit, which has a rigid route and schedule structure. Demand-responsive transit, which can provide much of the desired flexibility with curb-to-curb services, is considered costly to deploy and is therefore mostly limited to specialized operations such as paratransit for people with reduced mobility [
To address these issues, researchers and practitioners seek to introduce flexible transit services to meet the needs of new travel patterns in suburban and rural areas. All these flexible transit systems combine the efficiency of fixed-route transit with the flexibility of demand-responsive transit. They are regarded as fixed-route services in that they have a set of stops with predetermined schedules. On the other hand, they are considered as demand-responsive systems because passengers can ask for service at optional locations. Previous works based on actual operational data have shown that flexible transit services are more cost-efficient than pure demand-responsive transit [
Based on the investigation by Koffman [
According to a survey by Potts et al. [
Most of these studies revealed that flexible transit services are promising operating policies for shaping new travel patterns in low-demand areas and passengers are generally willing to use these innovative transit systems [
In this paper, we present a methodology to assist decision makers in choosing between route deviation and point deviation policies. Analytical models are developed to evaluate the system performance of two competing services. Using the analytical models, the critical demand, in which the two transit services have the same performance, can be identified, and the reliabilities of the two systems are further discussed. Our work serves as a meaningful step towards selecting between flexible transit services in areas with low and fluctuating travel demand.
Route deviation and point deviation policies differ in terms of degree of flexibility. More specifically, the route deviation systems are much more constrained than those allowed for point deviation; they must operate along a well-defined path and deviate to serve curb-to-curb requests within a service area around the path [
Although route deviation has been the most popular type of flexible transit services [
Most previous studies are conducted in operating environments with expected and predictable demand. Only a very limited number of studies focus on the uncertainty of travel demand in low-demand areas. Qiu et al. [
In this paper, we aim to investigate and establish the conditions that are fit for the implementation of route deviation or point deviation policy. The system performances are compared not only at expected demand levels, but also at unexpected demand levels to test the reliability of the two transit services. To our knowledge, this paper is the first to develop a methodology for solving this problem.
The service area in our study represents a residential community and is modeled as a rectangle of width
Route deviation operating policy.
Point deviation operating policy.
In general, the number of transit lines passing by the connection centers is very high; therefore, the temporal demand distribution at the connection centers is assumed to follow a Poisson distribution. It is also reasonable to assume that the trip origins and destinations outside checkpoints are uniformly and independently distributed in the service area according to a homogeneous spatial Poisson process. There are three main types of passengers in the service area with proportions of Type I: pick up and drop off both at checkpoints. Type II: pick up at checkpoints, and drop off not at checkpoints. Type III: pick up not at checkpoints, and drop off at checkpoints.
To compare the performance of the two flexible transit systems, both route deviation policy and point policy are implemented with the same fleet size
As shown in Figure
The slack time for route deviation service is allotted based on the expected demand levels of the flag requests and curb-to-curb requests. A no-rejection policy is applied for flag requests as the variation of travel demand has limited impact on the service cycle. The deviation service operates on a first come, first available basis. When the slack time is unable to accommodate the actual demand, some of the curb-to-curb customers who reserve later must be rejected due to the slack time limitation.
As another kind of flexible transit operating policy, service vehicles in point deviation system are not constrained to follow any predefined base route. Except for the time constraints of the checkpoints, the remainder of the service is demand-responsive and vehicles serve curb-to-curb requests within the service area (see Figure
Given that the path between the scheduled stops might change in each ride, flag requests are not possible. Instead, all types II and III passengers are required to make reservations to schedule their noncheckpoint stops through smartphones or the Internet. Similar to route deviation system, there is also a predefined slack time based on the expected demand level. Accepted curb-to-curb requests have no walking in their trip. If the actual demand exceeds the expected demand level, rejections may occur for curb-to-curb passengers.
In our study, passengers are assumed to be transit-dependent. Vehicle follows a rectilinear metric, which has been proven to be a good approximation of reality [
In practice, the actual travel demand frequently deviates from the expected demand level in low-demand service areas due to uncertainties (see Figure
Uncertainties in travel demand.
There is no designed idle time between trips, and we keep the same fleet under different transit policies. If we disregard the difference in complexity of the reservation and scheduling systems, which only account for a small fraction of long-term transit operation, the two transit policies are considered have the same operating cost. Thus, in our analysis, the performance measure of the transit system is defined as the user cost function
For route deviation service, we assume the proportions of the curb-to-curb type II and type III passengers are
At the expect demand level, all curb-to-curb requests can be accepted. The expected vertical distance between the base route and the request stops (see Figure
Assuming a vehicle serves
In route deviation service, another two relationships can be obtained:
Combining (
In the system, type I passengers do not walk as part of their trips (
Thus, the expected walking time per passenger is
The headway of route deviation system is
Curb-to-curb type III passengers can receive a scheduled pick-up time from the system when they make advanced notice. They are more likely to spend their time at their house or comfortable locations instead of waiting outside before the scheduled pick-up time. Therefore, their waiting time is defined as the interval between the scheduled pick-up time and the actual pick-up time. The waiting time for a curb-to-curb type III passenger
Thus, the expected waiting time per passenger is
Type I passengers travel from one terminal to another, so their expected riding time is
Types II and III passengers can be dropped off or picked up uniformly anytime in the trip between two terminals, and their expected riding time can be expressed as
Then, the expected riding time per passenger is
When
For each ride, the actual served passengers can be expressed as
The expected waiting time of curb-to-curb type III passengers can be obtained by replacing
At unexpectedly low-demand levels, there will be idle time at the terminal checkpoints. The expected riding times of different types of passengers can be obtained as follows:
Thus, the expected riding time per passenger at unexpectedly low-demand levels can be expressed as
When the actual demand exceeds the service capacity of deviation services, some of the curb-to-curb requests have to be rejected due to slack time limitation. These rejected customers may need to wait more than one operating cycle before pick-up. However, waiting for the next available vehicle makes it difficult for the rejected passengers to follow their schedules. Thus, we assume that rejected curb-to-curb passengers become flag request passengers for desired transit service.
When
We define
Because of the no-rejection policy, the last
At unexpectedly high demand levels, the expected waiting of the type I, type II, and flag request type III passengers can be calculated by replacing
Thus, the expected waiting time of all passengers is
Similarly, the expected riding time of type I passengers is
For point deviation service, a “no-backtracking constraint policy” is applied, which forbids backward movements of the service vehicles; therefore, passengers are served in order of horizontal coordinates [
At the expected demand level, we assume an ideal case in which no rejection occurs (
Similar to the previous analytical method for point deviation service, the following relationships can be obtained:
Combining (
The expected waiting time of different types of passenger can be expressed as
Thus, the expected value of waiting time per passenger is
Just as in the route deviation service, the expected riding time of type I passengers is
If
As the actual demand is lower than expected, the vehicle will arrive earlier than the schedule arrival time. The expected riding times of different types of passengers are
Thus, the expected riding time per passenger at unexpectedly low-demand levels can be expressed as
Unlike route deviation service, in point deviation service, the rejected passengers cannot issue a flag request since there is no base route for the service. Therefore, we assume that rejected customers utilize the nearest checkpoint for transit. Generally, curb-to-curb passengers are required to request service at least two hours in advance. Thus, the rejected passengers are considered to have sufficient time to reach the checkpoint before pick up.
For the last
Thus, the expected walking time per passenger can be expressed as
For the last
We define
Similarly, in the last
We can observe that the expected riding time of the
In this section, a case study is conducted based the Route 289 service in the suburban area of Zhengzhou City in China which currently operates under a pure flag stop policy [
Parameter values.
| |
---|---|
| 3 miles |
| 1 miles |
| 1 |
| 25 miles/h |
| 3 miles/h |
| 12 sec |
| 15 sec |
| 0.2/0.4/0.4 |
At the expected demand levels, the passenger cost indicators from the analytical models of both route deviation policy and point deviation policy are presented in Tables
Passenger cost indicators in route deviation service (
| | ||||||
---|---|---|---|---|---|---|---|
26 | 30 | 34 | 38 | 42 | 46 | 50 | |
| 8.38 | 8.54 | 8.71 | 8.89 | 9.08 | 9.27 | 9.47 |
| 3.60 | 3.60 | 3.60 | 3.60 | 3.60 | 3.60 | 3.60 |
| 8.04 | 8.20 | 8.37 | 8.54 | 8.72 | 8.91 | 9.11 |
| 5.03 | 5.13 | 5.23 | 5.33 | 5.45 | 5.56 | 5.68 |
| 20.27 | 20.53 | 20.80 | 21.08 | 21.37 | 21.67 | 21.99 |
Passenger cost indicators in point deviation service.
| | ||||||
---|---|---|---|---|---|---|---|
26 | 30 | 34 | 38 | 42 | 46 | 50 | |
| 12.02 | 13.08 | 14.36 | 15.91 | 17.84 | 20.30 | 23.55 |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 7.53 | 8.27 | 9.17 | 10.25 | 11.60 | 13.33 | 15.60 |
| 7.21 | 7.85 | 8.62 | 9.55 | 10.70 | 12.18 | 14.13 |
| 14.73 | 16.12 | 17.78 | 19.80 | 22.31 | 25.51 | 29.73 |
To test the influence of the curb-to-curb passengers' proportions, the user cost functions with different
Comparison of system performance at the expected demand levels.
The above results confirm that, in the designed demand range, point deviation service is desirable at low-demand levels. The difference in system performance narrows between the two policies with the increasing demand. Route deviation service is more suitable for the relatively higher demand levels. With an increase in the proportion of curb-to-curb passengers, route deviation service becomes more flexible but more sensitive to the demand. When this proportion is considerably large, point deviation service always performs better than route deviation service.
To test the reliability of the two transit services, the system performance at unexpected demand levels is presented in Figure
Comparison of system performance at unexpected demand levels.
However, at unexpectedly high demand levels, the user cost of point deviation service surges with increasing actual demand
Based on these observations, we can conclude that route deviation service is more reliable than point deviation service and is more suitable to apply in the service areas with great demand variations.
Sensitivity analysis is conducted under both expected and unexpected demand levels to examine how the performance of the two competing transit polices is affected by key input parameters. The results are presented in Figure
Sensitivity analysis for different parameters.
At expected demand (
At unexpected demand (
At expected demand (
At unexpected demand (
At expected demand (
At unexpected demand (
At expected demand (
At unexpected demand (
Another experiment with a long length (
In real-life cases, the permitted deviation ranges from 0.25 to 1.5 miles [
Furthermore, a two-vehicle case (
This paper helps planners to select the most appropriate flexible transit services in low-demand areas. Route deviation service and point deviation service are chosen as typical flexible policies in this study. The former is the most widely used in practice, while the latter has been extensively investigated by researchers.
The two flexible systems differ in operation rules and degree of flexibility offered. Generally, route deviations systems are much more constrained than those allowed for point deviation systems. By modeling a real-life transit service, we compare the system performance of the two competing transit policies under both expected and unexpected demands. The results suggest that point deviation policy is preferable at low-demand levels and that route deviation policy is better at low-to-moderate demand levels. When the proportion of on-demand requests is considerably large, route deviation is not preferred even at relatively high demand. Route deviation policy is considered to be more reliable because the rejected curb-to-curb customers can still get access to transit with a shorter walking distance. In contrast, point deviation policy might not be suitable when the demand in the service area fluctuates significantly.
In practical use, point deviation service is more complex to implement than route deviation service because it requires a more sophisticated navigation and scheduling system. In addition, the travel time between checkpoints is more difficult to determine in point deviation service since the path might change for each ride. These difficulties explain why this promising operating policy has been applied by only a small percentage of transit agencies compared to route deviation policy. Therefore, an automated dispatch system with high navigation accuracy and an imbedded routing algorithm are needed to promote the widespread use of point deviation service. For future study, we plan to develop simulation models to reproduce the operation of these two competing service types more accurately considering the vehicle capacity and passengers’ travel mode choice. Another possible research direction is to compare other kinds of flexible transit policies and define their application conditions.
The data used to support the findings of this study are available from the corresponding author upon request.
This paper is an extended version of paper “Flexible Transit Services Choosing between Route Deviation and Point Deviation Policy” presented in 2018 TRB Annual Meeting.
The authors declare that they have no conflicts of interest.
The research reported in this paper was supported by the National Natural Science Foundation of China (Grant no. 61573098).