Journal of Sensors

Volume 2017 (2017), Article ID 1321237, 8 pages

https://doi.org/10.1155/2017/1321237

## Operating Time Division for a Bus Route Based on the Recovery of GPS Data

School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China

Correspondence should be addressed to Yang Cao

Received 24 April 2017; Revised 22 June 2017; Accepted 11 July 2017; Published 14 August 2017

Academic Editor: Xiaolei Ma

Copyright © 2017 Jian Wang and Yang Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Bus travel time is an important source of data for time of day partition of the bus route. However, in practice, a bus driver may deliberately speed up or slow down on route so as to follow the predetermined timetable. The raw GPS data collected by the GPS device equipped on the bus, as a result, cannot reflect its real operating conditions. To address this concern, this study first develops a method to identify whether there is deliberate speed-up or slow-down movement of a bus. Building upon the relationships between the intersection delay, link travel time, and traffic flow, a recovery method is established for calculating the real bus travel time. Using the dwell time at each stop and the recovered travel time between each of them as the division indexes, a sequential clustering-based time of day partition method is proposed. The effectiveness of the developed method is demonstrated using the data of bus route 63 in Harbin, China. Results show that the partition method can help bus enterprises to design reasonable time of day intervals and significantly improve their level of service.

#### 1. Introduction

A well-designed bus schedule scheme is important for increasing bus transit ridership [1]. Bus passenger demand differs greatly at different time intervals during the everyday operation. Before the overall design of a bus schedule scheme, the operating time of a bus route should be divided into multiple time intervals for which different schedule schemes should be made. This greatly helps formulate precise operating and dispatching schemes for buses and reduce the operational costs of a bus transit enterprise.

In recent years, buses in a number of large cities in China have been equipped with GPS devices [2–5]. Bus enterprises can now directly retrieve the bus travel time between any two stops from this database. However, given the predetermined timetables, the travel time may not reflect the actual performance of a bus. When faced with traffic jams, a bus driver may deliberately accelerate if the bus is to arrive at a downstream stop no later than the scheduled time. Although it may manage to arrive on time, the bus typically undergoes frequent acceleration and deceleration enroute which not only reduces the comfort of passengers but also increases the probability of traffic accidents. In contrast, the bus driver may deliberately slow down in smooth traffic so as to avoid early arrival at the downstream stop. Consequently, the lowered travel speed may leave the passengers with the impression that the bus service is inefficient. These two kinds of drivers’ behavior are common in China [6, 7]. The root cause is that the initial timetables are usually nonoptimal considering the real-time traffic conditions. Therefore, the retrieved GPS data cannot be used directly. To obtain the actual travel speed and to further divide the operating time, the effect of drivers’ behavior should be considered.

Scholars have conducted much research on the optimization of bus schedule schemes but have rarely investigated the division of the operating time [8–11]. To evaluate the effectiveness of a bus schedule scheme, Patnaik et al. [12] selected as indexes the numbers of passengers boarding and alighting the bus and the number of midway stops. The buses from the starting stop were then divided into several classes. The data used to develop the models were collected by the Automatic Passenger Counters (APC) on buses operated by a transit agency in the northeast region of the United States. Guihaire and Hao [13] presented a global review of the crucial strategic and tactical steps of transit planning: the design and schedule of the network. They pointed out that the bus operating period mainly depended on the passengers’ requirements which were different at different times. However, no analytic method has been developed for time of day partition. Using ridership data from a bus smart card system, Yue [14] obtained an ordered sampling of the passengers’ arrival ratio curve and divided the operating time into multiple intervals using the Fisher optimal segmentation method. In his model, only the passenger volume was considered and the bus travel speed was neglected. As a result, the bus operating conditions were not fully considered during the partition. Shen et al. [15] proposed an improved -means clustering algorithm for the division of the bus operating period based on GPS data. However, only the bus travel speed was used and the passenger demand was not considered. Given that, in different time intervals, a transit agency tends to arrange different bus dispatching frequencies because of the different passenger demand, this study becomes less practically promising. Bie et al. [16] selected the dwell time at each stop and the travel time between each pair of them as indexes and developed a rapid division algorithm. This is the first study that considers both the bus travel speed and the passenger demand in time of day partition. However, the GPS data were used directly without considering the deliberate speed-up or slow-down movement.

The existing methods for operating time division exhibit two shortcomings: (i) only the passenger flow volume is taken into account and (ii) data are obtained typically through manual work which consumes much manpower and many other resources. The method proposed in this study builds the relationship between time division and bus schedule scheme and successfully addresses these shortcomings.

The contributions of this study are twofold. Firstly, we develop a method to identify whether there is deliberate speed-up or slow-down movement of a bus. A recovery method is then established for calculating the real bus travel time based on raw GPS data. To the best of our knowledge, no research so far has investigated this kind of problem. Secondly, a sequential clustering algorithm is developed to partition the operating period into multiple intervals based on the recovered bus travel time and dwell time at stops.

The structure of this paper is organized as follows. In Section 2, a recognition method for bus operating state is first developed followed by a recovery method for the bus travel time. A discussion is provided as to why the recovery travel time and dwell time are selected as division indexes. In Section 3, a sequential sample clustering algorithm is proposed to divide the operating time into multiple time intervals using the recovered travel time and dwell time. Section 4 presents a real case study and Section 5 concludes the paper.

#### 2. Development of the Operating Time Division Method

##### 2.1. Recognition of the Bus Operating State

In this paper, unless stated otherwise, all time is measured in units of seconds. Let us assume that a bus passes stops in total during an operating period . According to its timetable, the planned travel time of bus from the th stop to the th stop is denoted as . The planned operating time can be written as follows:

When traveling along a route, a bus usually passes through three different kinds of regions, namely, stops, road sections, and intersections. Therefore, the planned travel time of bus from the th stop to the th stop can be further divided as follows:where denotes the travel time spent at road sections, denotes the travel time spent at intersections, and denotes the travel time spent at bus stops.

, , and can be extracted from GPS data in combination with a geographic information system (GIS) map. The actual travel time of the bus from the th stop to the th stop, denoted as , can be rewritten as follows:

*(**1) Recognition of a Driver’s Deliberate Acceleration.* Theoretically, the bus travel time at road sections and intersections increases under traffic jams.

At intersections, bus drivers tend to reduce speed because of the queuing vehicles and the restriction of changing lanes. However, a driver can frequently accelerate and decelerate at road sections to reduce the travel time and to ensure punctual arrivals at the downstream stops.

*Case 1. *

In Case , although a bus may be delayed at intersections, it still arrives at the downstream stops on time due to deliberate acceleration at road sections.

*Case 2. *

In Case , although the driver may deliberately speed up the bus, it does not arrive on time at the downstream stops.

*Case 3. *

In Case , the increase in the bus travel time at road sections exceeds or equals the total increase in the travel time spent at intersections and in the dwell time at stops. The bus may run normally or undergo deliberate acceleration.

*(**2) Recognition of a Driver’s Deliberate Deceleration.* When the traffic volume is low, the bus travel times at road sections and intersections may decline.

Theoretically, if the timetable is not optimized in real time, the driver may deliberately slow down the bus to enable punctual arrivals according to the schedule.

*Case 1. *

In Case , although the bus is slightly delayed at intersections, it still arrives at the downstream stops on time, since the driver deliberately slows down the bus.

*Case 2. *

In Case , although the drive deliberately slows down the bus at road sections, the bus still arrives at the downstream stops ahead of the scheduled time.

*Case 3. *

In Case , the decrease in the bus travel time at road sections exceeds or equals the total decrease in the travel time spent at intersections and in the dwell time at stops. The bus may run normally or undergo deliberate deceleration.

##### 2.2. Recovery of the Optimal Travel Time on the Road

When a driver’s deliberate acceleration or deceleration is recognized as discussed in Section 2.1, the retrieved GPS data cannot be directly used for the optimization of the schedule scheme. This effect should be considered for recovering the optimal bus travel time on the road.

The delay time of a bus at an intersection can be calculated by subtracting the travel time at a preset speed from the travel time spent at an intersection. During the operating period, , a number of buses pass through the intersection and their average delay can be directly calculated. Assuming that denotes the average delay at the timetable’s initial operation stage, the traffic conditions will change after a certain period of time, and the average delay will become .

Generally speaking, the traffic flow on a road increases/decreases as a result of an increase/decrease in traffic flow at the adjacent intersection. According to the theory of traffic engineering, the travel time spent at a road section or at an intersection is directly proportional to the traffic flow. At a signalized intersection, the average delay can be calculated by the following [17].where , , and denote the green ratio, degree of saturation, and traffic capacity, respectively, of the phase for bus .* T *denotes the length of the analysis period and is generally set at 0.25 h.where and denote the ratios of the arrival and saturation flows of the entrance lane for bus , respectively.

For bus , when the average delay changes from to while the other variables remain unchanged, the variation ratio of the flow at the entrance lane can be derived according to (12)-(13). Since denotes the ratio of the flow after a certain period of time to the original one, can also denote the variation ratio of traffic flow which will be used for recovering the optimal travel time of the bus on the road.

Through field observations, a relationship is shown to exist between the average speed of traffic on urban roads and the flow. At low traffic flow, speed is insensitive to the increase in flow and only decreases slightly. When the flow increases and is close to the capacity of the road, the speed decreases significantly. When the flow is lower than the capacity of the road, the average speed varies with the flow in an approximate linear fashion:where denotes the flow in pcu/h of the road section, denotes the average speed of the traffic flow in km/h, and and are constants to be determined.

According to the characteristics of traffic flow, when free-flow speed occurs, the traffic flow equals 0 (). When the speed equals the optimal value , the traffic flow reaches the maximum and the saturation flow ratio is achieved. Therefore, the following equations hold:

By calculation, we can get , .

Assuming that the flow changes to after the bus dispatching scheme is executed for a certain period of time, the average travel speed of the bus can be calculated by

Defining /, the following expressions can be obtained:

Let denote the average travel time of the bus from the th to the th stop within the operating time period at the timetable’s initial operation stage. The optimal travel speed after a certain period of time becomes which denotes the recovered average speed from the th to the th stop.

is the most important parameter which plays a decisive role in the travel time recovery process. Figure 1 illustrates the overall process for calculating .