# A Bicycle Origin–Destination Matrix Estimation Based on a Two-Stage Procedure

## Abstract

**:**

## 1. Introduction

## 2. A Two-Stage Bicycle O–D Estimation

#### 2.1. Stage 1: Generation of a Primary Bicycle O–D Matrix

**Step 1.**Estimation of zonal productions and zonal attractions using existing planning data;**Step 2.**Estimation of a primary O–D matrix in the gravity model.

- T
_{ij}= Number of trips produced between zone i and zone j - P
_{i}= Number of trips produced in zone i - A
_{j}= Number of trips attracted to zone j - F
_{ij}= An empirically derived “friction factor,” which expresses the average area-wide effect of spatial separation on the trip interchanges between the two zones, i and j - K
_{i}, K_{j}= Empirically derived origin and destination adjustment factor in zone i and zone j

_{ij}, K

_{i}, and K

_{j}, but it is usually time-consuming [35]. In addition, the calibration process requires many factors, which is not established from travel surveys. In Stage 2, we introduce the alternative method, which is the refinement of the primary matrix.

#### 2.2. Stage 2: Bicycle O–D Matrix Refinemnet

#### 2.3. Route Generation in Stage 2

#### 2.3.1. Route Distance

#### 2.3.2. Bicycle Level of Service (BLOS)

#### 2.3.3. Bi-Objective Shortest Path

#### 2.4. Bicycle O–D Demand Adjustment Using Path Flow Estimator (PFE)

- ${f}_{k}^{rs}$ = Bicycle flow on route k connecting O–D pair rs
- ${U}_{k}^{rs}$ = Utility route k connecting O–D pair rs
- $P{S}_{k}^{rs}$ = Path-size factor on route k connecting O–D pair rs
- ${x}_{a}$ = Observed bicycle count on link a
- ${v}_{a}$ = Estimated bicycle flow on link a
- ${\mathsf{\epsilon}}_{a}$ = Percentage error of the bicycle count on link a
- ${P}_{r}$ and ${A}_{s}$ = Bicycle trip productions and bicycle trip attractions obtained from census data in origin r and destination s, respectively
- ${O}_{r}$ and ${D}_{s}$ = Refined bicycle trip productions and refined bicycle trip attraction in origin r and destination s, respectively
- ${\epsilon}_{r}$ and ${\epsilon}_{s}$ = Error bounds allowed for trip productions and trip attractions in origin r and destination s, respectively
- ${z}_{rs}$ = Target O–D flows connecting O–D pair rs, which are initially estimated bicycle O–D demand in Stage 1.
- ${q}_{rs}$ = Refined bicycle O–D flows connecting O–D pair rs
- ${\epsilon}_{rs}$ = Percentage error bound for the target O–D demands connecting O–D pair r
- ${\delta}_{ka}^{rs}$ = Path-link indicator, 1 if link a is on path k connecting O–D pair rs and 0 otherwise.
- $\overline{\mathrm{A}}$ = Set of network links
- $\overline{\mathrm{R}}$ and $\overline{\mathrm{S}}$ = Sets of origin and destination zones
- $\overline{\mathrm{RS}}$ = Set of target O–D pairs

- $P{S}_{k}^{rs}$ = PS factor of path k connecting O–D pair rs
- l
_{a}= Length of link a - ${L}_{k}^{rs}$ = Length of path k connecting O–D pair rs

## 3. Numerical Results

#### 3.1. Stage 1: Generate a Primary O–D Demand

_{i}= K

_{j}= 1 for all zones).

#### 3.2. Stage 2: Refine the Primary Bicycle O–D Matrix with PFE

#### 3.2.1. Efficient Route Generation

#### 3.2.2. Link Counts Data

#### 3.2.3. Utility Parameters and Error Bounds of Observed Data

#### 3.3. Comparisons of Analysis Results

## 4. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Link flow difference pattern and absolute link flow difference using Path Size Logit-based Assignment (PSLA) and PFE.

Input Data | Error Bound |
---|---|

Bicycle counts | +/-30%: all observed links |

Zonal production flows | +/-30%: all observed zones |

Zonal attraction flows | +/-30%: all observed zones |

Target O–D demand | Error-free: if demands are between 0 and 5 +/-60%: if demands are between 5 and 30 +/-30%: if demands are higher than 30 |

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**MDPI and ACS Style**

Ryu, S.
A Bicycle Origin–Destination Matrix Estimation Based on a Two-Stage Procedure. *Sustainability* **2020**, *12*, 2951.
https://doi.org/10.3390/su12072951

**AMA Style**

Ryu S.
A Bicycle Origin–Destination Matrix Estimation Based on a Two-Stage Procedure. *Sustainability*. 2020; 12(7):2951.
https://doi.org/10.3390/su12072951

**Chicago/Turabian Style**

Ryu, Seungkyu.
2020. "A Bicycle Origin–Destination Matrix Estimation Based on a Two-Stage Procedure" *Sustainability* 12, no. 7: 2951.
https://doi.org/10.3390/su12072951