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**Chapter 2 Optimal Combinations of Selected**

Tactics for Public-Transport

Transfer Synchronization

Published in:

Transportation Research Part C: Emerging Technologies. 48, 491-504.

(Nesheli and Ceder, 2014)

**Abstract**

Handling eﬃciently and eﬀectively real-time vehicle control is of major concern of public transport (PT) operators. One related problem is on how to reduce the uncertainty of simultaneous arrivals of two or more vehicles at a transfer point. Improper or lack of certain control actions leads to have missed transfers, one of the undesirable features of the PT service. Missed transfers result in increase of passenger waiting and travel times, and of passenger frustration. This work focuses on reducing the uncertainty of missed transfers by the use of control tactics in real-time operation. The developed model improves the PT service performance by optimally increasing the number of direct transfers and reducing the total passenger travel time. This model consists of two policies built upon a combination of two tactics: holding and skip-stop/segment, where a segment is a group of stops. The implementation of the concept is performed in two steps: optimization and simulation. The optimization searches for the best combination of operational tactics. The simulation serves as a validation of the optimal results under a stochastic framework. A case in Auckland, New Zealand is used. The results show that by applying the holding-skip stop, and holding-skip segment tactics the number of direct transfers are increased by about 100% and 150%, and the total passenger travel time is reduced by 2.14% and 4.1%, respectively, compared with the no-tactic scenario. The holding-skip segment tactic results with 47% more direct transfers than the holding-skip stop tactic for short headway operation.

**Introduction**

The lack of a prudent real-time transit control system is of major concern of public transport (PT) operators. Improper or lack of certain control actions leads to have missed transfers, one of the undesirable features of the PT service. Missed transfers results in increase of passenger waiting and travel times, and of passenger frustration.

A recent study by Ceder et al. (2013b) investigates how to use selected operational tactics in PT networks for increasing the actual occurrence of scheduled transfers. Their model determines the impact of instructing vehicles to either hold at or skip certain stops, on the total passenger travel time and the number of simultaneous transfers. While there is an extensive research conducted to analyze PT movements at a single control point, there are only a few analytical studies dealing with real-time control issues. Newell (1974) and Barnett (1974) demonstrate that a bus falling slightly behind schedule tends to pick up more passengers causing it to slow down until it eventually bunches with a trailing bus. Though the bunching could be eliminated to some extent by slowing down the trailing bus, this will lead to an increased travel time of the passengers onboard this bus.

Turnquist and Blume (1980), in a study on holding tactics, identify conditions under which those tactics are eﬀective. They implement a simple screening model to assess the eﬀectiveness of control policies. Their work focuses on measuring the headway variability and the proportion of total passengers who will be delayed as a result of a holding strategy. Li et al. (1992) focused on developing bus dispatching criteria at various stops. Based on proposed cost functions, a holding and stop skipping criterion is analyzed and optimized. They consider a single route, not taking into account transfers and transit centers. Their study shows that a tight stop skipping control strategy significantly increases the average waiting time, whereas the most critical decision variable is the holding control parameter. Generally speaking, and following Eberlein et al. (1999), control strategies can be divided into three categories: stop control, inter-stop control, and others. The first category contains two main classes of strategies which are known as holding and stop skipping. The second – includes speed control, traﬃc signal preemption, etc. The third – consists of strategies such as adding vehicles, splitting trains, and more. In a follow up study and as an inclusive analytical investigation in vehicle holding strategy Eberlein et al. (2001) formulate the holding problem as a deterministic quadratic program and develop an eﬃcient solution algorithm to solve it. At the same time Hickman (2001) presents a stochastic holding model at a given control station; a convex quadratic program with a single variable is formulated for corresponding to the time lapse during which buses are held. A following study by Sun and Hickman (2005) investigates the possibility of implementing a stop-skipping policy for operations control in a real-time manner. A non-linear integer programming problem for two diﬀerent stop-skipping policies is formulated to examine how the performance of the two policies changes with the variability of eﬀective parameters on the route.

Concerning new technologies, Dessouky et al. (2003) examines simulated systems in which holding and dispatching strategies are used. The dependence of system performance on new technologies is also investigated. They combined advanced PT systems with new technologies, such as AVL, APC and wireless communication, to accurately forecast the buses estimated arrival times and to use bus-holding strategies to coordinate transfers.

Strategies to increase eﬃciency of a high frequency PT route was studied by Daganzo (2009) who shows that without interventions, bus bunching is almost inevitable regardless of the driver’s or the passengers’ behavior. An adaptive control scheme was analyzed to mitigate the problem. The suggested model, dynamically determines bus holding times at routes control points based on real-time headway information.

Controlling methods using tactics is demonstrated by Hadas and Ceder (2008) in order to alleviate the uncertainty of simultaneous arrivals. They developed a new passenger-transfer concept which extends the commonly used single-point encounter (at a single transit stop) to a road-segment encounter (any point along the road-segment consti-tutes a possible encounter point). Their works has been extended for PT network connectivity in Hadas and Ceder (2010b). Furthermore, with the aid of operational tactics, Hadas and Ceder (2010a) improved optimal PT-service reliability via a dy-namic programming approach.

In the previous research by Ceder et al. (2013b) the potential of holding at stops and skipping certain individual stops is exhibited in a case study of Auckland, New Zealand. This work continues and refines the research of Ceder et al. (2013b) by introducing the possibility of skip-segment in additional to only skipping an individual stop, and for real-time operational control; the refinement takes place in the optimization formulation. That is, this work refers to three tactic scenarios: no-tactic case, holding and skip individual stops, and holding and skip segments. The objectives of work are to create simulation and optimization frameworks for optimally use the three scenarios and compare between the scenarios using a case study.

This work is organized as follows. Section 2.3 presents the model formulation and assump-tions. Section 2.4 describes the case study in Auckland, New Zealand utilizing simulation, optimization and simulation again. Section 2.5 depicts the analysis and results with a vali-dation procedure. Lastly, Section 2.6 summarizes the findings and draws conclusions.

**Formulation and Modeling Framework**

This work, as is mentioned above, is an extension of the research by Ceder et al. (2013b) especially in terms of adding the possibility of skipping segments. The methodology of work commences by the use of TransModeler simulation tool, Caliper (2013) to represent a real-life example and to generate random input data for the proposed optimization model. Then standard optimization software, ILOG, IBM (2012), is used to solve optimally a range of diﬀerent scenarios determined by the simulation runs. Finally, more simulation runs are made, containing the tactics determined by the optimization program, so as to validate the results attained by the model.

** Model Description**

The model developed considers PT networks consisting of main and feeder routes. The transfers occur at separate transfer points for each route. The formulation contains all the implemented tactics using a deterministic modeling. Analytically the model seeks to attain minimum total passenger travel time and to increase, in this way, the total number of direct transfers. The model formulates the tactics of holding vehicles, skipping individual stops, and skipping segments, as well as indication of missing or making a direct transfer.

The scope of this work is to describe and explain the conjunction of the holding tactic with skip-stop and skip-segment tactics. This model is not addressing individual controlling tactics as appear in the literature, e.g., Sun and Hickman (2005), Delgado et al. (2012, 2013), and Liu et al. (2013), but a combined optimal set of tactics . The control decision consists of when to hold at and skip a stop or to hold at and skip a segment (one or more consecutive stop) given that a direct transferring is feasible. It is to note that the variables and formulation related to the hold and skip stop tactics are similar to those appearing in Ceder et al. (2013b). However, this work is based on new notations and formulation so as to more accurately accommodate the three tactics dealt with, and moreover to allow for an easy extension of the concept used to include more operational tactics.

State Variables:

N Set of all bus stops, in which n ∈ N

R Set of all bus routes in which r, r´ ∈ R

T F Set of all transfer points, in which tr ∈ T F

Qmaxr Passenger capacity of bus of route r

lrn Passengers’ load of route r at stop n

bnr The number of boarding passengers of route r at stop n

anr The number of alighting passengers of route r at stop n

pnrr´ The number of transferring passengers of route r to route r´ at stop n

dnr Bus dwell time of route r at stop n (in seconds) hr Bus headway of route r

cnr Bus running time of route r at stop n from the previous stop

Anr Bus arrival time of route r at stop n

Drn Bus departure time of route r at stop n

Ω(t)nr Time penalty function of route r at stop n

nr Time to reach a desired stop skipped of route r at stop n

Tr Bus schedule deviation of route r

T Prtr Transfer stop of route r at transfer point of tr

Er Bus elapsed time of route r from the previous stop to the current position

mr Maximum total number of stops of route r

kr Positional stop of route r for a snapshot

ω Ratio between the average speed of a bus and the average walking speed of pedestrian (same ratio for all routes and stops).

Parameters:

θrn

βrn

γrn

λnr

The number of passengers of route r for a bus departing stop n

The number of passengers waiting at stops further along the routes with respect to route r and stop n (future passengers)

The number of passengers who wish to have transfers at transfer points with respect to route r and stop n

The waiting time per passenger at previous stops due to applied tactics.

Decision Variables:

HOrn Bus holding time of route r at stop n

Srn Bus skipping stop of route r at stop n; if stop skipped= 1, otherwise= 0

Yrnr´ Possible transferring from route r to route r´ at transfer stop n, pre-tactics; if a possible transfer occurs= 0, otherwise= 1

Zrnr´ Possible transferring from route r to route r´ at transfer stop n, post-tactics; if a possible transfer occurs= 0, otherwise= 1.

Assumptions:

The model is designed deterministically. Therefore the following assump-

tions are made:

• There is foreknowledge of the route information, including average travel times, average passenger demand, average number of transferring passengers and average dwell times.

• Passenger demand is independent of bus arrival time.

• Vehicles are operated in FIFO manner with an evenly scheduled headway.

• Passengers will wait at their stop until a bus arrives (none leaves the system without taking the first arrived bus).

• The bus arriving subsequently to a bus that skipped stop cannot use any of the two tactics considered.

• Passengers onboard a bus that will skip segment will be informed on this action at the time of the decision so as they can alight before or after the skipped segment; it is to note that the formulation of optimization minimizes these type of passengers and in most cases tested it is nil.

• Stops where passengers want to transfer cannot be skipped.

• Planned transfers exist (as part of the operations planning phase).

**Formulation and Properties of Holding Tactic**

Holding a vehicle is a tactic considered operationally for regulating undesired scheduled deviations, reducing bunching and approaching a direct transfer at transfer points. However, using the holding tactic has some drawbacks on the total travel time of the passengers. That is, the holding tactic would aﬀect three groups of passengers: a) those onboard the bus defined as θrn, b) those waiting for the bus further along the route defined as βrn, and c) those who wish to have transfers defined as γrn. The following formulation can now takes place. It is to note that, the term ’route’ describes a PT service that serves a series of stops (e.g., Route 858). A route is made up of a collection Chapter 2. Optimal Combinations of Selected Tactics for Public-Transport Transfer of ’trips’; each trip represents a single run, based on a certain departure time, along the series of stops of the route. It is to note that this work refers to routes, not to buses; the buses are only associated with a given route (no interlining). When we’re referring to anr, as the number of alighting passengers of route r at stop n, we mean that it can be related to a few buses in a given time period, not to a specific bus.

**1 Introduction **

1.1 Overview and Research Motivation

1.2 Background and Significance of the Research

1.3 Research Problem

1.4 Scope of Research and Objectives

1.5 Research Methodology

1.6 Thesis Outline

**2 Optimal Combinations of Selected Tactics for Public-Transport Transfer Synchronization **

2.1 Abstract

2.2 Introduction

2.3 Formulation and Modeling Framework

2.4 Case Study of Real-Time Tactics Implementation

2.5 Result and Analysis

2.6 Concluding Remarks

**3 A Robust, Tactic-Based, Real-Time Framework for Public-Transport Transfer Synchronization **

3.1 Abstract

3.2 Introduction

3.3 Literature Review

3.4 System Characteristics

3.5 Math Formulation

3.6 Problem Formulation

3.7 Model Optimization

3.8 Simulation

3.9 Library of Tactic Frameworks: Combined Tactic-based Problem (CTP)

3.10 Case Study

3.11 Analysis

3.12 Conclusions

**4 Improved Reliability of Public Transportation Using Real-Time Transfer Synchronization **

4.1 Abstract

4.2 Introduction

4.3 Public Transport Service-Reliability Characteristics

4.4 System Performance Indicator Model

4.5 Analysis of the Methodology

4.6 Case Study

4.7 Results

4.8 Concluding Remarks

**5 Real-time Public-Transport Operational Tactics Using Synchronized Transfers to Eliminate Vehicle Bunching **

5.1 Abstract

5.2 Introduction

5.3 Control Methodology

5.4 Simulation Experiments

5.5 Case Study

5.6 Analysis of the Results

5.7 Conclusions

**6 Synchronized Transfers in Headway-Based Public Transport Service Using Real-Time Operational Tactics**

6.1 Abstract

6.2 Introduction

6.3 System Control Models

6.4 Simulation Analysis

6.5 Case Study

6.6 Analysis of Results

6.7 Conclusions

**7 Energy Efficiency of Public Transport Systems Using Real-Time Control Method **

7.1 Abstract

7.2 Introduction

7.3 Methodology

7.4 Case Study

7.5 Analysis and Results

7.6 Conclusion

**8 Matching Public Transport Demand Using Tactic-Based Guidelines **

8.1 Abstract

8.2 Introduction

8.3 STAGE 1: Methodology and Findings of Users’ Perception of The Service Factor

8.4 Decision Models

8.5 STAGE 2: Effects of Tactics on Users’ Perception and Decision

8.6 Conclusions and Future Research

**9 Public Transport Service-Quality Elements Based on Real-Time Operational Tactics **

9.1 Abstract

9.2 Introduction

9.3 Literature Review

9.4 Attributes of Service Quality in advanced PT system

9.5 Methodology

9.6 Results and Discussion

9.7 Conclusion and Remarks

**10 Summary, Conclusion and Recommendations **

10.1 Summary of the Thesis

10.2 Main Research Findings

10.3 Limitations

10.4 Future Research

**Bibliography**

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