This presentation outlines a generic approach for rescheduling public transit timetables to reduce passenger waiting times. It involves three stages: pre-optimization analysis of transit data, optimization of timetables using mathematical models, and post-optimization analysis. The approach is demonstrated on Athens' metro system, showing potential waiting time reductions of up to 9% through rescheduling. Further research is needed to handle larger networks and incorporate operator criteria.

1. A generic approach
for the rescheduling
of public transit
services Dimitris Rizopoulos, M.Sc. student
Prof. Georgios K.D. Saharidis
University of Thessaly
Presentation for the 5th International Conference on Energy, Sustainability and Climate Change

2. Contents of the presentation
1. The problem of rescheduling timetables
2. The data & the literature
3. Outline of the approach and the modelling assumptions
4. Pre-optimization stage of the approach
5. The mathematical models used for the optimization of the timetables
6. Post-optimization stage of the approach
7. Case study: Athens’ metro system
8. Meaning of results and next steps
5thInternationalConferenceonEnergy,Sustainabilityand
ClimateChange,ESCC,4-6June2018,Mykonos,Greece
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3. The problem (1)
Definition: Given a timetable of a set of routes R, a set of trips T and a set of
stops S of a public transit agency, decide on the changes* on the timetable that
will result on a new timetable whose routes and trips will reduce the waiting
time at the stops of the network where a passenger can make a transition
from one route to another
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Important note: The problem is interconnected with
the problem of journey/route planning and multi-
modality. In order for us to consider Waiting Time,
we need to first analyze a network and check where
and when a passenger can change modes of
transport or hop on and off a bus/metro route

4. The problem (2)
• A graphical representation of a journey that can be rescheduled
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• The whole multi-modal trip from Larisa to Volos
in Central Greece
• The part of the journey inside Volos which could benefit from our
rescheduling optimization approach

5. The data & the literature (1)
The data – General transit feed
specification(GTFS)
A set of rules according to which every public
transport agency should publish their
schedules and information about their
network
Goal of the specification: Provide a framework
through which those data could be
incorporated into any platform or digital
system
A single feed of GTFS data is a collection of 6
up to 13 files in .csv format contained within
a .zip file.
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6. The data & the literature (2)
Previous work on the problem
The scheduling of transit networks or problem of timetabling has been addressed in several studies.
Differences between the studies refer to:
• Definition of the welfare of the passengers or the operators of the services
• Definition of what waiting time is
• Definition of a transitional node – Nodes that a passenger can make a transition from one mode or trip to
another
• Techniques to model and solve the problem – Genetic algorithms, Global optimization, Variable
neighborhood search
What we noticed: Great results, but most approaches were case-specific and ad-hoc.
What our work is proposing
Create a way to solve a problem based on GTFS integration models which will work for any agency that will
provide their data in GTFS format
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7. Outline of the approach & modelling
assumptions
The analysis happens in three stages:
1. Pre-optimization phase: The data are analyzed and only specific parts of them are kept and
stored in specific data structures
2. Optimization phase: The mathematical models introduced are utilized to produce the results
3. Post-optimization phase: Results are combined into a weekly schedule that can be used by the
public transit agencies
Assumptions:
• Arrival time at a stop of the network is the same the departure time and we will call it Time of
Service(ToS) of the stop
• Waiting time exists only between two services of different routes that serve a single node of the network
• Waiting time exists only between two services whose difference in ToS is only between 2 min at minimum
and 20 at maximum
• Waiting time exists only between services that start in the same day – Daily analysis
• All analysis of ToS happens in minutes
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8. Pre-optimization stage
The goal: Analyze the network and find the smallest
part of the data that should incorporated into the
model and analyzed.
Steps to follow:
• GTFS data are read, analyzed and stored in the
appropriate data structures
• The nodes of the network where there is an
intersection and create a simplified network
• A number of feasible transitions are measured
between at the nodes where pairs of routes intersect
• Group the several feasible transactions into separate
days – in order to reduce size of models
• We decide on the number of variables and constraints
that should be declared in the main-optimization
phase of the approach.
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9. Mathematical models used
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Indices
r
Index used to indicate route
𝑡
Index used to indicate trip
𝑠
Index used to indicate the stop
Parameters
𝑁𝑆𝐷𝑇𝒔𝒓𝒕
Non-synchronized departure times
for route r and trip t at stop s
(current)
𝑁𝑆𝐴𝑇𝒔𝒓𝒕
Non-synchronized arrival times for
route r and trip t at stop s (current)
𝐴𝑃𝑟𝑡
Allowed Percentage of change in
departure or arrival time for route
r (determined in pre-optimization)
𝑅𝐹𝑟𝑡
Route Frequency of the execution
of the trips for a route r (calculated
in pre-optimization)
𝑇𝑇𝑠1 𝑠2 𝑟𝑡
Transportation time between stop s1,
stop s2, route r and trip t
𝑻𝑹 𝒔,𝒓𝟏,𝒕𝟏,𝒓𝟐,𝒕𝟐
Time required for the transition
between service of r1 and t1, and
service of r2 and t2
Decision Variables
𝑇𝑂𝑆𝑠𝑟𝑡
Time when route r with trip t
serves the stop s
The mathematical model used

10. Post-optimization analysis
Goal of the analysis is to turn the optimization results into a meaningful
result for the agency operating the public transit services
*Notice: We have optimized the waiting time for the transitions for each separate day of the week
Since we have a set of 7 solutions for the same problem, they need to be efficiently combined in order
to produce a pareto-optimal solution.
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Use the schedule
for each day as is
Create a new solution space
for the problem and solve a
LP
Sweet spot in the analysis:
Use optimized parts of the schedule that are
unique for a specific day and optimize on a
second level the parts of the opt. schedule that
run for multiple days
Final decision depends completely on the operators and their criteria.
Let’s move on to see a case study for our approach ..

11. Case study of Athens’ Metro (1)
The network investigated
• Number of stations: 65
• Number of stations that a transition can happen: 4
• Number of routes: 3
• Number of trips throughout the week: 3636
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Route Route(from –
to)
Number of
stations
Avg.
duration of
trips
Established
in
Last
development
happened in
1 Piraius –
Kifissia
24 51 min 1869 2004
2 Anthoupoli –
Elliniko
20 29 min 2000 2013
3 Agia Marina
– El.
Venizelos
Airport
21 50 min 2000 2013

12. Results matrix for the case of Athens
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Monday Tuesday Wednesday Thursday Friday Saturday Sunday Weekly
Non-synced 290520 min 290520 min 290520 min 290520 min 301867 min 91665 min 88943 min 1.644.555 min
Parameter(
𝑨𝑷 𝒓𝒕, 𝑹𝑭 𝒓𝒕)
285566
1.7%
285556
1.7%
285566
1.7%
285566
1.7%
296761
1.69%
88560
3.37%
86017
3.28%
1.613.602
1.88%
±𝟏𝟓 280122
3.57%
280122
3.57%
280122
3.57%
280122
3.57%
291263
3.51%
87539
4.49%
84757
4.7%
1.584.047
3.67%
±𝟑𝟎 271122
6.67%
271122
6.67%
271122
6.67%
271122
6.67%
281876
6.62%
84548
7.76%
82029
7.77%
1.532.941
6.78%
±𝟒𝟓 264236
9.04%
264236
9.04%
264236
9.04%
264236
9.04%
274966
8.91%
82105
10.4%
79636
10.4%
1.493.651
9.17%
Time needed for
preprocessing
5309.77 s 5703.70 s 5396.80 s 4893.29 s 6438.14 s 1936.56 s 2095.94 s
-
Time needed for the
optimization(avg.)
2.09 s 1.70 s 2.06 s 1.95 s 2.06 s 0.57 s 0.50 s
-
Cells that refer to the optimization cases
( 𝑤𝑎𝑖𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑎𝑓𝑡𝑒𝑟 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛)
Case study of Athens’ Metro (2)

13. Meaning of results & next steps
For the specific application of rescheduling:
• Less overall waiting time is feasible to be achieved by rescheduling but messing with the schedule of the agency can be
tricky, so any kind of changes require effective communication in order to be applied
For the methodology and how to approach such problems:
• Multi-stage analysis and the use of appropriate data structures can lead to smaller model sizes by selecting parts of the data
to include in the optimization phase – where exhaustive search is applied
• A pre-optimization stage requires(in most of the cases) a post optimization phase
• A pre-optimization phase gives us more flexibility on how to model the problem and solve a model that is not associated with
meaning for the physical system without a post-optimization phase
Questions to be answered:
• How does the execution times change with bigger networks and datasets?
• How to include the criteria for the systems operators?
• What is the best way to communicate the results to the agencies?
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14. Thank you for your attention.
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Are there any questions?
P.S. Send us data from your region to reschedule them.
dimrizopoulos@gmail.com