Introduction+How can Tsukuba provideconvenient, accessible, andsustainable public transportation?

Future trajectory:1. Smaller spheres of living2. Local infrastructure3. Fewer individual trips

Proposed Park-and-Ride● Cost Comparison:○○

Convenience via Queueing ModelEnvironment via Emissions Model● Available Datasets:○○

Person Trip SurveyBus Location

1. Mt. Tsukuba2. Oho Toyosato3. Sakura4. Yatabe5. KayasakiCentral Hub

Queueing analysis: A/S/

queuing modelExamples of Kendall’s notation

M : MemorylessorMarkovianD : Deterministic(fixed)G : General

Modelling & AnalysisPerformance measures (output):

Waiting time, Total time, Number of waiting customers, …

Queueing model for Park-and-Ride(from Suburbto the city center)

Virtual queueing modelto express the trafficcongestion

Service Station

Traffic congestion model(Van Woensel, 2007)● Maximum traffic density(vehicle/km):○ Maximum number of vehicles on per unit road○ → physical size of the service station =● Service station = G/D/1 queue○ General arrival process■ Convolution of arrival processes of cars and buses (numerically obtained)○ Deterministic (fixed) service time =○(veh/h) =○(h) =(Nominal speed) (km/h) ××(distance) (km) ×(vehicle/km)(sojourn time) (h/vehicle)(main output:) Traveling time on roadAnalysis of Park-and-Ride queueing model● Under two stability conditions (for the number of customers in a queuedoes not diverge to infinity):(1)(for the queue of bus customers)(2)(for the queue of vehicles in the service station)● Lettinganddenote the numbers of vehicles in the service stationand the waiting bus customers,becomesa multidimensional continuous time stochastic process under the set space→ obtain the steady state probability numerically:

Performance measures (output)By a simulation, we obtain: Speed of a car (km/hr): Sojourn time of a car in the service station (hr): Waiting time for a bus customer (hr): Traveling time for a vehicle on the road (hr)

: Total trip time for a customer (hr)Assumptions for simulation (1)— estimation of a maximum traffic density(vehicle/km)

Approximation: the service station on the current road is an M/D/1 queueAlmost all of the vehicles are private cars(Poisson arrivals represented by M)Procedure(original assumption: G/D/1 queue)

Analytical result of expectedsojourn time for M/D/1 queuerelationshipFrom real data(=Service station) (Medhi, 2002)Our goal !!
(Van Woensel, 2007)(Expected traveling time)※parameters: from real dataFrom real data

Assumptions for simulation (1)— estimation of a maximum traffic density(vehicle/km)

Solution of the last equation:※: Current arrival rate of all the vehicles (From real data)

Simple assumption:Every driver travels at thenominal speed

Exception: Drivers in the real worldsometimes do not keep the nominal speed…

Assumptions for simulation (2)— introduction of bus policy coefficient:To satisfy the stability condition (1) for the bus customers, i.e.,

We assume that the bus departure interval is as follows:※: Capacity of a bus

Queueing Model Parameters: Implementation● Clean person-trip survey dataset provided arrival rates for customers andvehicles, as well as initial travel times● Bus capacity was fixed at 80 (number of customers) for all scenarios● Nominal speed was fixed at 80 km/hr for all scenarios● % car usage ranged from 0-90% and results were computed for every 10%● Bus policy coefficient (r) was obtained for each % car use, for each hub, via abrute force search in the linear space [0,1) for the minimizer of total trip time:We will look at some results for one hub - Sakura districtin more detailQueueing Results: Average Trip Times

Queueing Results: Time of Day Effects

Queueing Results: Trip Time Trend for % car use

Queueing Results: Waiting Time Trend for % car use

Emission Estimations● Evaluating environmental impact of new and conventional traffic system● Focus on the emission product● Two types of mathematical emission model.
1. Dynamic model → instantaneous2. Static model → average● Use static model [1][1]: Jo, H.; Kim, H. Developing a Traffic Model to Estimate Vehicle Emissions: An Application in Seoul,Korea. Sustainability 2021, 13, 9761. https://doi.org/10.3390/su13179761

Emission Function●Numerous emission functions depending onthe parameters●The argument of the function is the averagespeed.

●No CO2 function in this paper, so we usednational emission factor data.

Algorithm● The unit of emission function is g/km● Emissions are calculated by the product of the emission function and thedistance.
● By calculating the sum, one can calculate the total emission of theemission product.

Output from Real DataCalculating Emission from Person Trip andBus Location data.
(above: Private Car, below: Bus)●Determine parameter from National Data(eg. the number of car by fuel)●The emission of Private Car is much biggerthan Bus.

●The emission of Private Car is high in rushhour time

●Bus emission is constant during the day●CO2 is major emission productQueueing Model → Emission Model● Combine emission model withQueueing Model● Velocity and distance is requiredfor emission model.
● Distance and sojourn time in theservice station are outputs fromQueueing model● Velocity are obtained by equationfrom Queueing Model

Emission from Queueing ModelPlot emission for each probability(Car Usage)●Almost monotonically increasing with respectto probability●It is thought to be due to capacity of thevehicle (Bus: 80, Private Car: 1)●CO2 emission is proportional to distance andthe number of vehicle in the road●As bus user increases, the number of vehicleson the road decreases.

Convenience Cost vs. Environmental Cost

As pincreases,so does thenumber ofprivatecars.

Convenience Cost vs. Environmental Cost

Convenience Cost vs. Environmental Cost● Bus location data onlyhas data for one buscompany● Slow speed contributions● Choice of r optimal fortotal traveling time.

Does a PnR system make asignificant difference?

● Does the current publictransport in Tsukuba onlyserve 15% of thepopulation?

Conclusions:

Future Directions:● Queueing good method to modeltraffic behavior under variousscenarios

1. Queueing:● Emissions need to be quantified toalign with future goals

2. Emissions:● Results imply current publictransport in Tsukuba only optimalfor current usage

3. Input parameters:

a.
b.
c.
d.

a.
b.

a.
b.
c.
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Other service process and more serversDecision between private car and publictransportChoice of parameter r‘Strategic’ queueing model

Static vs. Dynamic modelConsider hybrids and electric vehiclesConsider particular populationsFiner time scalesOther modes of transport, more dataMachine learning to select policyparametersRelevant References:General Transportation Policy Division, T. C. P. D. (2021). Tsukuba city regional public transportation plan.
https://www.city.tsukuba.lg.jp/_res/projects/default_project/_page_ /001/014/531/R3_keikakusyo.pdfJo, H.; Kim, H. Developing a Traffic Model to Estimate Vehicle Emissions: An Application in Seoul, Korea. Sustainability2021, 13, 9761. https://doi.org/10.3390/su13179761Medhi, J.Stochastic models in queueing theory. Elsevier, 2002.
Van Woensel, T., Vandaele, N. Modeling traffic flows with queueing models: a review. Asia-Pacific Journal of OperationalResearch, 24(4), 435-461, 2007.