SI – 2124 PENGANTAR REKAYASA TRANSPORTASI

KULIAH KE -9KULIAH KE -9(Karakteristik Lalu Lintas)

Dosen: Harun al-Rasyid LUBIS

Outline• Introduction

• Basic Traffic Flow Theory

• Definitions ; LHR, VJP

• PHF (Peak Hour Factor)

• Speed (space mean speed Vs time mean speed)

• Traffic Density, Headway and spacing

• Basic Relationship

• Simple Car following theory

• Queueing theory

Volume Jam Perencanaan (VJP)

Basic Relationship (S,D,V)

ILLUSTRASI LOS

Traffic Flow Concepts• Volume, speed and density

• Average travel speed or space mean speed and time mean speed

• If travel times t1, t2, t3,...,tn are measured for n vehicles traversing a

segment of length L, the average travel speed (space mean speed) would

be

∑

∗=∑∗

= nntLn

tnLu)/1( ∑∗

∑∗= n

n

tn

ilnu 1

)/1(

)/1( speaking, Generally

• 5 vehicles over a given one-mile section with travel times (in minutes) of

1.0, 1.2, 1.5, 0.75 and 1.0 respectively. Average travel time = 5.45/5=1.09

min = 0.0182 hr. u = 1/0.0182 = 55.05 mph.

• Time mean speed is the arithmetic average of all vehicles passing a given

“spot” on a roadway section. Space mean speed < time mean speed

∑∑∗ nn

ititn11

)/1( ∑∗= n

ilitn

u

1 ,)/1(

speaking, Generally

Speed-Flow-Density Relationships

• Density is defined as the number of vehicles occupying a given length of a lane or roadway at a particular instant; density can be computed using the relationship: k = n/l. Alternatively, if q is the rate of flow and u is average travel speed, k = q/u. Unit of density is vehicles per mile (vpm).

• Spacing is defined as the distance (ft) between successive vehicles • Spacing is defined as the distance (ft) between successive vehicles in a traffic stream, as measured from front bumper to front bumper; headway is the time (sec) between successive vehicles, as their front bumpers pass a given point. Headway (sec/veh) = spacing (ft/veh)/speed (ft/sec). Density = 5,280/spacing. Flow rate or practical capacity = 3,600/average headway.

jkk - 1

fu =u

j

2

f kk

-k u = q

fu

2u -u j

k = qmmm ku = q ∗

2/k = kjm

2/f

u = mu

4j

kf

u = mq

∗

0

uf

Speed

Greenshields’ Model (1935)

Alternative Functional Forms

kj0Density

q)Optimal flow

or capacity,qmax

Flow-Density Relationship

Flow

(q

Density (k) Optimal density, ko

Jam density, kj

Uncongested flow

Congested flow

Free-Flow Speed, uf

Uncongested flow

Speed-Flow Relationship

Spee

d (u

)

Flow (q)

Congested flow

Empirical Speed-Flow Relationship

Traffic flow is not uniform. Rather may follow a Poisson processdescribed by p(n) = e-λt (λt)n /n! Poissonian arrivals also imply anegative exponential distribution for vehicle headways

Speed-Flow relationships

Speed(S) Figure 1: A typical speed-flow relationship

S0

S SF

SC

F C Flow (V)

Equation of S-F Relationship

• S1(V) = A1 – B1V V < F ........................ (2)• S2(V) = A2 – B2V F < V < C ............ (3)

• A1 = S0 B1 = (S0 – SF) / F• A2 = SF + {F(SF – SC)/(C – F)} B2 = (SF – SC) / (C – F)

– S1(V) and S2(V) = speed (km/h)– V = flow per standard lane (veh/h)– F = flow at ‘knee’ per standard lane (veh/h)– C = flow at capacity per standard lane (veh/h)– S0 = free-flow speed (km/h)– SF = speed at ‘knee’ (km/h)– SC = speed at capacity (km/h)

Flow-Delay Curves• Exponential function appropriate to represent effec ts of

congestion on travel times. • At low traffic, an increase in flows would induce s mall increase in

delay.• At flows close to capacity, the same increase would induce a

much greater increase in delays.

Time (t) Figure 2: Effects of Congestion on Travel Times tC

t0

C Flow (V)

Equation of F-D Curve

• t(V) = t 0 + aVn V < C ........................ (4)

– t(V) = travel time on link t 0 = travel time on link at free flow– a = parameter (function of capacity C with power n)– n = power parameter input explicitly V = flow on link

• Parameter n adjusts shape of curve according to link type. (e .g.urban roads, rural roads, semi-rural, etc.)

• Must apply appropriate values of n when modelling links ofcritical importance.

Converting S-F into F-D• If time is t = L / S equations 2 and 3 could be written:

– t1(V) = L / (A1 – B1V) V < F .......................... (5)– t2(V) = L / (A2 – B2V) F < V < C ............. (6)

• These equations represent 2 hyperbolic (time-flow) curves of ashape as shown in figure 3.

• Use ‘similar areas’ method to calculate equations. Tables 1 inpaper gives various examples of results.

Time (t) Figure 3: Conversion of Flow-Delay CurvetC

tF

t0 F C Flow (V)

Fundamentals of Queuing Theory • Arrivals – uniform or random

• Departures – uniform or random

• Service rate – departure channels

• Discipline – first-in-first-out (FIFO) and last-in-first-out (LIFO) being popular first-out (LIFO) being popular

• Notation of queues: X/Y/N

– X – arrival rate nature

– Y – departure rate nature

– N – number of service channels

• Popular notations: D/D/1, M/D/1, M/M/1, and in general M/M/N

Simple Queuing Theory Applications

• Use D/D/1 only when absolutely sure that both arrivals and departures are deterministic

• Use M/D/1 for controls unaffected by neighboring controls

• Use M/M/1 or M/M/N as general case

• Factors that could affect your analysis:

Neighboring system (system of signals)– Neighboring system (system of signals)

– Time-dependent variations in arrivals and departures

• Peak hour effects in traffic volumes, human service rate changes

– Breakdown in discipline

• People jumping queues! More than one vehicle in a lane!

– Time-dependent service channel variations

• Grocery store counter lines

Graphically Analyzing QueuesV

ehic

les

QueueDissipation

Delaymax

Qmax

D/D/1V

ehic

les

Time

Queue at time t1

Delay of nth

arriving vehicle

Total Vehicle Delay

t1

Queuing Components

Multi-Channel Queues

Numerically Analyzing Queues

M/M/1

Average Arrival Rate

Average Departure Rate

1and λ/µ,ρ <=

M/D/1

µλ

M/M/N

−ρ1ρ

2µ1 = w

ρ)-2(12ρ-2ρ = Q

−ρ1ρ-2

2µ1 = t

−λµ

λ

µ

1 = w

ρ)-(1ρ = Q

λ-µ1 = t

µ

1 = wλ

Q −

( )N1N!N

P =

1+N0

NnP

ρρ−>

( )ρ = Q

Nρ1

1

NN!

ρ P2

1+N0 +

−

λ

Q = t

∑−

= −+

=1

0

0

)1(!!

1N

n

N

C

n

C

C

NNn

P

ρρρ

KULIAH KE-10Kapasitas Jalan Indonesia

(KAJI)

• KONSEP KAPASITAS • KONSEP KAPASITAS (Ruas dan simpang)

• DEGREE OF SATURATION

• KECEPATAN PD ARUS BEBAS

Kecepatan pd Arus Bebas

FV = (FVo +FVw) x FFVsf x FFVcs

Dimana:

FV = kecepatan arus bebas kendaraan ringan (km/jam)

FVo = kecepatan arus bebas dasar kendaraan FVo = kecepatan arus bebas dasar kendaraan ringan (km/jam) – lihat Tabel

FVw = penyesuaian lebar lajur lalu lintas efektif (km/jam) – lihat Tabel

FFVsf = Faktor penyesuaian kondisi hambatan samping – lihat Tabel

FFVcs = Faktor penyesuaian ukuran kota – lihat Tabel

FVo

FVw

FFVsf (ada bahu jalannya)

FFVsf ( hanya ada kerb)

FFVcs : koreksi ukuran kota

KAPASITAS RUAS (JALAN KOTA)

DEGREE OF SATURATION

DS = Q / C

Q = arus (volume)Q = arus (volume)C = kapasitas

SI – 2241PENGANTAR SISTEM

TRANSPORTASI

KULIAH KE -11KULIAH KE -11

PERSIMPANGAN DAN KENDALI LALU LINTAS

Jenis-jenis Pengaturan Simpang

Jenis-jenis konflik

Konflik PrimerKonflik Sekunder

Arus KendaraanArus Pejalan Kaki

Keterangan :

Yield Sign

R-236” x 36” x 36”

R1-130" x 30"

Stop Sign

Contoh Simpang dengan Channelization

Contoh Konflik Primer dan Sekunder Pada Persimpangan dengan Lampu

Konflik Primer

Konflik Sekunder

Arus Kendaraan

Arus Pejalan Kaki

Keterangan :

Penentuan Titik Konflik Kritis dan Jarak untuk Kelu ar (S ) dan Masuk (S )Penentuan Titik Konflik Kritis dan Jarak untuk Kelu ar (SE) dan Masuk (S A)

Kontrol dua-fasa, hanya konflik primer yang dipisah

Dua-fasa + pemutusan hijau untuk meningkatkan kapas itas arus belok kanan.

Multi-fasa dengan fasa terpisah untuk lalu lintas b elok kanan pada jalan utama.

Contoh Pola Pengendalian Pada Persimpangan Empat-Ka ki dengan Kedua Jenis Pengendalian Untuk Konflik Sekunder.

Tipikal Diagram Pengaturan Waktu untuk Pengendalian Dua-fasa

Peralatan Sistem Pengendali Sinyal Lalu Lintas

Perhitungan Lampu Lalu Lintas

Perhitungan Lampu Lalu Lintas: Pengaturan Waktu Lam pu Lalu Lintas yang Diturunkan sebagai Contoh.

1. Penambahan lajur-pembagian mendekati dua kali kap asitas pada kasus ini.2. Penambahan lajur terpisah untuk lalu Iintas belok biasanya kurang efektif.

Pengaruh Penambahan Lajur Pada Persimpangan

Penempatan Penyeberangan Pejalan Kaki yang Memungki nkan Kendaraan Belok Menunggu Tanpa Menghalangi Lalu Lintas Lurus Pada L ajur yang Sama

Contoh Penempatan Sinyal Primer & Sekunder pada Per simpangan Dengan Sinyal.

Total flow entering intersection (veh/hour)

Cycle Time

Ave

rage

del

ay p

er v

ehic

le (

S)

Hasil Simulasi dari Pengaruh Variasi Panjang Waktu Siklus Terhadap Tundaan, untuk Persimpangan 4 kaki 2 fasa, Arus sama untuk seluruh kaki, Arus jenuh sama sebesar

1800 kend/jam, Waktu hijau sama. Kehilangan Waktu/ Waktu Siklus = 10 s