si – 2124 pengantar rekayasa transportasi kuliah ke · pdf filesi – 2124...
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SI – 2124 PENGANTAR REKAYASA TRANSPORTASI
KULIAH KE -9KULIAH KE -9(Karakteristik Lalu Lintas)
Dosen: Harun al-Rasyid LUBIS
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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
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Volume Jam Perencanaan (VJP)
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Basic Relationship (S,D,V)
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ILLUSTRASI LOS
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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
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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
∗
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0
uf
Speed
Greenshields’ Model (1935)
Alternative Functional Forms
kj0Density
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q)Optimal flow
or capacity,qmax
Flow-Density Relationship
Flow
(q
Density (k) Optimal density, ko
Jam density, kj
Uncongested flow
Congested flow
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Free-Flow Speed, uf
Uncongested flow
Speed-Flow Relationship
Spee
d (u
)
Flow (q)
Congested flow
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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
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Speed-Flow relationships
Speed(S) Figure 1: A typical speed-flow relationship
S0
S SF
SC
F C Flow (V)
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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)
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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)
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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.
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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)
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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
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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
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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
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Queuing Components
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Multi-Channel Queues
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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
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KULIAH KE-10Kapasitas Jalan Indonesia
(KAJI)
• KONSEP KAPASITAS • KONSEP KAPASITAS (Ruas dan simpang)
• DEGREE OF SATURATION
• KECEPATAN PD ARUS BEBAS
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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
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FVo
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FVw
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FFVsf (ada bahu jalannya)
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FFVsf ( hanya ada kerb)
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FFVcs : koreksi ukuran kota
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KAPASITAS RUAS (JALAN KOTA)
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DEGREE OF SATURATION
DS = Q / C
Q = arus (volume)Q = arus (volume)C = kapasitas
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SI – 2241PENGANTAR SISTEM
TRANSPORTASI
KULIAH KE -11KULIAH KE -11
PERSIMPANGAN DAN KENDALI LALU LINTAS
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Jenis-jenis Pengaturan Simpang
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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
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Contoh Simpang dengan Channelization
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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)
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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
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Peralatan Sistem Pengendali Sinyal Lalu Lintas
Perhitungan Lampu Lalu Lintas
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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
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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
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