SI – 2124 PENGANTAR REKAYASA TRANSPORTASI
KULIAH 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 n
u=
L n∗L n = n (1 / n ) ∗ ∑ t ∑ ti i 1 1
Generally
(1/ n ) ∗ ∑ l 1 i speaking, u = n (1/ n ) ∗ ∑ t 1 i,l i
• 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
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 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.
u = u 1- k f k j
k2 q = u k - f k j
2 u q=k u-u j f
um = u / 2 q m = u m ∗ k m f u ∗k km = k / 2 q = f j j m 4
Greenshields’ Model (1935)
Speed
uf
Alternative Functional Forms 0
Density
kj
Flow-Density Relationship
Flow (qq)
Optimal flow or capacity,qmax
Uncongested flow
Congested flow Density (k)
Optimal density, ko
Jam density, kj
Speed-Flow Relationship Free-Flow Speed, uf
Speed (u)
Uncongested flow
Congested flow Flow (q)
Empirical Speed-Flow Relationship
Traffic flow is not uniform. Rather may follow a Poisson process described by p(n) = e-λt (λt)n /n! Poissonian arrivals also imply a negative exponential distribution for vehicle headways
Speed-Flow relationships Speed(S)
Figure 1: A typical speed-flowrelationship
S0 SF
SC F
C
Flow(V)
Equation of S-F Relationship • •
S1(V) = A1 – B1V S2(V) = A2 – B2V
• •
A1 = S0 A2 = SF + {F(SF – SC)/(C – F)} – – – – – – –
V < F ........................ (2) 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 effects of congestion on travel times. At low traffic, an increase in flows would induce small 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) = t0 + aVn
V
........................ (4)
– t(V) = travel time on link t0 = 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 of critical 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) – t2(V) = L / (A2 – B2V)
V
•
These equations represent 2 hyperbolic (time-flow) curves of a shape as shown in figure 3.
•
Use ‘similar areas’ method to calculate equations. Tables 1 in paper gives various examples of results. Time (t) tC
Figure 3: Conversion of Flow-Delay Curve
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-infirst-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)
–
Time-dependent variations in arrivals and departures •
–
Breakdown in discipline •
–
Peak hour effects in traffic volumes, human service rate changes People jumping queues! More than one vehicle in a lane!
Time-dependent service channel variations •
Grocery store counter lines
Graphically Analyzing Queues Delaymax
D/D/1 Qmax
Vehicles
Queue Dissipation
Total Vehicle Delay Delay of nth arriving vehicle
Queue at time t1 t1
Time
Queuing Components
Multi-Channel Queues
Numerically Analyzing Queues ρ = λ/µ, and <1
Average Arrival Rate
M/D/1
M/M/1
2 2ρ ρ Q= 2(1- ρ)
Q= ρ (1- ρ)
1 ρ w= 2µ 1−ρ
1 2 - ρ t= 2µ 1−ρ
1 λ w= µ µ −λ
1 t= µ -λ
λ
Average Departure Rate
µ
M/M/N
Q=
P0 ρN+1 1 N!N (1− ρ N)2
Q λ
w =
1 − µ
Q t= λ
+ρ P0 =
1 N −1
ρn
∑n
nC = 0
C
C!
P n>N
+
ρN N !(1 −
ρ N
)
P0 ρ N +1 = N! N(1 − ρ N )
KULIAH KE-10 Kapasitas Jalan Indonesia (KAJI) • 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 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) C = kapasitas
SI – 2241 PENGANTAR SISTEM TRANSPORTASI
KULIAH KE-11 PERSIMPANGAN DAN KENDALI LALU LINTAS
Jenis-jenis Pengaturan Simpang
Jenis-jenis konflik
Keterangan : Konflik Primer Konflik Sekunder Arus Kendaraan Arus Pejalan Kaki
Yield Sign
Stop Sign
R-2 36” x 36” x 36” R1-1 30" x 30"
Contoh Simpang dengan Channelization
Contoh Konflik Primer dan Sekunder Pada Persimpangan dengan Lampu
Keterangan : Konflik Primer Konflik Sekunder Arus Kendaraan Arus Pejalan Kaki
Penentuan Titik Konflik Kritis dan Jarak untuk Keluar (SE) dan Masuk (SA)
Kontrol dua-fasa, hanya konflik primer yang dipisah
Dua-fasa + pemutusan hijau untuk meningkatkan kapasitas arus belok kanan.
Multi-fasa dengan fasa terpisah untuk lalu lintas belok kanan pada jalan utama.
Contoh Pola Pengendalian Pada Persimpangan Empat-Kaki 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 Lampu Lalu Lintas yang Diturunkan sebagai Contoh.
1. Penambahan lajur-pembagian mendekati dua kali kapasitas pada kasus ini. 2. Penambahan lajur terpisah untuk lalu Iintas belok biasanya kurang efektif.
Pengaruh Penambahan Lajur Pada Persimpangan
Penempatan Penyeberangan Pejalan Kaki yang Memungkinkan Kendaraan Belok Menunggu Tanpa Menghalangi Lalu Lintas Lurus Pada Lajur yang Sama
Contoh Penempatan Sinyal Primer & Sekunder pada Persimpangan Dengan Sinyal.
Average delay per vehicle (S)
Total flow entering intersection (veh/hour)
Cycle Time
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
