SIMULATION ANALYSIS OF A TOTALLY ASYMETRIC SIMPLE EXCLUSION PROCESS TO DETERMINE THE PROFIL OF THE ONE-BODY CORRELATION FUNCTION, TWO-BODY CORRELATION FUNCTION AND THREE-BODY CORRELATION FUNCTION AROUND THE ENDS OF THE LATTICE WITH LATTICE NUMBER VARIATIO
SIMULATION ANALYSIS OF A TOTALLY ASYMETRIC SIMPLE
EXCLUSION PROCESS TO DETERMINE THE PROFIL OF THE ONE-BODY
CORRELATION FUNCTION, TWO-BODY CORRELATION FUNCTION AND
THREE-BODY CORRELATION FUNCTION AROUND THE ENDS OF THE
LATTICE WITH LATTICE NUMBER VARIATION
ABSTRACT
This study aimed to determine the behavior of one-body, two-body and threebody correlation functions of the model dynamics TASEP with sequential updating
rules and open boundary conditions, especially around the ends of the lattice, to
compare the behavior of one-body, two-body, and three-body correlation functions
generated by varying the number of lattice, especially around the ends of the lattice,
and determine the interpretation of results obtained from the purpose of 1 ) and 2 )
for vehicular traffic around the end of the traffic light.
The study began with determining the simulation programming algorithm to
model the dynamics of TASEP with sequential updating rules. Furthermore, the
program code was made to solve the problem using the C++ language. In the
programs that have been made input (α), output rate (β), and a number of the lattice
(N) were varied. Then the program was run with a time limit t and a specific number
of system (M). The data generated by program were particle density (one-body
correlation function), the two-body correlation function, and the three-body
correlation function. The data were then presented in the form of graphs.
The value of one-body correlation function determined the average occupancy
of lattice site i at time t. Two-body correlation function determined the average
occupancy of particles to occupy lattice i when there was another particle occupying
nearest neighbor lattice site, i+1 at time t. Three-body correlation function
determined the average occupancy of particles to occupy lattice site i when there was
another particle occupying nearest neighbor lattice site, i+1 and i+2 at time t. The
value of the one-body correlation function was larger than two-body correlation
function. Whereas, the two-body correlation function was larger than three-body
correlation function for all phases. The most important the linkage of TASEP models
with vehicle traffic was the length of the road. The longer the road, the correlation on
each vehicle against another vehicle would be greater, which was seen in the
correlation of the coexistence phase of which were 45 % and 55 %.
Keywords : TASEP, sequential updating, the one-body correlation function, the
correlation function of two-body, three-body correlation function, and
the simulation of vehicle traffic.
viii
ANALISIS SIMULASI TOTALLY ASYMETRIC SIMPLE EXCLUSION
PROCESS UNTUK MENENTUKAN PROFIL ONE-BODY CORRELATION
FUNCTION, TWO-BODY CORRELATION FUNCTION DAN THREE-BODY
CORRELATION FUNCTION DI SEKITAR UJUNG-UJUNG KEKISI
DENGAN VARIASI JUMLAH KEKISI
Oleh:
Robby Arbanis Adipurno
09306141037
ABSTRAK
Penelitian ini bertujuan untuk mengetahui perilaku one-body, two-body, dan
three-body correlation functions dari model TASEP dengan aturan dinamika
sequential updating dan kondisi batas terbuka, terutama di sekitar ujung- ujung kekisi,
membandingkan perilaku one-body, two-body, dan three-body correlation functions
yang dihasilkan dengan memvariasi jumlah kisi, terutama di sekitar ujung-ujung
kekisi, dan mengetahui interpretasi hasil yang diperoleh dari tujuan 1) dan 2) untuk
lalu lintas kendaraan di sekitar ujung lampu lalu lintas kendaraan.
Penelitian ini dimulai dengan menentukan algoritma pemrograman simulasi
model TASEP dengan aturan dinamika sequential updating. Selanjutnya, dibuat
coding (program) untuk menyelesaikan permasalahan menggunakan bahasa C++.
Pada program yang telah dibuat divariasi nilai laju input (α), nilai laju output (β), dan
jumlah kisi (N). Kemudian menjalankan program dengan batasan waktu (t) dan
jumlah sistem (M) tertentu. Data yang dihasilkan oleh pemrograman berupa
kepadatan partikel (one-body correlation function), two-body correlation function,
dan three-body correlation function. Data tersebut selanjutnya dibuat dalam bentuk
grafik.
Nilai one-body correlation function menentukan peluang rata-rata partikel
untuk menduduki kekisi i pada waktu t. Two-body correlation function menentukan
peluang rata-rata partikel untuk menduduki kekisi i ketika ada partikel lain
menduduki kekisi tetangga terdekat, i+1 pada waktu t. Three-body correlation
function menentukan peluang rata-rata partikel untuk menduduki kekisi i ketika ada
partikel lain menduduki kekisi tetangga terdekat, i+1 dan i+2 pada waktu t. Nilai onebody correlation function > two-body correlation function > three-body correlation
function untuk semua fase. Keterkaitan untuk model TASEP dengan lalu lintas
kendaraan ini yang menjadi hal terpenting terdapat pada panjang suatu jalan. Semakin
panjang jalan tersebut, maka korelasi yang diberikan pada masing- masing kendaraan
terhadap kendaraan yang lain akan semakin besar, seperti yang terdapat pada
coexistence phase dengan korelasi antar kendaraan sebesar 45% dan 55%.
Kata kunci: TASEP, sequential updating, one-body correlation function, two-body
correlation function, three-body correlation function, lalu lintas
kendaraan dan simulasi.
vii
EXCLUSION PROCESS TO DETERMINE THE PROFIL OF THE ONE-BODY
CORRELATION FUNCTION, TWO-BODY CORRELATION FUNCTION AND
THREE-BODY CORRELATION FUNCTION AROUND THE ENDS OF THE
LATTICE WITH LATTICE NUMBER VARIATION
ABSTRACT
This study aimed to determine the behavior of one-body, two-body and threebody correlation functions of the model dynamics TASEP with sequential updating
rules and open boundary conditions, especially around the ends of the lattice, to
compare the behavior of one-body, two-body, and three-body correlation functions
generated by varying the number of lattice, especially around the ends of the lattice,
and determine the interpretation of results obtained from the purpose of 1 ) and 2 )
for vehicular traffic around the end of the traffic light.
The study began with determining the simulation programming algorithm to
model the dynamics of TASEP with sequential updating rules. Furthermore, the
program code was made to solve the problem using the C++ language. In the
programs that have been made input (α), output rate (β), and a number of the lattice
(N) were varied. Then the program was run with a time limit t and a specific number
of system (M). The data generated by program were particle density (one-body
correlation function), the two-body correlation function, and the three-body
correlation function. The data were then presented in the form of graphs.
The value of one-body correlation function determined the average occupancy
of lattice site i at time t. Two-body correlation function determined the average
occupancy of particles to occupy lattice i when there was another particle occupying
nearest neighbor lattice site, i+1 at time t. Three-body correlation function
determined the average occupancy of particles to occupy lattice site i when there was
another particle occupying nearest neighbor lattice site, i+1 and i+2 at time t. The
value of the one-body correlation function was larger than two-body correlation
function. Whereas, the two-body correlation function was larger than three-body
correlation function for all phases. The most important the linkage of TASEP models
with vehicle traffic was the length of the road. The longer the road, the correlation on
each vehicle against another vehicle would be greater, which was seen in the
correlation of the coexistence phase of which were 45 % and 55 %.
Keywords : TASEP, sequential updating, the one-body correlation function, the
correlation function of two-body, three-body correlation function, and
the simulation of vehicle traffic.
viii
ANALISIS SIMULASI TOTALLY ASYMETRIC SIMPLE EXCLUSION
PROCESS UNTUK MENENTUKAN PROFIL ONE-BODY CORRELATION
FUNCTION, TWO-BODY CORRELATION FUNCTION DAN THREE-BODY
CORRELATION FUNCTION DI SEKITAR UJUNG-UJUNG KEKISI
DENGAN VARIASI JUMLAH KEKISI
Oleh:
Robby Arbanis Adipurno
09306141037
ABSTRAK
Penelitian ini bertujuan untuk mengetahui perilaku one-body, two-body, dan
three-body correlation functions dari model TASEP dengan aturan dinamika
sequential updating dan kondisi batas terbuka, terutama di sekitar ujung- ujung kekisi,
membandingkan perilaku one-body, two-body, dan three-body correlation functions
yang dihasilkan dengan memvariasi jumlah kisi, terutama di sekitar ujung-ujung
kekisi, dan mengetahui interpretasi hasil yang diperoleh dari tujuan 1) dan 2) untuk
lalu lintas kendaraan di sekitar ujung lampu lalu lintas kendaraan.
Penelitian ini dimulai dengan menentukan algoritma pemrograman simulasi
model TASEP dengan aturan dinamika sequential updating. Selanjutnya, dibuat
coding (program) untuk menyelesaikan permasalahan menggunakan bahasa C++.
Pada program yang telah dibuat divariasi nilai laju input (α), nilai laju output (β), dan
jumlah kisi (N). Kemudian menjalankan program dengan batasan waktu (t) dan
jumlah sistem (M) tertentu. Data yang dihasilkan oleh pemrograman berupa
kepadatan partikel (one-body correlation function), two-body correlation function,
dan three-body correlation function. Data tersebut selanjutnya dibuat dalam bentuk
grafik.
Nilai one-body correlation function menentukan peluang rata-rata partikel
untuk menduduki kekisi i pada waktu t. Two-body correlation function menentukan
peluang rata-rata partikel untuk menduduki kekisi i ketika ada partikel lain
menduduki kekisi tetangga terdekat, i+1 pada waktu t. Three-body correlation
function menentukan peluang rata-rata partikel untuk menduduki kekisi i ketika ada
partikel lain menduduki kekisi tetangga terdekat, i+1 dan i+2 pada waktu t. Nilai onebody correlation function > two-body correlation function > three-body correlation
function untuk semua fase. Keterkaitan untuk model TASEP dengan lalu lintas
kendaraan ini yang menjadi hal terpenting terdapat pada panjang suatu jalan. Semakin
panjang jalan tersebut, maka korelasi yang diberikan pada masing- masing kendaraan
terhadap kendaraan yang lain akan semakin besar, seperti yang terdapat pada
coexistence phase dengan korelasi antar kendaraan sebesar 45% dan 55%.
Kata kunci: TASEP, sequential updating, one-body correlation function, two-body
correlation function, three-body correlation function, lalu lintas
kendaraan dan simulasi.
vii