S MAT 1006638 Table of content
DAFTAR ISI
PERNYATAAN ............................................................................................ i
ABSTRAK ....................................................................................................
ii
KATA PENGANTAR ..................................................................................
iii
UCAPAN TERIMAKASIH ......................................................................... iv
DAFTAR ISI ................................................................................................. vi
DAFTAR TABEL ......................................................................................... viii
DAFTAR GAMBAR ....................................................................................
ix
DAFTAR LAMPIRAN ................................................................................
x
BAB I
PENDAHULUAN ........................................................................ 1
1.1 Latar Belakang ........................................................................
1
1.2 Rumusan Masalah ...................................................................
3
1.3 Tujuan Penulisan .....................................................................
3
1.4 Batasan Masalah ...................................................................... 3
1.5 Manfaat Penulisan ...................................................................
4
1.6 Sistematika Penulisan .............................................................. 4
BAB II
LANDASAN TEORI ...................................................................
6
2.1 Peubah Acak ........................................................................... 6
2.2 Nilai Ekspektasi ...................................................................... 6
2.3 Fungsi Pembangkit ................................................................. 7
2.3.1 Fungsi Pembangkit Peluang ........................................... 8
2.3.2 Fungsi Pembangkit Momen ...........................................
2.4
8
Fungsi Kepadatan Peluang .................................................... 8
2.4.1 Fungsi Kepadatan Peluang Peubah Acak Diskrit .......... 9
2.4.2 Fungsi Kepadatan Peluang Peubah Acak Kontinu ........ 9
2.5
Distribusi Poisson .................................................................. 9
2.6
Distribusi Eksponensial ......................................................... 10
2.7
Konsep Antrian .....................................................................
vi
Elyzabeth, 2014
Aplikasi Model Antrian Multiserver dengan Vacation Pada Sistem Antrian di Bank BCA
Cabang Ujung Berung
Universitas Pendidikan Indonesia | repository.upi.edu |perpustakaan.upi.edu
10
vii
2.7.1 Sejarah Teori Antrian ...................................................
10
2.7.2 Sistem Antrian ............................................................... 11
2.7.3 Struktur Antrian ............................................................. 13
2.8 Proses Markov ........................................................................ 16
2.9 Proses Birth and Death ...........................................................
17
2.10 Notasi Model Antrian ............................................................. 20
2.11 Model Antrian M/M/c ............................................................
BAB III MODEL ANTRIAN MULTISERVER DENGAN VACATION
21
28
3.1
Quasi Birth-Death (QBD) Process ......................................... 29
3.2
Antrian M/M/c dengan Multiple Asynchronous Vacation ......
31
3.2.1 Rate matrix R ...............................................................
32
3.2.2 Matriks Generator B[R] ...............................................
35
3.2.3 Banyaknya Customer dalam Sistem ............................. 36
3.2.4 Waktu Tunggu Customer dalam Sistem ........................ 38
BAB IV STUDI KASUS ............................................................................. 39
4.1 Laju Kedatangan ...................................................................
39
4.2 Laju Pelayanan ......................................................................
41
4.3 Waktu Vacation ..................................................................... 44
4.4 Faktor Utilitas Server atau Peluang Server Sibuk ................. 46
4.5 Ukuran Keefektifan Sistem ...................................................
BAB V
47
PENUTUP ..................................................................................... 58
5.1 Kesimpulan ............................................................................. 58
5.2 Saran ....................................................................................... 59
DAFTAR PUSTAKA ...................................................................................
60
LAMPIRAN .................................................................................................. 62
RIWAYAT HIDUP ......................................................................................
Elyzabeth, 2014
Aplikasi Model Antrian Multiserver dengan Vacation Pada Sistem Antrian di Bank BCA
Cabang Ujung Berung
Universitas Pendidikan Indonesia | repository.upi.edu |perpustakaan.upi.edu
83
PERNYATAAN ............................................................................................ i
ABSTRAK ....................................................................................................
ii
KATA PENGANTAR ..................................................................................
iii
UCAPAN TERIMAKASIH ......................................................................... iv
DAFTAR ISI ................................................................................................. vi
DAFTAR TABEL ......................................................................................... viii
DAFTAR GAMBAR ....................................................................................
ix
DAFTAR LAMPIRAN ................................................................................
x
BAB I
PENDAHULUAN ........................................................................ 1
1.1 Latar Belakang ........................................................................
1
1.2 Rumusan Masalah ...................................................................
3
1.3 Tujuan Penulisan .....................................................................
3
1.4 Batasan Masalah ...................................................................... 3
1.5 Manfaat Penulisan ...................................................................
4
1.6 Sistematika Penulisan .............................................................. 4
BAB II
LANDASAN TEORI ...................................................................
6
2.1 Peubah Acak ........................................................................... 6
2.2 Nilai Ekspektasi ...................................................................... 6
2.3 Fungsi Pembangkit ................................................................. 7
2.3.1 Fungsi Pembangkit Peluang ........................................... 8
2.3.2 Fungsi Pembangkit Momen ...........................................
2.4
8
Fungsi Kepadatan Peluang .................................................... 8
2.4.1 Fungsi Kepadatan Peluang Peubah Acak Diskrit .......... 9
2.4.2 Fungsi Kepadatan Peluang Peubah Acak Kontinu ........ 9
2.5
Distribusi Poisson .................................................................. 9
2.6
Distribusi Eksponensial ......................................................... 10
2.7
Konsep Antrian .....................................................................
vi
Elyzabeth, 2014
Aplikasi Model Antrian Multiserver dengan Vacation Pada Sistem Antrian di Bank BCA
Cabang Ujung Berung
Universitas Pendidikan Indonesia | repository.upi.edu |perpustakaan.upi.edu
10
vii
2.7.1 Sejarah Teori Antrian ...................................................
10
2.7.2 Sistem Antrian ............................................................... 11
2.7.3 Struktur Antrian ............................................................. 13
2.8 Proses Markov ........................................................................ 16
2.9 Proses Birth and Death ...........................................................
17
2.10 Notasi Model Antrian ............................................................. 20
2.11 Model Antrian M/M/c ............................................................
BAB III MODEL ANTRIAN MULTISERVER DENGAN VACATION
21
28
3.1
Quasi Birth-Death (QBD) Process ......................................... 29
3.2
Antrian M/M/c dengan Multiple Asynchronous Vacation ......
31
3.2.1 Rate matrix R ...............................................................
32
3.2.2 Matriks Generator B[R] ...............................................
35
3.2.3 Banyaknya Customer dalam Sistem ............................. 36
3.2.4 Waktu Tunggu Customer dalam Sistem ........................ 38
BAB IV STUDI KASUS ............................................................................. 39
4.1 Laju Kedatangan ...................................................................
39
4.2 Laju Pelayanan ......................................................................
41
4.3 Waktu Vacation ..................................................................... 44
4.4 Faktor Utilitas Server atau Peluang Server Sibuk ................. 46
4.5 Ukuran Keefektifan Sistem ...................................................
BAB V
47
PENUTUP ..................................................................................... 58
5.1 Kesimpulan ............................................................................. 58
5.2 Saran ....................................................................................... 59
DAFTAR PUSTAKA ...................................................................................
60
LAMPIRAN .................................................................................................. 62
RIWAYAT HIDUP ......................................................................................
Elyzabeth, 2014
Aplikasi Model Antrian Multiserver dengan Vacation Pada Sistem Antrian di Bank BCA
Cabang Ujung Berung
Universitas Pendidikan Indonesia | repository.upi.edu |perpustakaan.upi.edu
83