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Matakuliah
Tahun
: J1186 - Analisis Kuantitatif Bisnis
: 2009/2010
SISTEM ANTREAN
Pertemuan 12
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Framework
•
•
•
•
Sistem Antrean Ganda
Beda Antrean Tunggal dan Ganda
Populasi dan Sistem Antrean Ganda
Masalah Bisnis dan Aplikasi Model Antrean Ganda
Bina Nusantara University
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Antrean Tunggal vs Antrean Ganda
Service system
Arrivals
Queue
Service
facility
Served
units
Service
facility
Model Antrean Tunggal
Bina Nusantara University
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Antrean Tunggal vs Antrean Ganda
Service system
Arrivals
Queue
Service
facility
Service
facility
Service
facility
Service
facility
Served
units
Model Antrean Ganda
Bina Nusantara University
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Aplikasi : Model Antrean Ganda
Rumus :
Probabilitas tidak ada Pelanggan
dalam Sistem
P0 
Bina Nusantara University
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M 1 1  λ  n  1  λ  M Mμ
     
 
 n 0 n!  μ   M!  μ  Mμ  λ


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Aplikasi : Model Antrean Ganda
Rumus :
Rata-rata Jumlah Pelanggan dalam Sistem
M

 




Ls 
P
M  ! M    
Bina Nusantara University
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Aplikasi : Model Antrean Ganda
Rumus :
Waktu rata-rata yang dibutuhkan di dalam
Sistem
M
  



Ws 
P 
M  !M   

Bina Nusantara University
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Aplikasi : Model Antrean Ganda
Rumus :
Waktu rata-rata yang dibutuhkan di dalam
Antrean dan dalam Sistem
L q  Ls



Wq  Ws
Bina Nusantara University



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Soal Latihan
Average arrival rate is 10 per hour. Average service
time is 5 minutes for each of 2 servers.
 = 10/hr,  = 12/hr, and S=2
Q1: What is the average wait in the system?
Ws =
412
= 0.1008 hours = 6.05 minutes
2
2
4(12) -(10)
Bina Nusantara University
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 = 10/hr,  = 12/hr, and S=2
Q2: What is the average wait in line?
(10)2
Wq =
= 0.0175 hrs = 1.05 minutes
12 (212 + 10)(212 - 10)
Also note:
1
Ws = Wq + 
1
so Wq = W s
 = 0.1008 - 0.0833 =0.0175 hrs
Bina Nusantara University
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 = 10/hr,  = 12/hr, and S=2
Q3: What is the average number of customers in line
and in the system?
L q =  Wq = 10/hr  0.0175 hr = 0.175 customers
L s =  Ws = 10/hr  0.1008 hr = 1.008 customers
Bina Nusantara University
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 = 10/hr and  = 12/hr
Q4: What is the fraction of time the system is empty
(server is idle)?
P0 =
212 - 10
= 41.2% of the time
212 + 10
Bina Nusantara University
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