Analysis of a Single Node Service system
Salvador Moreno Carrillo
Real system & method
Real system & method
The system to be analyzed will be the Hesburger 's "order" queue in Centrālā Stacija.
Real system & method
The system to be analyzed will be the Hesburger 's "order" queue in Centrālā Stacija.
We will measure the amount of costumers that arrive and leave in a given amount of time and how much time the cashier takes to take their order and how much it will take for the order to be fulfilled.
Real system & method
The system to be analyzed will be the Hesburger 's "order" queue in Centrālā Stacija.
We will measure the amount of costumers that arrive and leave in a given amount of time and how much time the cashier takes to take their order and how much it will take for the order to be fulfilled.
We will divide the system into two subsystems: "order" s1 and "serving food" s2
Model Abstraction
Model Abstraction
Cashier
Model Abstraction
Cashier
Kitchen
Model Abstraction
Cashier
Kitchen
Model Abstraction
Cashier
Kitchen
S1
S2
Model Abstraction
Cashier
Kitchen
S1
S2
Model Abstraction
Cashier
Kitchen
S1
S2
\lambda_{sys} = \lambda_1
Model Abstraction
Cashier
Kitchen
S1
S2
\lambda_{sys} = \lambda_1
Model Abstraction
Cashier
Kitchen
S1
S2
\lambda_{sys} = \lambda_1
\mu_1=\lambda_2
Model Abstraction
Cashier
Kitchen
S1
S2
\lambda_{sys} = \lambda_1
\mu_1=\lambda_2
Model Abstraction
Cashier
Kitchen
S1
S2
\lambda_{sys} = \lambda_1
\mu_1=\lambda_2
\mu_2=\mu_{sys}
Model Abstraction
Cashier
Kitchen
Model Abstraction
Cashier
Kitchen
Queue
Server
Empirical Data
Empirical Data
- Tobs= 30 min
Empirical Data
- Tobs= 30 min
- Number of costumers that arrived = 15
Empirical Data
- Tobs= 30 min
- Number of costumers that arrived = 15
- Number of costumers that left (with their orders) = 8
Empirical Data
- Tobs= 30 min
- Number of costumers that arrived = 15
- Number of costumers that left (with their orders) = 8
- Number of costumers that ordered = 12
- Tbusy = 30 min
Model
Model
\lambda_{sys}=15/T_{obs}=15/30=1/2
jobs/min
Model
\lambda_{sys}=15/T_{obs}=15/30=1/2
jobs/min
\mu_{sys}=8/T_{busy}=8/30
jobs/min
Model
\lambda_{sys}=15/T_{obs}=15/30=1/2
jobs/min
\mu_{sys}=8/T_{busy}=8/30
jobs/min
\mu_1 = 12/30=2/5
jobs/min
T_{Busy}=T_{obs}
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
\overline{N}_{sys}=\lambda*\overline{W}_{sys}=1/2*30/8=1.875
jobs
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
\overline{N}_{sys}=\lambda*\overline{W}_{sys}=1/2*30/8=1.875
jobs
\overline{N}_{serv}=\lambda*\overline{W}_{serv}=1/2*2.5=1.25
jobs
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
\overline{N}_{sys}=\lambda*\overline{W}_{sys}=1/2*30/8=1.875
jobs
\overline{N}_{serv}=\lambda*\overline{W}_{serv}=1/2*2.5=1.25
\overline{N}_{queue}=\lambda*\overline{W}_{queue}=1/2*1.25=0.625
jobs
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
\overline{N}_{sys}=\lambda*\overline{W}_{sys}=1/2*30/8=1.875
jobs
\overline{N}_{serv}=\lambda*\overline{W}_{serv}=1/2*2.5=1.25
\overline{N}_{queue}=\lambda*\overline{W}_{queue}=1/2*1.25=0.625
jobs
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
\overline{N}_{sys}=\lambda*\overline{W}_{sys}=1/2*30/8=1.875
jobs
\overline{N}_{serv}=\lambda*\overline{W}_{serv}=1/2*2.5=1.25
\overline{N}_{queue}=\lambda*\overline{W}_{queue}=1/2*1.25=0.625
jobs
costumers=jobs
Model
\overline{W}_{sys} = 1/\mu_{sys}= 30/8
mins/job
\overline{W}_{serv}=1/\mu_1=5/2=2.5
mins/job
\overline{W}_{queue}=\overline{W}_{sys}-\overline{W}_{serv}=1.25
mins/job
\overline{N}_{sys}=\lambda*\overline{W}_{sys}=1/2*30/8=1.875
jobs
\overline{N}_{serv}=\lambda*\overline{W}_{serv}=1/2*2.5=1.25
\overline{N}_{queue}=\lambda*\overline{W}_{queue}=1/2*1.25=0.625
jobs
costumers=jobs
Analysis of a Single Node Service system
By salvador_moreno_carrillo
Analysis of a Single Node Service system
- 97
