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
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