From Simio and Simulation: Modeling, Analysis, Applications

Chapter 5 Problem # 1

What is the difference between an object propery and an object state?

An object property is a value that is specified when an object is instantiated in a model. These are input by the user to customize a given object’s behavior. Properties are part of the Object Instance and do not change definition during runtime. Examples would be service time or interarrival time.

In contrast, an object state is a dynamic value that can change during a model’s execution. An object state is part of the Object Runspace and can be associated with an object and the model. States have two categories – Discrete and Continuous.

Chapter 5 Problem # 2

Consider a process associated with a Server object. What is the difference between a token’s parent object and its associated object?

In this scenario the token’s parent object would be a server object whereas its associated object is a separate object that triggered the process to execute.

Chapter 5 Problem # 3

Develop a queueing model that gives the steady-state values analogous to the values in Table 5.2 (Model 5-1 with exponential processing times at both stations.)

Simulation execution using existing Model 5-1 to produce initial results.

Metric being estimated Simulation
Placement Utilization (\(\rho_p\)) 0.66763 \(\pm\) 0.0024
Inspection Utilization (\(\rho_i\)) 0.500536 \(\pm\) 0.0018
Number in system (L) 1.8487 \(\pm\) 0.0175
Time in system (W) 0.184631 \(\pm\) 0.0012
Avg Number Good Parts 9205.4 \(\pm\) 34.5877
Avg Number Bad Parts 806.32 \(\pm\) 12.3569

The results above a consistent with the results listed in Table 5.3

Simulation execution using exponential processing times

  • Processing time for Placement Server = Random.Exponential(4)
  • Processing time for Inspection Server = Random.Exponential(3)
Metric being estimated Simulation
Placement Utilization (\(\rho_p\)) 0.666207 \(\pm\) 0.0041
Inspection Utilization (\(\rho_i\)) 0.497866 \(\pm\) 0.0031
Number in system (L) 2.99228 \(\pm\) 0.0596
Time in system (W) 0.299688 \(\pm\) 0.0052
Avg Number Good Parts 9178.48 \(\pm\) 44.5022
Avg Number Bad Parts 803.28 \(\pm\) 11.4010

Chapter 5 Problem # 4

Consider an office where people come to get their drivers’ license.

The process involves three steps for arriving customers – reception/application; a vision exam; and a written exam.
Assume that customer arrivals are Poisson with a rate of 6 per hour (i.e., interarrival times are exponentially distributed with mean 10 minutes).

The processing time distributions for the three processes are given by Table 5.8.

Process Processing time distribution
Reception/Application triangular(5, 8, 11)
Vision Exam triangular(2, 4, 6)
Written Exam triangular(15, 15, 30)

Assume that the office opens at 9:00 am and closes at 5:00 pm.

Performance Metrics of interest:

  • time that the customers spend in the system
  • utilization of the office employees
  • utilization of the computer stations
  • average and maximum numbers of customers in the reception/application queue
  • average and maximum numbers of customers in the vision exam queue
  • average and maximum numbers of customers in the written exam queue

Simio Model

Results

On average, we’re seeing a customer spend about 46 minutes in system. Utilization of the reception employee is approximately 78% while the employee manning the vision exam station has a utilization of 38%.

All the computer exam stations have a utilization of 51% - 52% each.

The reception station appears to be the area where the most waiting in queue occurs with an average number in queue at 1.2 customers and a maximum of 5.1 customers.

The vision queue has an average of 0 customers waiting and a maximum of 1 customer. These numbers are similar for the computer stations at 0 and 1, respectively.

I ran 6 different scenarios with increasing numbers of executions from 50, 100, 500, 1000, 2500, annd 3000.

I would feel confident in the results using the 2500 - 3000 range of replications. It’s in this range that we see the half widths begin to converge.

Simio model is located here: https://github.com/kfolsom98/DATA604/blob/master/Week6/Model_05_04.spfx

Chapter 5 Problem # 5

Animate the model from Problem 4.