Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 10: WAITING LINE ANALYSIS AND SIMULATION (WAITING LINE ANALYSIS…
Chapter 10: WAITING LINE ANALYSIS AND SIMULATION
WAITING LINE ANALYSIS AND QUEUING THEORY
The economics of Waiting Lines Issue
Central to many service systems is waiting lines management
When the waiting person is an employee, it is easy to calculate the value of their time
When the person waiting is a guest it is very difficult to calculate the value of their time
Queuing System
The source population and the way customers arrive at the system
The servicing system
The condition of the customers exiting the system
Components of Queuing System Visually
Customers come in
Finite population: limited-size customer pool that will use the service and, at times, form a line
Infinite population: population large enough so that the population size caused by subtractions or additions to the population does not significantly affect the system probabilities
Customers are served
Customers leave
Distribution of Arrivals
Arrival rate
Constant arrival distribution: periodic, with exactly the same time between successive arrivals
Varable arrival distribution: arrivals probabilities described statistically
Exponential distribution: when arrivals at a service facility occur in a purely random fashion
Poisson distribution: where one is interested in the number of arrivals during some time period T
Arrival Characteristics
Arrival patterns
Size of arrival units
Degree of patience
Waiting Lines and Servers
Line legth
Infinite potential length
Limited capacity
Number of lines
Single
Multiple
Queue discipline
First come, first served
Shortest processing time
Reservations first
Emergencies first
Limited needs
Service Time Distribution
Constant: Service provided by automation
Variable
Service provided by humans
Described using exponential distribution
Line Structure
Single channel, single pharse
Single channel, multiphase
Multichannel, single pharse
Multichannel, multiphase
Mixed
Exiting the Queuing System
The customer may return to the source population and immediately become a copeting candidate for service again
There may be a low probability of service
SIMULATING WAITING LINES
Example: A Two- Stage Assembly Line
Data Collection
example in textbook page 242
Spreadsheet Simulation
Simulation Programs and Languages
simulation models
Continuous
Based on mathematical equations
Discrete
Occurs only at specific points
Event simulation: points in between either have no value to our simulation or cannot be computed because of the lack of some sort of mathematical relationship to link the succeeding events
Operations and supply management applications almost exclusively us discrete (event) simulation
Simulation programs
Purpose
Special Purpose
simulate specific applications
ex: provisions in the model allow for specifying the number of workcenters, their description, arrival rates, processing time, batch sizes, quantities of work in process,....
the program may allow the observer to watch the animated operation and see the quantities and flows throughout the system as the simulation is running