Queuing Theory
Waiting Line Models
The Structure of a Waiting Line System
Queuing Systems
Queuing System Input Characteristics
Queuing System Operating Characteristics
Analytical Formulas
Single-Channel Waiting Line Model with Poisson
Arrivals and Exponential Service Times
Multiple-Channel Waiting Line Model with Poisson
Arrivals and Exponential Service Times
Economic Analysis of Waiting Lines
Slide 1
Structure of a Waiting Line System
Queuing theory is the study of waiting lines.
Four characteristics of a queuing system are:
•the manner in which customers arrive
•the time required for service
•the priority determining the order of service
•the number and configuration of servers in the system. Slide 2
Structure of a Waiting Line System
Distribution of Arrivals
•Generally, the arrival of customers into the system is a random event.
•Frequently the arrival pattern is modeled as a
Poisson process.
Distribution of Service Times
•Service time is also usually a random variable.
•A distribution commonly used to describe service time is the exponential distribution.
Slide 3
Structure of a Waiting Line System
Queue Discipline
•Most common queue discipline is first come, first served (FCFS).
•An elevator is an example of last come, first served
(LCFS) queue discipline.
•Other disciplines assign priorities to the waiting units and then serve the unit with the highest priority first.
Slide 4
Structure of a Waiting Line System
Single Service Channel
Customer
arrives
Waiting line
Multiple Service Channels
System
S1
Customer leaves System
S1
Customer
arrives
Waiting line
S2
Customer leaves S3
Slide 5
Examples of Internal Service Systems
That Are Queueing Systems
Type of System
Customers
Server(s)
Secretarial services
Employees
Secretary
Copying services
Employees
Copy machine
Computer programming
The Structure of a Waiting Line System
Queuing Systems
Queuing System Input Characteristics
Queuing System Operating Characteristics
Analytical Formulas
Single-Channel Waiting Line Model with Poisson
Arrivals and Exponential Service Times
Multiple-Channel Waiting Line Model with Poisson
Arrivals and Exponential Service Times
Economic Analysis of Waiting Lines
Slide 1
Structure of a Waiting Line System
Queuing theory is the study of waiting lines.
Four characteristics of a queuing system are:
•the manner in which customers arrive
•the time required for service
•the priority determining the order of service
•the number and configuration of servers in the system. Slide 2
Structure of a Waiting Line System
Distribution of Arrivals
•Generally, the arrival of customers into the system is a random event.
•Frequently the arrival pattern is modeled as a
Poisson process.
Distribution of Service Times
•Service time is also usually a random variable.
•A distribution commonly used to describe service time is the exponential distribution.
Slide 3
Structure of a Waiting Line System
Queue Discipline
•Most common queue discipline is first come, first served (FCFS).
•An elevator is an example of last come, first served
(LCFS) queue discipline.
•Other disciplines assign priorities to the waiting units and then serve the unit with the highest priority first.
Slide 4
Structure of a Waiting Line System
Single Service Channel
Customer
arrives
Waiting line
Multiple Service Channels
System
S1
Customer leaves System
S1
Customer
arrives
Waiting line
S2
Customer leaves S3
Slide 5
Examples of Internal Service Systems
That Are Queueing Systems
Type of System
Customers
Server(s)
Secretarial services
Employees
Secretary
Copying services
Employees
Copy machine
Computer programming