1. Queuing Systems
63.210
Don Sutton

2. Why Waiting Lines
Random Arrivals
Service Time Distribution

3. Cost Trade-off
Wait Cost
Service Cost

4. Characteristics of a Queuing System
Arrival Characteristics
Calling population
Pattern of arrivals
Arrival behavior
Waiting Line Characteristics
Queue length
Queue discipline
Static or dynamic

5. Characteristics of a Queuing System (cont)
Service Facility Characteristics
Queuing Configuration
Service Time Distribution

6. Operational Characteristics
Key variables
λ - mean number of arrivals per time period
μ – mean number of people or items serviced per time period
Definitions
L = the average number of customers or units in the system
W = the average time a customer spends in the system

7. Operational Characteristics (cont)
Definitions (cont)
Lq = The average number of customers in the queue
Wq – The average time a customer spends waiting in the queue
ρ = the probability that the service facility is being used
Po = the probability that no one is in the system

8. Different equations for the operational characteristics for each model
Two Queuing Models
Single channel
Multiple channel
Different equations for the operational characteristics for each model