1. WAITING LINES AND SIMULATION
PART SEVEN
WAITING LINES AND SIMULATION
Chapter Nineteen
Waiting Lines
Chapter 19 Supplement
Simulation

2. Chapter 19
Waiting Lines

3. Goal of queuing analysis is to minimize the sum of two costs
Waiting Lines
Queuing theory: Mathematical approach to the analysis of waiting lines.
Goal of queuing analysis is to minimize the sum of two costs
Customer waiting costs
Service capacity costs

4. Implications of Waiting Lines
Cost to provide waiting space
Loss of business
Customers leaving
Customers refusing to wait
Loss of goodwill
Reduction in customer satisfaction
Congestion may disrupt other business operations

5. Queuing Analysis Figure 19-1 Cost Service capacity Optimum Total cost
Customer
waiting cost
Capacity
cost = +
Total cost
Cost
Cost of service capacity
Cost of customers
waiting
Service capacity
Optimum

6. System Characteristics
Population Source
Infinite source: customer arrivals are unrestricted
Finite source: number of potential customers is limited
Number of observers (channels)
Arrival and service patterns
Queue discipline (order of service)

7. Elements of Queuing System
Arrivals
Service
Waiting
line
Exit
Processing
order
System

8. Queuing Systems
Multiple channel
Multiple phase

9. Poisson Distribution
Figure 19-4

10. System Performance Measured by: Average number of customers waiting
Average time customers wait
System utilization
Implied cost
Probability that an arrival will have to wait

11. Waiting Time vs Utilization
Figure 19-6
System Utilization
Average number on time waiting in line
100%

12. Queuing Models: Infinite-Source
Single channel, exponential service time
Single channel, constant service time
Multiple channel, exponential service time
Multiple priority service, exponential service time

13. Queuing Models Single channel, exponential service time
Single channel, constant service time
Multiple channel, exponential service time
Multiple priority service

14. Priority Model Arrivals Service Waiting line Exit Processing order
System 1 2 3
Arrivals are assigned
a priority as they arrive

15. Finite-Source Formulas
Table 19-6
Average number being served
Service factor
Average number waiting
Average waiting time
Average number running
Number in population

16. Finite-Source Queuing
Not waiting or
being served
Waiting
Being
served J L H U W T