Module 2 - Queues and waiting Lines (Part 1)

Question 1

Examples of industries with Queues

Answer 1

Hospitals, airport, banks, supermarket, entertainment parks, restaurants, call centers

Importance of call center industry
* All 500 companies have at least one call center
* Each firm has an average of 4,500 agents acrross all sites
* North american call centers: 2.9 million agents in 55,000 facilties
* 300 billion spent annually on call centers

Question 2

How to reduce delay?

Answer 2

Demand side
* Appointments/Reservation
* EZ Pass
* Fast Pass (Disney)
Both
* Surge Pricing
* Self Checkout
Supply side
* Flexible Servers (cross trained)
* Triage

Question 3

There is a way to optimize the waiting line costs.

Answer 3

Cost - Level of service (y and x diagrams)

• Optimal is the lowest point of total cost
• Decision Problem: Balance capacity cost with waiting cost

Question 4

Performance measures (5)

Answer 4

Question 5

Define the 3 parts of the Queue

Answer 5

1. System (hole process)
2. Queue
3. Serve r (service)

Question 6

How do you define a single server queue?

Answer 6

Question 7

What is the M/M/1 Queueing system and what are the assumptions?

Answer 7

The simplest queuing model

We impose assumptions:

1. Single server
2. FCFS dischipline
3. Exponential interarrival time
4. Exponential service time

Question 8

What is the Exponential service time?

Answer 8

The time it takes to serve a cusotmer follows an Exponential distribution with parameter u

Time between two successive customer arrivals follows an Exponential distribution with parameter (lambda).

Question 9

What is the formula for the probability of service time?

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Model equation of the m/m/1

Answer 12

Question 13

The graffic of a single server queuing system

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

What is the average time in th system and the system utilization?

Answer 16

Question 17

Suppose the cost of keeping a customer in the system is $5 per
minute, and the cost of having a server with capacity µ
customers per hour, is equal to $(150µ) per hour. What is the
optimal level of capacity for this system

Answer 17

Question 18

Answer 18

Question 19

2. What is the average time in the system and the system utilization?

Answer 19

Question 20

Answer 20

Question 21

Key takeways

Answer 21

• Waiting lines form due to variability
• Basic tradeoff between cost and quality
• Decision:
• Service capacity: service rate (and number of servers)
• System configuration
• Perofrmance measures
• M/M/1 model - Under Exponential service and interarrival times.
• General universal relationship (Little’s Law)