1. Queueing Theory Average person spends almost 6 months of their lifetime in queues; 3 days a year.

2. Examples of Queues What’s the longest you’ve waited in line for something? Has anybody left a queue early because it was taking too long?

3. Underground bunker (Disney Operational Command Center) beneath Cinderella Castle. Team dedicated to waiting times.

4. Festival Toilets You are organising a festival. 5000 people will be attending and it will last 7 hours. How many toilets do you need?

6. Aim Aim of all queues is to serve “customers” as quickly as possible. Waiting times depend on: Demand/arrival rate (how many people are there) Service time (how long does it take to serve a customer) To reduce waiting times we need more staff/checkouts.

8. Class Investigation Should the local supermarket change from a queueing system with multiple queues to one with a single queue? We will simulate both queueing systems using 2 servers and compare the mean wait times.

9. Simulation Simulation is a technique used extensively in business to aid the planning of new processes and investigate better ways of working current systems Cost: much cheaper to run a computer simulation than to experiment with a store in real world. Time: simulate long periods of time in seconds. Experiment: easy to change many different factors to see what effect they have.

10. Customer Arrival Time Service Start Time Wait Time Finish Time A0 B1 C8 D9 E10 F11 G H12 I J K15 L M17 N18 1 Queue 2 Queues Customer Arrival Time Service Start Time Wait Time Finish Time A0 B1 C8 D9 E10 F11 G H12 I J K15 L M17 N18

12. Additional slide