QueueingTheory

Average person spends almost 6 months of their lifetime in queues; 3

days a year.

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?

Underground bunker (Disney Operational Command Center) beneath Cinderella Castle.

Team dedicated to waiting times.

Festival Toilets

You are organising a festival.

5000 people will be attending and it will last 7 hours.

How many toilets do you need?

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.

http://www.the-latest.com/sites/default/files/images/2818728350_dc4ea96906.jpg

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.

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.

Customer Arrival Time

Service Start Time

Wait Time

Finish Time

A 0

B 1

C 8

D 9

E 10

F 11

G 11

H 12

I 12

J 12

K 15

L 15

M 17

N 18

1 Queue 2 QueuesCustomer Arrival

TimeService

Start TimeWait Time

Finish Time

A 0

B 1

C 8

D 9

E 10

F 11

G 11

H 12

I 12

J 12

K 15

L 15

M 17

N 18

Additional slide