516 Queuing

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Delays at DDM International Airport Ryan Hess Tonisha Morris Sandra Nasilowski Phil Sampona

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Transcript of 516 Queuing

Page 1: 516 Queuing

Delays at DDM International Airport

Ryan HessTonisha Morris

Sandra NasilowskiPhil Sampona

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Queuing Theory

• Queuing= waiting lines– Orderly fashionElements of a queue

• Arrivals that need service of some kind.• Service facilities that take care of the arrivals.• The queue, where the arrivals wait until they can be serviced.

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Queuing TheoryExamples of Queuing

M/M/1: • This is the simplest queuing system to analyze. Here the arrival and service time

are negative exponentially distributed (Poisson process). The system consists of only one server. This queuing system can be applied to a wide variety of problems as any system with a very large number of independent customers can be approximated as a Poisson process

M/D/n: • Here the arrival process is Poisson and the service time distribution is

deterministic. The system has n servers. (e.g. a ticket booking counter with n cashiers) Here the service time can be assumed to be same for all customers)

G/G/n: • This is the most general queuing system where the arrival and service time

processes are both arbitrary. The system has n servers. No analytical solution is known for this queuing system

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Queuing TheoryExamples of Queuing

Arrivals• Shoppers• Patients• Customers• Machine breakdowns• Finished goods• Pharmaceuticals• Airplanes• Telephone calls

Arrivals Factors• Arrival distribution

– When do new customers arrive? At random? In groups or singly?

• Size of population from which customers are drawn – Is the population effectively infinite

or is it small enough that each arrival means one less new customer in the future?

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Queuing TheoryExamples of Queuing

Servers• Clerks• Doctor• Operating teams• Stock• Repair persons• Dealer• Pharmacy in hospital• Runways• Circuits• Fire fighters

Service factors• Service time distribution

– how long it takes to serve an arrival

• Number of parallel channels or servers – how many checkout

counters at the grocery store

• How many stages of service there are

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Queuing TheoryExamples of Queuing

The Queue• Checkout line• In waiting room• Waiting list• Back orders• Broken machines• Inventory• Stack in air• Uncompleted calls• Burning buildings

Queue factors• How many queues --

one or more than one?• Service priority among

customers. – Possibilities include first

come first served

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Airport Conditions in Good Weather

• Capacity of 120 planes per hour• # of arrivals = # of departures• 3 runways in operation, 2 runways used for arrivals• 45-60 arrivals per hour• Cost of Delays– $350 per plane per hour for a 19 seat plane– $1500 for a 150 seat plane– $600 for regional jets– Passenger cost of waiting is $25 per hour

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• Delayed flight is one arriving or departing 15 minutes past schedule

• 70% plane capacity• Describe the operating conditions, average

delay times (i.e. waiting times), and operational and passenger delay costs – What proportion of flights will be delayed?

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Inclement Weather

• In bad weather– 2 runways for both arrival and departure– Capacity of 45 planes per hour

• Severe Weather– 10 days per year– 1 runway for both arrivals and departures– Capacity of 30 planes per hour

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Problem

• Describe relevant operating conditions for these moderate and severe weather conditions and associated costs for the three types of planes. – proportion of flights will be delayed?

• What would happen if an additional runway costing $1 million was built– Should it be built?– Most efficient use of it?

• Assuming 18 hour days and 365 operating days

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RESULTS

MODERATE WEATHER

Arrival Rate: 45 – 59Service Rate: 30

Servers: 2

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Moderate Weather

45 46 47 48 49 50 51 52 53 54 55 56 57 58 590

0.1

0.2

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0.5

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0.9

1

Ave Time Waiting per Arrivals/hr

Total

Arrivals per hr

Tim

e W

aitin

g in

Que

ue (h

r)

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Moderate Weather

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 600

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Percent Delayed by Arrivals/hr

Series1

Arrivals Per Hour

Perc

ent D

elay

ed

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Moderate Weather

45 47 49 51 53 55 57 590

100

200

300

400

500

600

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1000

Operating Costs of Wait Time

Operating Costs of Wait Time

Arrivals Per Hr

Ope

ratin

g Co

sts

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Inclement Weather

Arrival Rate: 35 – 44Service Rate: 22.5

Servers: 2

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Inclement Weather

35 36 37 38 39 40 41 42 43 440

0.2

0.4

0.6

0.8

1

1.2

Ave Waiting Time per Plane per Hour

Total

Arrivals & Departures / hr

Wai

ting

Tim

e (h

r)

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Inclement Weather

35 36 37 38 39 40 41 42 43 44 450

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Percent Delayed by Arrivals/hr

Arrivals Per Hour

Perc

ent D

elay

ed

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Inclement Weather

34 36 38 40 42 44 460

200

400

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1000

1200

1400

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Operating Cost of Waiting Time

Operating Cost of Waiting Time

Arrivals Per Hr

Ope

ratin

g Co

sts

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SEVERE INCLEMENT WEATHER

Arrival Rate: 20 – 29Service Rate: 30

Servers: 1

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Severe Weather

20 21 22 23 24 25 26 27 28 290

0.2

0.4

0.6

0.8

1

1.2

Percent Delayed by Planes/hr

Total

Number of Planes per hr

Wai

t Tim

e (h

r)

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Severe Weather

20 21 22 23 24 25 26 27 28 29 300

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Percent Delayed by Arrivals/hr

Arrivals Per Hour

Perc

ent D

elay

ed

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Severe Weather

20 21 22 23 24 25 26 27 28 29 300

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400

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1000

1200

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Operating Costs by Wait Time

Severe Weather

Planes per hr

Ope

ratio

n Co

sts (

dolla

rs)

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Costs

Plane Rate Normal With Extra Strip Savings/hr Days Total SavingsNormal 55 324.45 18.03 306.42 255 1406467.8Moderate 40 306.43 18.03 288.4 100 519120Severe 25 306.43 18.03 288.4 10 51912

Total Savings $ 1,977,499.80 / year

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Recommendations

• With the savings being nearly $2 million per year, it is a no-brainer to add another runway.

• The most efficient way to use the new runway would be for departures when all runways are in use.

• During inclement weather it would be use for both arrivals and departures.