516 Queuing
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Transcript of 516 Queuing
Delays at DDM International Airport
Ryan HessTonisha Morris
Sandra NasilowskiPhil Sampona
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.
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
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?
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
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
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
• 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?
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
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
RESULTS
MODERATE WEATHER
Arrival Rate: 45 – 59Service Rate: 30
Servers: 2
Moderate Weather
45 46 47 48 49 50 51 52 53 54 55 56 57 58 590
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ave Time Waiting per Arrivals/hr
Total
Arrivals per hr
Tim
e W
aitin
g in
Que
ue (h
r)
Moderate Weather
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 600
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Percent Delayed by Arrivals/hr
Series1
Arrivals Per Hour
Perc
ent D
elay
ed
Moderate Weather
45 47 49 51 53 55 57 590
100
200
300
400
500
600
700
800
900
1000
Operating Costs of Wait Time
Operating Costs of Wait Time
Arrivals Per Hr
Ope
ratin
g Co
sts
Inclement Weather
Arrival Rate: 35 – 44Service Rate: 22.5
Servers: 2
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)
Inclement Weather
35 36 37 38 39 40 41 42 43 44 450
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Percent Delayed by Arrivals/hr
Arrivals Per Hour
Perc
ent D
elay
ed
Inclement Weather
34 36 38 40 42 44 460
200
400
600
800
1000
1200
1400
1600
1800
2000
Operating Cost of Waiting Time
Operating Cost of Waiting Time
Arrivals Per Hr
Ope
ratin
g Co
sts
SEVERE INCLEMENT WEATHER
Arrival Rate: 20 – 29Service Rate: 30
Servers: 1
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)
Severe Weather
20 21 22 23 24 25 26 27 28 29 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Percent Delayed by Arrivals/hr
Arrivals Per Hour
Perc
ent D
elay
ed
Severe Weather
20 21 22 23 24 25 26 27 28 29 300
200
400
600
800
1000
1200
1400
1600
1800
2000
Operating Costs by Wait Time
Severe Weather
Planes per hr
Ope
ratio
n Co
sts (
dolla
rs)
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
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.