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Congestion Pricing and Queuing Theory

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Airline Comments. Priority based on accrued delay rewards poor airline performance! ... What about encouraging provision of up-to-date flight status information?? 28 ... – PowerPoint PPT presentation

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Title: Congestion Pricing and Queuing Theory


1
Congestion Pricing and Queuing Theory
  • Giovanni Andreatta and Guglielmo Lulli

2
Demand versus Capacity
  • Fast and steady increase of demand (up
    to 11 September 2001 ...)
  • Modest increase of capacity
  • Need to address demand

3
Demand Management Strategies should
  • Limit demand for access to busy airfields and/or
    congested airspace
  • Modify temporal (and/or spatial) distribution of
    demand

4
LGA demand before and after the lottery
Scheduled operations per hour on weekdays
  • Scheduled operations reduced by 10 (from 1,348
    to 1,205/day)

Capacity of 75/hr does not include allocation of
six slots for g.a. operations
Time of day, e.g. 5 0500 - 0559
from Odoni Fan November 2000 as a
representative profile prior to slot lottery at
LaGuardia August 2001 as a representative after
slot lottery Source Official Airline Guide
5
Small reduction in demand may lead to dramatic
reduction in delays
Minutes of delay per operation
  • Average delay reduced by gt80 during evening
    hours
  • Lottery was critical in improving operating
    conditions at LGA

Time of day
Capacity 75 operations/hr
from Odoni Fan
6
Objective of this presentation
  • Use queue theory models to show the possible
    benefits of the demand management approach
  • Highlight fairness/equity issues
  • Investigate different approaches (mix of
    administrative and market-based measures)
  • Provide a demonstration of the approaches through
    an example

7
What has already been done
  • Peak period pricing in general (widely
    investigated)
  • Applications to congestion-pricing of
    transportation facilities (more recent)
  • Applications to air transportation (fewer)
  • Concentrated on airport congestion
  • Very limited work (unpublished) on airspace side

8
Airport environmentIllustrative example

9
(No Transcript)
10
Case 1 No congestion fee
11
Congestion pricing
  • (One) Objective of congestion pricing (or
    auctions) operators should pay a price for
    using a slot that is at least equal to the
    marginal cost of using that slot ?
  • flights scheduled during high demand periods will
    be high revenue flights, e.g. large passenger
    loads, high paying customers or

12
Optimal congestion fee
  • A congestion fee on a user is optimal when it is
    equal to the external costs that the user imposes
    on the other users.
  • For a M/G/1 queue
  • Marginal Internal External
  • cost cost cost



13
  • MC Marginal Cost
  • c (delay) cost per unit time per customer
  • Wq Expected queuing time per customer
  • l demand rate

14
System of non-linear equation
15
Optimization Model
16
Case 2 Optimal congestion fee

17
(No Transcript)
18
What is fair?
  • No formal definition available in the literature
  • Subjective measure
  • Up to the Airport Authority

19
Alternative Approaches
  • Two-phase (choose PST)
  • No economic interpretation
  • Constrained market-based
  • Bounds on the minimum PST are imposed
  • Intra-class congestion fee
  • Reduced external costs
  • Implement different concepts of fairness

20
Comparison of the cases
21
Comparison of the cases (ctd.)
22
Comments
  • We analyze other pricing structures
  • Constrained market-based provides balanced PST
  • Market-based mechanism
  • When demand is dynamic, use DELAYS instead of
    Queuing Theory
  • Estimation of demand functions li(x)
    (challenging problem!)
  • MbDM approaches are as much political and
    institutional as they are technical the proposed
    analysis can provide significantly more
    quantitative details.

23
Thanks !
24
Comparison between the two cases
  • By charging a congestion fee equal to the
    external delay costs, we have
  • Reduced the utilization of the runway system
    (89.9 vs. 99.2)
  • Greatly reduced the average delay per aircraft
    (315 vs. 4315)
  • Greatly reduced the delay costs per aircraft
    (135 from 1802, 54 from 721, 22 from 288)
  • Augmented the no. of pax per hour (9600 vs. 5900)

25
Equity Metrics aka Measures of Dispersion
  • The following measures are suggested for
    measuring the equity of the distribution of funds
    to school districts
  • Variance squared deviation from the mean
    related measure -- coefficient of variation
    square root of variance divided by mean
  • Gini coefficient average difference between
    each pair of values divided by two times the
    mean.
  • McLoone coefficient -- assesses equity in the
    lower half of a distribution average of the
    difference between the median and the value of
    each element below the median (oriented toward
    distribution of money assumes lower half is worse
    half should change to upper half for delay
    allocation).
  • Assumption perfect equity ? each claimant
    receives same allocation

26
Reducing dispersion and pair-wise comparison
principle
  • 1st solution can be improved using the
    following type of exchange
  • oag(f1) 400 eta(f1) 500 D(f1) 60 m
  • oag(f2) 430 eat(f2) 450 D(f2) 20 m
  • Exchange
  • oag(f1) 400 eta(f1) 450 D(f1) 50 m
  • oag(f2) 430 eta(f2) 500 D(f2) 30 m
  • Average delay is same 80/2 40 m but
    dispersion is less
  • Note that this exchange represent a pair of
    flights that do not satisfy the pair-wise
    comparison principle
  • if flight f has been assigned t units of delay,
    it should not be possible to reduce the delay
    assigned to f without increasing the delay
    assigned to another flight a value of t or
    higher.

27
Airline Comments
  • Priority based on accrued delay rewards poor
    airline performance!!
  • ? airlines that have late departures (due to
    their own inefficiencies) are given priority
    later.
  • Devise systems that allows airlines to compete by
    rewarding better performance and better internal
    management systems
  • But
  • RBS has this same property
  • What about encouraging provision of up-to-date
    flight status information??

28
Resource Allocation Concept Balance Major
Traffic Flow Categories
  • Need to balance major flow categories
  • Possible balance criterion proportional to
    historical traffic flows
  • Can be throughput/fairness tradeoff
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