Congestion Pricing and Queuing Theory

1. Dip. di Matematica Pura ed Applicata - Università di Padova 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 >80% during evening hours • Lottery was critical in improving operating conditions at LGA Time of day Capacity = 75 operations/hr *** from Odoni & Fan

6. Objective ofthis 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(more recent) • Applications to air transportation (fewer) • Concentrated on airport congestion • Very limited work (unpublished) on airspace side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 environment:Illustrative example

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

18. What is fair? • No formal definition available in the literature • Subjective measure • Up to the Airport Authority

19. 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 Alternative Approaches

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 (3’15’’ vs. 43’15’’) • 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) = 4:00; eta(f1) = 5:00; D(f1) = 60 m oag(f2) = 4:30; eat(f2) = 4:50; D(f2) = 20 m Exchange: oag(f1) = 4:00; eta(f1) = 4:50; D(f1) = 50 m oag(f2) = 4:30; eta(f2) = 5:00; 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