The resource allocation problem to mitigate the demand-capacity imbalance by allo- cating ground delays, in other words slots, to the flights is well known in the literature as the Ground Holding Problem (GHP). Under CDM, the FAA initially allocates the available capacity during a GDP to the airlines with a procedure called the Ration- By-Schedule (RBS). Next, the FAA provides a medium for inter-airline exchange of slots using procedures like Compression and Slot Credit Substitution. The following description of these procedures are as described by Vossen and Ball [VB05].
The RBS algorithm is used to ration the arrival slots among the airlines on a first-scheduled-first-served basis by pushing back the arrival schedule to match the capacity. The strength of RBS is that it is very easy to implement, it is local and decentralized by airport and it is accepted by the airlines. The details of RBS are as follows:
Algorithm 5.2.1. Ration-By-Schedule.
1. Order the flights by their original scheduled time of arrival.
2. Select the first flight with an unassigned slot. If none exists, the algorithm terminates. Otherwise, assign the flight the first unassigned slot considering its scheduled time of arrival.
The rationale behind slots being assigned based on scheduled arrival time as op- posed to the most recent estimated arrival time (which could be different from sched- uled arrival time because of various uncertainties) is that airlines are then not penal- ized for reporting a delay or cancellation (which is what happened prior to CDM in the Grover Jack approach [VB05]).
Vossen and Ball in [VB05] show that RBS, in fact, lexicographically minimizes the maximum ground delays allocated to the different flights. In practice, RBS also accounts for flights that are already airborne and those that are exempted from the GDP (for example, international flights, some long-haul flights) and respects the al- locations of prior GDPs that were executed. The result of the RBS is an assignment of slots to airlines rather than to flights. Hence after this initial allocation, airlines are free to reschedule flights according to their private objectives through substitu- tions and cancellations. Substitutions and cancellations are very important from the standpoint of an airline. Vossen and Ball provide empirical results from actual GDPs showing that the number of substitutions and cancellations can be very large [VB06]. Substitutions and cancellations create gaps (open slots) in the arrival schedule. The utilization of the runway is improved using the Compression procedure that essentially moves flights up in the schedule to fill the open slots. The airlines have an incentive to provide information regarding open slots as they are in some sense “paid back” for the slots they release by getting priority for the next available slots that they are able to use. Compression is in fact a very simple inter-airline exchange mechanism premised on the principle that airlines like to schedule any flight as early as possible, with constraints restricting the new schedule no earlier that the original scheduled flight arrival times, that is, the earliest arrival time. The details of the compression algorithm (which is run periodically) is given below.
Algorithm 5.2.2. Compression. The following steps are performed for each open slot s in the sequence of open slots, C, based on the current schedule. We refer to the owner of the slot s as As. We begin with the first open slot.
1. Check if any flight, f , of As can be moved up to slot s respecting its earliest
arrival time. If there exists no such flight, go to step 2; otherwise swap the slot assignments of flight f to slot s and repeat step 2 for the newly vacated slot, denoted by sf, whose owner continues to be As.
2. Determine the first flight f0 in the schedule that belongs to another airline that
Slot B2 - 1.04 A3 - 1.06 B1 - 1.02 1 - 1.00 A2 - 1.01 C1 - 1.03 C2 - 1.05 A1 - 1.00 2 - 1.02 3 - 1.04 4 - 1.06 5 - 1.08 6 - 1.10 7 - 1.12
Flight, EAR Slot
1 - 1.00 2 - 1.02 3 - 1.04 4 - 1.06 5 - 1.08 6 - 1.10 7 - 1.12 B2 - 1.04 B1 - 1.02 A2 - 1.01 C1 - 1.03 C2 - 1.05 A1 - 1.00 A3 - 1.06 Flight, EAR
RBS Allocation Compression Assignment
Figure 5-2: Illustration of the compression procedure
go to step 3; otherwise swap the slot assignment of flight f0 to slot s and repeat
step 2 with vacated slot sf0 whose new owner is As.
3. If no flight can be assigned to slot s, return to step 2 with the next open slot in C.
In Fig. 5-2, we illustrate an example of the compression algorithm implemented over an RBS allocation. In this example, A,B and C represent three different airlines with the earliest arrival time (EAR) as shown. We consider a scenario in a GDP where the time taken to land an aircraft doubles, from 1 to 2 minutes. RBS allocates the slots to the airlines by simply pushing the schedule down in time. We illustrate the compression algorithm when airline A cancels flight A2. The compression algorithm moves B1 and C1 up by one slot because of the following reasons: A3 does not arrive before 1.06; B1 arrives at 1.02; and C1 arrives at 1.04. A3 has a priority over every released slot and is allocated to the slot at 1.06 released by C1.
With compression, the slots that an airline cannot use are exchanged it in such a way that all airlines receive a reduction in delay. However, there are some key disadvantages of the compression procedure:
1. Compression requires a central authority like the FAA to run the procedure periodically (in discrete time-intervals not continuously) in real-time. Because it is not run continuously, traffic managers use the vacant slots of cancelled
flights during the time-interval to schedule general aviation flights that are not scheduled and do not compress often as the slots are occupied.
2. Compression lacks expressiveness being an inter-airline exchange. As a simple example, an airline cannot state explicitly what slot it needs in return for giving up a particular slot. In Chapter 2, we discussed that airlines have a non-linear value for the slots over which they operate. This means they would be interested in a group of slots more than the individual pieces allocated separately. This is because airlines operate as a network and different elements of the network interact with each other and hence it might be essential to get all or none of the slots. See example in Chapter 2. The same applied even to the case of the inter-airline exchange.
3. An airline has no guarantee when it cancels a slot that any of its other delayed flights will be moved up. Though there is a priority, there is no guarantee that this indeed will happen. Hence, airlines must cancel flights without the knowl- edge of the particular trade-offs being made. In the language of mechanism design, this is called the exposure problem i.e., the airline is exposed to the risk of cancelling a plane without receiving something in return.
To overcome some of these disadvantages, a more dynamic form of compression, called the Slot Credit Substitution (SCS)[How01], is currently in place. Under SCS, airlines can submit a “conditional cancellation” request of the form: “I am willing to release slot at time t1 by cancelling the flight f1, if I can move flight f2 up into
slots between time interval (t2, t3)”. The FAA examines available flights in the time
range t1 to t3 and tries to move a sequence of flights into earlier slots (including that
at t1) to get a later slot (between t2 and t3) for the requesting airline. The FAA
monitors such requests on a continuous basis, thereby implementing a continuous real-time compression procedure. SCS also provides increased trading opportunities over compression (i.e., more expressive than compression) because of the continuous response as well as the conditional nature of the requests. However, because SCS is limited to a 1-for-1 trading scheme, it has limited expressiveness and continues to
have the exposure problems when airlines prefer more complex schemes, for example, a 2-for-2 trade, which they must submit as two 1-for-1 trades.
Since March 2007, an adaptive compression procedure has been in effect [BE04]. This is essentially the compression algorithm running continuously in real-time, with airlines having the ability to control the flights that are a part of the adaptive proce- dure. The benefit of this procedure is that scheduled flights always get priority over flights that are not scheduled (general aviation) unlike the regular compression proce- dure that fitted them in the vacated slots before running the compression algorithm.