Giovanni Andreatta

AIRCRAFT FLOW MANAGEMENT UNDER CONGESTION

Airport congestion is one of the main causes of costly aircraft delays. Sometimes costs may be reduced by imposing on some aircraft a delay at take off time in order to later avoid a more expensive airborne delay. The objective of the Flow Management Problem (F.M.P.) is to find an optimal delay strategy so that the total expected delay cost is minimized. In this paper an idealized and greatly simplified version of F.M.P. is investigated. In particular the airways network considered is star-shaped and congestion is allowed only in the central (arrival) airport. For this particular version a model is presented and a polynomial solution algorithm is derived. Landing priorities among aircraft can also influence the total expected delay cost: the optimal priority rule for our version of the F.M.P. is derived. Another algorithm is presented for the case where the number of aircraft not to be delayed on the ground is given a priori. Possible extensions of the proposed model to more realistic situations are mentioned.

Stochastic shortest paths with recourse

This paper considers Stochastic Shortest Path (SSP) problems in probabilistic networks. A variety of approaches have already been proposed in the literature. However, unlike in the deterministic case, they are related to distinct models, interpretations and applications. We have chosen to look at the case where detours from the original path must be taken whenever the “first-choice” arc fails. The main results obtained include the proof of some counterintuitive facts (e.g., the SSP may contain a cycle), the proof of the validity of applying stochastic programming to this problem and the proof that the computational complexity of a particular SSP problem is polynomial.

An operations research model for the evaluation of an airport terminal: SLAM (simple landside aggregate model)

The Simple Landside Aggregate Model (SLAM) is a model for estimating capacity and delays in airport passenger terminals. SLAM is designed to answer “what if†questions about alternative configurations of the various processing and holding facilities in a terminal. It consists of a network of modules, one for each facility of the terminal. These modules are based on a set of quite simple mathematical formulas to be used for the estimation of the capacity of each facility (in terms of passengers per hour) and the level of service (LOS) associated with it. LOS is quantified both in terms of “space available per facility occupant†and waiting time for being processed.

Estimation of Finite Population Properties When Sampling is without Replacement and Proportional to Magnitude

Abstract Geologists often evaluate aggregate volumes of discovered plus undiscovered oil and/or gas in a petroleum basin by use of geologic-volumetric methods. Although sophisticated geological reasoning may be employed, the essential idea behind these methods is simple: estimate (a) the volume of hydrocarbon bearing sediment in the basin, (b) the amount of hydrocarbons present per unit volume of sediment, and (c) the fraction of hydrocarbons present per unit volume that is technologically recoverable. The product of (a) and (b) is interpretable as a point estimate of the sum of amounts of oil and gas in place in individual oil and gas deposits (fields) in the basin. The product of (a), (b), and (c) is a point estimate of amounts of oil and gas recoverable from all individual deposits in the basin.

Models for the Ground Holding Problem

Traffic congestion has become pervasive in the most developed air transportation systems in the world, i.e., those. of North America, Western Europe and East Asia. While the available statistics on the magnitude of air traffic delays are not very precise, there is no doubt that the total direct and indirect costs of these delays are very large. If one combines the various numbers reported, worldwide direct airline costs may add up to

Properties of the k-centra in a tree network

5 billion or more per year. By comparison the world’s scheduled airlines suffered in 1990, one of the worst years in aviation history in economic terms, a total net loss of

Multi-Airport Ground Holding Problem: A Heuristic Approach Based on Priority Rules

4.3 billion. An equally telling statistic is that ground-holding delays (please see below for a definition) to airline aircraft in the United States averaged 2000 hours per day in 1986, approximately equivalent to grounding the entire fleet (250 aircraft at that time) of Delta Airlines, the third largest carrier in the United States. With significant increases in demand expected to continue, congestion is now cited by many experts and organizations as one of the principal impediments to the future growth of the airline industry.

An aggregate stochastic programming model for air traffic flow management

The k-centrum of a graph G - (V, E)is the set of vertices each minimizing the sum of the distances from it to the corresponding k farthest vertices of G. In this article properties of k-centrum of trees, where edges have positive real lengths, are investigated.

Evaluating terminal management performances using SLAM : The case of Athens international Airport

In recent years, many sophisticated mathematical models have been proposed to address the problem of reducing congestion at major airports by means of Ground Holding (GH) Policies, i.e., by imposing a ground delay to selected aircraft in order to reduce and possibly to avoid airborne delays and congestion. These models, which are usually optimization models, have found little application in practice so far, probably because they are not easy to understand. In this paper we introduce and analyze a family of simple, easy to understand, heuristics. Each heuristic is based on a specific “priority rule”. The flights are grouped dynamically into a manageable number of classes. Each “priority rule” specifies, for any two flights of different classes, which one has priority over the other. The performances of the proposed heuristics are compared among themselves, and with that of an “optimal” policy, on a set of test problems.

k-eccentricity and absolute k-centrum of a probabilistic tree

In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneously taking into account three important issues: (i) the model explicitly incorporates uncertainty in the airport capacities; (ii) it also considers the trade-off between airport arrivals and departures, which is a crucial issue in any hub airport; and (iii) it takes into account the interactions between different hubs. The level of aggregation proposed for the mathematical model allows us to solve realistic size instances with a commercial solver on a PC. Moreover it allows us to compute solutions which are perfectly consistent with the Collaborative Decision-Making (CDM) procedure in ATFM, widely adopted in the USA and which is currently receiving a lot of attention in Europe. In fact, the proposed model suggests the number of flights that should be delayed, a decision that belongs to the ATFM Authority, rather than assigning delays to individual aircraft.