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This paper considers the problem of constructing a dynamic time series model for local fluctuations in traffic parameters from observations collected during periods when the rate of traffic flow is not constant application of linear high-pass filters to serially correlated data obtained through a measurement queue is considered in both the time and frequency domains. For the filtered series, a general autoregressive moving average model is postulated to describe the local fluctuations. Throughout the paper, an eight-hour sample of air traffic in the local control sector at New York's LaGuardia Airport serves as a case study for the techniques described.

This paper considers the problem of modeling dynamic fluctuations in aircraft concentration within a group of air traffic control sectors. Using simultaneous time series recorded for each of the sectors, a multiple transfer function noise model is constructed. The modeling procedure demonstrates a data-dependent approach to ATC systems analysis which does not rely on describing the movement of individual aircraft.

This article discusses the use of continuous autoregressive models to describe the behavior of traffic indices. From discretely sampled data, second-order differential equation models are constructed to represent dynamic traffic fluctuations as the response of a linear system to a stochastic forcing function. The results are compared to the more common M/G/∞ queueing model approach, and the analysis is demonstrated on time series of aircraft concentration in thirty-one enroute air traffic control sectors.

The statistical analysis of counting processes obtained from extensive sets of traffic data is often complicated by the presence of long‐term fluctuations in the rate of traffic flow. This paper describes a technique which corrects for the effects of a non‐homogeneous rate function by transforming the observed process to a time scale in which the traffic rate is approximately constant. The transformation is based on properties of the non‐homogeneous Poisson process, but it is useful in estimation and testing of a much broader class of point process models. In determining the appropriate transformation for a sequence of aircraft arrivals, both kernel estimators and exponential polynomial models for the rate function are employed. The effect of the transformation on the estimated coefficient of variation for the headway distribution and on tests for serial dependence is demonstrated. The transformation allows stationary parametric models to be constructed for traffic indices in periods of fluctuating flow r...

The construction of forecasts using interactive data analysis systems is greatly aided by the availability of graphical procedures. Data exploration, model identification and estimation, and interpretation of final forecasts are made considerably easier by the visual relay of information. This article discusses some recent developments in time series graphics designed to assist in the forecasting process. A discussion of requirerients for effective use of graphics in interactive forecasting is included as illustrated through an application of the Box-Jenkins methodology. Illustrations are included from the STATGRAPHICS system, a prototype implementation in APL.

The dynamic behavior of traffic indices in continuous time is modeled by a linear differential equation with stochastic forcing function. The general model postulated is that of a continuous stationary autoregressive moving average process. Estimates of the parameters in the continuous model are obtained from their correspondence to parameters in a discrete time model fitted to uniformly sampled traffic data. The technique is demonstrated on a time series of aircraft concentration in a low altitude air traffic control sector.

The establishment of standards for lateral separation between adjacent jet routes depends in large part on an adequate description of aircraft path-keeping ability. While it has been accepted for many years that deviations from route centreline follow a distribution which is more peaked in the core and longer tailed than the gaussian distribution which was initially assumed, the selection of an alternative distribution is still moot. Early studies of oceanic data suggested that a double exponential distribution gave a much better description of the core data. However, this distribution still appeared to underestimate the frequency of occurrence of very large errors, so that a double-double exponential distribution was proposed and is currently used for establishment of MNPS (Minimum Navigational Performance Specification) criteria for the North Atlantic organized track system. A physical rationale for the occurrence of the double-double exponential distribution has recently been derived, with suggestions for consideration of alternative formulations.

A parametric time series model is employed to simulate the number of aircraft present in an air traffic control sector. Borrowing from the work of Box and Jenkins, the identification, parameter estimation and associated tests of adequacy are illustrated using data from a low altitude control sector. The fitted model provides a useful algorithm and reflects the time dependency which exists between the number of aircraft measured in consecutive time periods. The simulation is part of a larger air communications system simulation which is under development.

The proper role of the computer in data analysis is one of increasing the ability of the analyst to extract information. This requires a high degree of user control within an interactive environment, not only over data manipulation and computations but also over graphical display. An interactive statistical graphics system such as that described in this paper allows the user to break away from constraints imposed by most statistical packages.