Worst-case Source Research Articles

Environmental noise predictions using a statistical approach

Noise pollution from industrial premises has the potential to have an impact on neighbouring properties. In New South Wales the Environment Protection Authority has developed the Noise Policy for Industry (NPfI). The NPfI requires noise assessments to be conducted using a typical assessment procedure that results in setting project noise trigger levels (PNTLs) which are the benchmark levels against which potential noise impacts from industrial developments are judged. The PNTLs are then used in Environmental Protection Licences to regulate the premises. The NPfI requires noise assessments to consider worst-case (i.e., noise-enhancing) meteorological conditions. In addition, regulators and consent authorities often require noise assessments to include a range of other conservative assumptions such as worst-case source levels and locations. This process appears to be very conservative, particularly considering that the PNTL in each assessment period (day, evening and night) are based on lowest 10th percentile background noise levels. This paper, through a statistical approach of using random probability distributions, will identify the likelihood that modelled noise levels and associated impacts are likely to occur and comment on the appropriateness of the conservative assessment process.

Source location impact on relative tsunami strength along the U.S. West Coast

Tsunami propagation simulations are used to identify which tsunami source locations would produce the highest amplitude waves on approach to key population centers along the U.S. West Coast. The reasons for preferential influence of certain remote excitation sites are explored by examining model time sequences of tsunami wave patterns emanating from the source. Distant bathymetric features in the West and Central Pacific can redirect tsunami energy into narrow paths with anomalously large wave height that have disproportionate impact on small areas of coastline. The source region generating the waves can be as little as 100 km along a subduction zone, resulting in distinct source-target pairs with sharply amplified wave energy at the target. Tsunami spectral ratios examined for transects near the source, after crossing the West Pacific, and on approach to the coast illustrate how prominent bathymetric features alter wave spectral distributions, and relate to both the timing and magnitude of waves approaching shore. To contextualize the potential impact of tsunamis from high-amplitude source-target pairs, the source characteristics of major historical earthquakes and tsunamis in 1960, 1964, and 2011 are used to generate comparable events originating at the highest-amplitude source locations for each coastal target. This creates a type of “worst-case scenario,” a replicate of each region's historically largest earthquake positioned at the fault segment that would produce the most incoming tsunami energy at each target port. An amplification factor provides a measure of how the incoming wave height from the worst-case source compares to the historical event.

Worst Case Traffic from Regulated Sources

We address the problem of finding the worst possible traffic a user of a telecommunications network can send. We take “worst” to mean having the highest effective bandwidth, a concept that arises in the Large Deviation theory of queueing networks. The traffic is assumed to be stationary and to satisfy “leaky bucket” constraints, which represent the a priori knowledge the network operator has concerning the traffic. Firstly, we show that this optimization problem may be reduced to an optimization over periodic traffic sources. Then, using convexity methods, we show that the realizations of a worst case source must have the following properties: at each instant the transmission rate must be either zero, the peak rate, or the leaky bucket rate; it may only be the latter when the leaky bucket is empty or full; each burst of activity must either start with the leaky bucket empty or end with it full.

Maximal Effective Bandwidth of Constrained Traffic

We investigate the worst possible behavior of a stationary traffic source when the traffic emanating from it is required to meet certain constraints. Specifically, the peak rate of the source is required not to exceed a level ρ and realizations must obey a “leaky bucket” constraint with bucket size β and leak rate σ. The worst case source is considered to be the one with the largest effective bandwidth, a concept which arises in the large deviation theory of queueing networks and governs the asymptotic loss rate when a large number of sources send traffic to a single server queue. We conjecture the form of the worst case traffic in general and prove the conjecture for the special case when T, the time-scale parameter of the effective bandwidth, is less than both β/(ρ−σ) and β/σ, the times taken respectively to fill and empty the leaky bucket.

Towards optimal policing in ATM networks

This paper proposes a framework for optimal policing in ATM networks. A general approach to modeling controllers which implement the policing function is described, using finite-state automata. The theory of finite-state accepting automata and regular expressions enables the explicit representation of all traffic patterns which pass through the policing controller, without modification. This in turn enables the symbolic computation of the worst-case source and therefore provides a unified framework for the formulation and derivation of optimal bandwidth enforcement schemes. Exhaustive searches are performed for small cases to find optimal finite-state automata. These optimal results are extended to obtain near-optimal solutions for larger-state automata. The optimal and near-optimal policing controller designs are compared to conventional schemes, such as leaky buckets, and improvement in performance is achieved, where performance is measured in terms of cell loss rate for the declared source and throughput of the corresponding worst case source.

The rate-distortion function on classes of sources determined by spectral capacities

The quantity \sup_{a \in \cal R} R{a}(D) is considered, where \cal R is a class of homogeneous n -parameter sources and R_{a}(D) denotes the single-letter mean-square-error (MSE) rate-distortion function for the individual source a. In particular, the case in which the class \cal R is specified in terms of spectral information is treated for general classes of spectral measures whose upper measures are capacities (in the sense of Choquet) alternating of order two. This type of class includes many common models for spectral uncertainty such as mixture models, spectral band models, and neighborhoods generated by variation and Prohorov metrics. It is shown that each such class contains a worst-case source whose rate-distortion function achieves the supremum over the class for each value of distortion. This source is characterized as having a spectral density that is a derivative (in the sense of Huber and Strassen) of the upper spectral measure with respect to Lebesgue measure on [-\pi,\pi]^{n} . Moreover it is shown that the spectral measure of the worst-case source is closest, in a sense defined by directed divergence, to Lebesgue measure (which corresponds to a memoryless source). Numerical results are presented for the particular case in which the source spectral measure is a mixture of a Gauss-Markov spectrum and an unknown contaminating component.