Packet loss characteristics for M/G/1/N queueing systems

In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional loss probability. Some numerical examples then illustrate our results

Selection and Estimation for Mixed Graphical Models

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's conditional distribution is in the exponential family. We identify restrictions on the parameter space required for the existence of a well-defined joint density, and establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our theoretical results, we investigate the selection of edges between nodes whose conditional distributions take different parametric forms, and show that efficiency can be gained if edge estimates obtained from the regressions of particular nodes are used to reconstruct the graph. These results are illustrated with examples of Gaussian, Bernoulli, Poisson and exponential distributions. Our theoretical findings are corroborated by evidence from simulation studies

Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed

Estimating the Propagation of Interdependent Cascading Outages with Multi-Type Branching Processes

In this paper, the multi-type branching process is applied to describe the statistics and interdependencies of line outages, the load shed, and isolated buses. The offspring mean matrix of the multi-type branching process is estimated by the Expectation Maximization (EM) algorithm and can quantify the extent of outage propagation. The joint distribution of two types of outages is estimated by the multi-type branching process via the Lagrange-Good inversion. The proposed model is tested with data generated by the AC OPA cascading simulations on the IEEE 118-bus system. The largest eigenvalues of the offspring mean matrix indicate that the system is closer to criticality when considering the interdependence of different types of outages. Compared with empirically estimating the joint distribution of the total outages, good estimate is obtained by using the multitype branching process with a much smaller number of cascades, thus greatly improving the efficiency. It is shown that the multitype branching process can effectively predict the distribution of the load shed and isolated buses and their conditional largest possible total outages even when there are no data of them.Comment: Accepted by IEEE Transactions on Power System

HetHetNets: Heterogeneous Traffic Distribution in Heterogeneous Wireless Cellular Networks

A recent approach in modeling and analysis of the supply and demand in heterogeneous wireless cellular networks has been the use of two independent Poisson point processes (PPPs) for the locations of base stations (BSs) and user equipments (UEs). This popular approach has two major shortcomings. First, although the PPP model may be a fitting one for the BS locations, it is less adequate for the UE locations mainly due to the fact that the model is not adjustable (tunable) to represent the severity of the heterogeneity (non-uniformity) in the UE locations. Besides, the independence assumption between the two PPPs does not capture the often-observed correlation between the UE and BS locations. This paper presents a novel heterogeneous spatial traffic modeling which allows statistical adjustment. Simple and non-parameterized, yet sufficiently accurate, measures for capturing the traffic characteristics in space are introduced. Only two statistical parameters related to the UE distribution, namely, the coefficient of variation (the normalized second-moment), of an appropriately defined inter-UE distance measure, and correlation coefficient (the normalized cross-moment) between UE and BS locations, are adjusted to control the degree of heterogeneity and the bias towards the BS locations, respectively. This model is used in heterogeneous wireless cellular networks (HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic on the network performance. This network is called HetHetNet since it has two types of heterogeneity: heterogeneity in the infrastructure (supply), and heterogeneity in the spatial traffic distribution (demand).Comment: JSA

Statistical properties of determinantal point processes in high-dimensional Euclidean spaces

The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these functions as determinants of $N\times N$ matrices and then extrapolate to $N\to\infty$. This formulation allows for a quick and accurate numerical evaluation of these quantities for point processes in Euclidean spaces of dimension $d$. We also implement an algorithm due to Hough \emph{et. al.} \cite{hough2006dpa} for generating configurations of determinantal point processes in arbitrary Euclidean spaces, and we utilize this algorithm in conjunction with the aforementioned numerical results to characterize the statistical properties of what we call the Fermi-sphere point process for $d = 1$ to 4. This homogeneous, isotropic determinantal point process, discussed also in a companion paper \cite{ToScZa08}, is the high-dimensional generalization of the distribution of eigenvalues on the unit circle of a random matrix from the circular unitary ensemble (CUE). In addition to the nearest-neighbor probability distribution, we are able to calculate Voronoi cells and nearest-neighbor extrema statistics for the Fermi-sphere point process and discuss these as the dimension $d$ is varied. The results in this paper accompany and complement analytical properties of higher-dimensional determinantal point processes developed in \cite{ToScZa08}.Comment: 42 pages, 17 figure