An approximate analysis of a bernoulli alternating service model

We consider a discrete-time queueing system with one server and two types of customers, say type-1 and type-2 customers. The server serves customers of either type alternately according to a Bernoulli pro- cess. The service times of the customers are deterministically equal to 1 time slot. For this queueing system, we derive a functional equation for the joint probability generating function of the number of type-1 and type-2 customers. The functional equation contains two unknown partial generating functions which complicates the analysis. We investigate the dominant singularity of these two unknown functions and propose an approximation for the coefficients of the Maclaurin series expansion of these functions. This approximation provides a fast method to compute approximations of various performance measures of interest

Recovery of Low-Rank Plus Compressed Sparse Matrices with Application to Unveiling Traffic Anomalies

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with traffic anomaly detection in backbone networks, and subsumes compressed sensing as well as the timely low-rank plus sparse matrix recovery tasks encountered in matrix decomposition problems. Leveraging the ability of $\ell_1$- and nuclear norms to recover sparse and low-rank matrices, a convex program is formulated to estimate the unknowns. Analysis and simulations confirm that the said convex program can recover the unknowns for sufficiently low-rank and sparse enough components, along with a compression matrix possessing an isometry property when restricted to operate on sparse vectors. When the low-rank, sparse, and compression matrices are drawn from certain random ensembles, it is established that exact recovery is possible with high probability. First-order algorithms are developed to solve the nonsmooth convex optimization problem with provable iteration complexity guarantees. Insightful tests with synthetic and real network data corroborate the effectiveness of the novel approach in unveiling traffic anomalies across flows and time, and its ability to outperform existing alternatives.Comment: 38 pages, submitted to the IEEE Transactions on Information Theor