A Fluid-Diffusion-Hybrid Limiting Approximation for Priority Systems with Fast and Slow Customers

The paper “Fluid-Diffusion-Hybrid (FDH) Approximation” proposes a new heavy-traffic asymptotic regime for a two-class priority system in which the high-priority customers require substantially larger service times than the low-priority customers. In the FDH limit, the high-priority queue is a diffusion, whereas the low-priority queue operates as a (random) fluid limit, whose dynamics are driven by the former diffusion. A characterizing property of our limit process is that, unlike other asymptotic regimes, a non-negligible proportion of the customers from both classes must wait for service. This property allows us to study the costs and benefits of de-pooling, and prove that a two-pool system is often the asymptotically optimal design of the system.

Anomaly Detection based on Compressed Data: an Information Theoretic Characterization

<div>We analyze the effect of lossy compression in the processing of sensor signals that must be used to detect anomalous events in the system under observation. The intuitive relationship between the quality loss at higher compression and the possibility of telling anomalous behaviours from normal ones is formalized in terms of information-theoretic quantities. Some analytic derivations are made within the Gaussian framework and possibly in the asymptotic regime for what concerns the stretch of signals considered.</div><div>Analytical conclusions are matched with the performance of practical detectors in a toy case allowing the assessment of different compression/detector configurations.</div>

Anomaly Detection based on Compressed Data: an Information Theoretic Characterization

<div>We analyze the effect of lossy compression in the processing of sensor signals that must be used to detect anomalous events in the system under observation. The intuitive relationship between the quality loss at higher compression and the possibility of telling anomalous behaviours from normal ones is formalized in terms of information-theoretic quantities. Some analytic derivations are made within the Gaussian framework and possibly in the asymptotic regime for what concerns the stretch of signals considered.</div><div>Analytical conclusions are matched with the performance of practical detectors in a toy case allowing the assessment of different compression/detector configurations.</div>

Nudge: Stochastically Improving upon FCFS

The First-Come First-Served (FCFS) scheduling policy is the most popular scheduling algorithm used in practice. Furthermore, its usage is theoretically validated: for light-tailed job size distributions, FCFS has weakly optimal asymptotic tail of response time. But what if we don't just care about the asymptotic tail? What if we also care about the 99th percentile of response time, or the fraction of jobs that complete in under one second? Is FCFS still best? Outside of the asymptotic regime, only loose bounds on the tail of FCFS are known, and optimality is completely open. In this paper, we introduce a new policy, Nudge, which is the first policy to provably stochastically improve upon FCFS. We prove that Nudge simultaneously improves upon FCFS at every point along the tail, for light-tailed job size distributions. As a result, Nudge outperforms FCFS for every moment and every percentile of response time. Moreover, Nudge provides a multiplicative improvement over FCFS in the asymptotic tail. This resolves a long-standing open problem by showing that, counter to previous conjecture, FCFS is not strongly asymptotically optimal.

Low-Cost Active Anomaly Detection with Switching Latency

Consider the problem of detecting anomalies among multiple stochastic processes. Each anomaly incurs a cost per unit time until it is identified. Due to the resource constraints, the decision-maker can select one process to probe and obtain a noisy observation. Each observation and switching across processes accompany a certain time delay. Our objective is to find a sequential inference strategy that minimizes the expected cumulative cost incurred by all the anomalies during the entire detection procedure under the error constraints. We develop a deterministic policy to solve the problem within the framework of the active hypothesis testing model. We prove that the proposed algorithm is asymptotic optimal in terms of minimizing the expected cumulative costs when the ratio of the single-switching delay to the single-observation delay is much smaller than the declaration threshold and is order-optimal when the ratio is comparable to the threshold. Not only is the proposed policy optimal in the asymptotic regime, but numerical simulations also demonstrate its excellent performance in the finite regime.

Ohmic and viscous damping of the Earth's Free Core Nutation

&lt;p&gt;The cause for the damping of the Earth's Free Core Nutation (FCN) and the Free Inner Core Nutation (FICN) eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid outer core, where important dissipation processes can take place. We present a linear numerical model for the FCN that includes viscous dissipation and Ohmic heating. We find an asymptotic regime, appropriate for Earth's parameters, where viscous and Ohmic processes contribute equally to the total damping, with the dissipation taking place almost exclusively in the boundary layers. By matching the observed nutational damping we infer an enhanced effective viscosity matching and validating methods from previous studies. We suggest that turbulence caused by the Earth's precession can be a source for the FCN's damping.&amp;#160;&lt;/p&gt;

On the Tidal Prism: The Roles of Basin Extension, Bottom Friction and Inlet Cross-Section

The prism of the Lignano tidal inlet was approximately constant over the last forty years, although the section width has halved. This has led to questions concerning the factors that most influence the tidal prism, and on the applicability of the well-known A–P relationship. A conceptual scheme of the sea–channel–lagoon system has been used to perform a sensitivity analysis of different parameters that characterize both the basin and the inlet cross-section. A 2D hydrodynamic model has been applied to evaluate the prism and compare it to the one derived by a static method, which is the basis of the analytical derivation of the A–P linkage. Three regimes have been found in the prism variability as a function of the basin extension: a linear static regime between prism and basin area; an asymptotic regime in which the prism depends only on the basin bottom friction; and an intermediate one. In addition, the roles of the inlet and channel sizes on the prism value have been investigated. The results, compared to the empirical relationships between the prism and the inlet cross-section, show that a variation in the cross-sectional area does not always corresponds to a change in tidal prism.

Big Jobs Arrive Early: From Critical Queues to Random Graphs

We consider a queue to which only a finite pool of n customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement S arrives to the queue after an exponentially distributed time with mean S-α for some [Formula: see text]; therefore, larger service requirements trigger customers to join earlier. This finite-pool queue interpolates between two previously studied cases: α = 0 gives the so-called [Formula: see text] queue and α = 1 is closely related to the exploration process for inhomogeneous random graphs. We consider the asymptotic regime in which the pool size n grows to infinity and establish that the scaled queue-length process converges to a diffusion process with a negative quadratic drift. We leverage this asymptotic result to characterize the head start that is needed to create a long period of activity. We also describe how this first busy period of the queue gives rise to a critically connected random forest.

On Asymptotic Dynamical Regimes of Manakov N-soliton Trains in Adiabatic Approximation

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the Manakov model. The evolution of Manakov N-soliton trains is described by the complex Toda chain (CTC) which is a completely integrable dynamical model. Calculating the eigenvalues of its Lax matrix allows us to determine the asymptotic velocity of each soliton. So we describe sets of soliton parameters that ensure one of the two main types of asymptotic regimes: the bound state regime (BSR) and the free asymptotic regime (FAR). In particular we find explicit description of special symmetric configurations of N solitons that ensure BSR and FAR. We find excellent matches between the trajectories of the solitons predicted by CTC with the ones calculated numerically from the Manakov system for wide classes of soliton parameters. This confirms the validity of our model