We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The scheme first takes a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution and estimate the time derivative of the slow components. These estimated time derivatives are then used in an (outer) RungeKutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the timestep restriction on the outer time step is similar to the stability condition for the limiting macroscopic equation. Moreover, the number of inner time steps is also independent of the scaling parameter. We analyse stability and consistency, and illustrate with numerical results.

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Shift design is an essential step in workforce planning in which staffing requirements must be obtained for a set of shifts which best cover forecasted demand given as a demand pattern. Existing models for this challenging optimization problem perform well when these demand patterns fluctuate around an average without any strong variability in demand. However, when demand is irregular, these models inevitably generate solutions with a significant amount of over-or understaffing or an excessive use of short shifts. The present paper explores a strategy which involves modifying the demand patterns such that the variable workload may be better matched using an acceptable number of shifts. Integer programming is employed to solve the resulting optimization problem. A computational study of the proposed model reveals interactions between different problem parameters which control the scope of demand modification and the type of the selected shifts. Moreover, the potential impact from an economic point-of-view is discussed and the time before profitability of the approach is evaluated. These insights enable operations management to better understand the trade-off between solution quality and different types of flexibility which may be realized in an organization.

We study a projective integration scheme for a kinetic equation in both the diffusive and hydrodynamic scaling, on which a limiting diffusion or advection equation exists. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large, macroscopic time step. With an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the limiting equation, whereas the required number of inner steps does not depend on the small-scale parameter. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the limiting equation in the limit of vanishing small parameter. We show how to obtain arbitrary-order, general, explicit schemes for kinetic equations as well as for systems of nonlinear hyperbolic conservation laws, and provide numerical results.

Communication networks are complex systems consisting of many components each producing a multitude of system metrics that can be monitored in real-time. Anomaly Detection (AD) allows to detect deviant behavior in these system metrics. However, in communication networks, large amounts of domain knowledge and huge manual efforts are required to efficiently monitor these complex systems. In this paper, we describe how AutoEncoders (AE) can elevate the manual effort for unsupervised AD in communication networks. We show that AE can be applied, without domain knowledge or manual effort and evaluate different types of AE architectures and how they perform on a variety of anomaly types found in communication networks.