15,829 research outputs found
Timely-Throughput Optimal Scheduling with Prediction
Motivated by the increasing importance of providing delay-guaranteed services
in general computing and communication systems, and the recent wide adoption of
learning and prediction in network control, in this work, we consider a general
stochastic single-server multi-user system and investigate the fundamental
benefit of predictive scheduling in improving timely-throughput, being the rate
of packets that are delivered to destinations before their deadlines. By
adopting an error rate-based prediction model, we first derive a Markov
decision process (MDP) solution to optimize the timely-throughput objective
subject to an average resource consumption constraint. Based on a packet-level
decomposition of the MDP, we explicitly characterize the optimal scheduling
policy and rigorously quantify the timely-throughput improvement due to
predictive-service, which scales as
,
where are constants, is the
true-positive rate in prediction, is the false-negative rate, is the
packet deadline and is the prediction window size. We also conduct
extensive simulations to validate our theoretical findings. Our results provide
novel insights into how prediction and system parameters impact performance and
provide useful guidelines for designing predictive low-latency control
algorithms.Comment: 14 pages, 7 figure
A Comparative Study of an Asymptotic Preserving Scheme and Unified Gas-kinetic Scheme in Continuum Flow Limit
Asymptotic preserving (AP) schemes are targeting to simulate both continuum
and rarefied flows. Many AP schemes have been developed and are capable of
capturing the Euler limit in the continuum regime. However, to get accurate
Navier-Stokes solutions is still challenging for many AP schemes. In order to
distinguish the numerical effects of different AP schemes on the simulation
results in the continuum flow limit, an implicit-explicit (IMEX) AP scheme and
the unified gas kinetic scheme (UGKS) based on Bhatnagar-Gross-Krook (BGk)
kinetic equation will be applied in the flow simulation in both transition and
continuum flow regimes. As a benchmark test case, the lid-driven cavity flow is
used for the comparison of these two AP schemes. The numerical results show
that the UGKS captures the viscous solution accurately. The velocity profiles
are very close to the classical benchmark solutions. However, the IMEX AP
scheme seems have difficulty to get these solutions. Based on the analysis and
the numerical experiments, it is realized that the dissipation of AP schemes in
continuum limit is closely related to the numerical treatment of collision and
transport of the kinetic equation. Numerically it becomes necessary to couple
the convection and collision terms in both flux evaluation at a cell interface
and the collision source term treatment inside each control volume
Propagation of boundary-induced discontinuity in stationary radiative transfer
We consider the boundary value problem of the stationary transport equation
in the slab domain of general dimensions. In this paper, we discuss the
relation between discontinuity of the incoming boundary data and that of the
solution to the stationary transport equation. We introduce two conditions
posed on the boundary data so that discontinuity of the boundary data
propagates along positive characteristic lines as that of the solution to the
stationary transport equation. Our analysis does not depend on the celebrated
velocity averaging lemma, which is different from previous works. We also
introduce an example in two dimensional case which shows that piecewise
continuity of the boundary data is not a sufficient condition for the main
result.Comment: 15 pages, no figure
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