A tight bound on the throughput of queueing networks with blocking

In this paper, we present a bounding methodology that allows to compute a tight lower bound on the cycle time of fork--join queueing networks with blocking and with general service time distributions. The methodology relies on two ideas. First, probability masses fitting (PMF) discretizes the service time distributions so that the evolution of the modified network can be modelled by a Markov chain. The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the orresponding interval. Second, we take advantage of the concept of critical path, i.e. the sequence of jobs that covers a sample run. We show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a lower bound on the original cycle time. The tightness of the bound is shown on computational experiments. Finally, we discuss the extension to split--and--merge networks and approximate estimations of the cycle time.queueing networks, blocking, throughput, bound, probability masses fitting, critical path.

Importance sampling in systems simulation: A practical failure?

sampling;queuing theory;operations research

Signal and noise in regime systems: a hypothesis on the predictability of the North Atlantic Oscillation

Studies conducted by the UK Met Office reported significant skill at predicting the winter NAO index with their seasonal prediction system. At the same time, a very low signal-to-noise ratio was observed, as measured using the `ratio of predictable components' (RPC) metric. We analyse both the skill and signal-to-noise ratio using a new statistical toy-model which assumes NAO predictability is driven by regime dynamics. It is shown that if the system is approximately bimodal in nature, with the model consistently underestimating the level of regime persistence each season, then both the high skill and high RPC value of the Met Office hindcasts can easily be reproduced. Underestimation of regime persistence could be attributable to any number of sources of model error, including imperfect regime structure or errors in the propagation of teleconnections. In particular, a high RPC value for a seasonal mean prediction may be expected even if the models internal level of noise is realistic.Comment: Published in the Quarterly Journal of the Royal Meteorological Society (2019

An early warning indicator for atmospheric blocking events using transfer operators

The existence of persistent midlatitude atmospheric flow regimes with time-scales larger than 5-10 days and indications of preferred transitions between them motivates to develop early warning indicators for such regime transitions. In this paper, we use a hemispheric barotropic model together with estimates of transfer operators on a reduced phase space to develop an early warning indicator of the zonal to blocked flow transition in this model. It is shown that, the spectrum of the transfer operators can be used to study the slow dynamics of the flow as well as the non-Markovian character of the reduction. The slowest motions are thereby found to have time scales of three to six weeks and to be associated with meta-stable regimes (and their transitions) which can be detected as almost-invariant sets of the transfer operator. From the energy budget of the model, we are able to explain the meta-stability of the regimes and the existence of preferred transition paths. Even though the model is highly simplified, the skill of the early warning indicator is promising, suggesting that the transfer operator approach can be used in parallel to an operational deterministic model for stochastic prediction or to assess forecast uncertainty

Designable electron transport features in one-dimensional arrays of metallic nanoparticles: Monte Carlo study of the relation between shape and transport

We study the current and shot noise in a linear array of metallic nanoparticles taking explicitly into consideration their discrete electronic spectra. Phonon assisted tunneling and dissipative effects on single nanoparticles are incorporated as well. The capacitance matrix which determines the classical Coulomb interaction within the capacitance model is calculated numerically from a realistic geometry. A Monte Carlo algorithm which self-adapts to the size of the system allows us to simulate the single-electron transport properties within a semiclassical framework. We present several effects that are related to the geometry and the one-electron level spacing like e.g. a negative differential conductance (NDC) effect. Consequently these effects are designable by the choice of the size and arrangement of the nanoparticles.Comment: 13 pages, 12 figure

Optimisation of stochastic networks with blocking: a functional-form approach

This paper introduces a class of stochastic networks with blocking, motivated by applications arising in cellular network planning, mobile cloud computing, and spare parts supply chains. Blocking results in lost revenue due to customers or jobs being permanently removed from the system. We are interested in striking a balance between mitigating blocking by increasing service capacity, and maintaining low costs for service capacity. This problem is further complicated by the stochastic nature of the system. Owing to the complexity of the system there are no analytical results available that formulate and solve the relevant optimization problem in closed form. Traditional simulation-based methods may work well for small instances, but the associated computational costs are prohibitive for networks of realistic size. We propose a hybrid functional-form based approach for finding the optimal resource allocation, combining the speed of an analytical approach with the accuracy of simulation-based optimisation. The key insight is to replace the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a single simulation run. We develop two implementations of this approach and conduct extensive computational experiments on complex examples to show that it is capable of substantially improving system performance. We also provide evidence that our approach has substantially lower computational costs compared to stochastic approximation