Instability in Stochastic and Fluid Queueing Networks

The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence (stability) of a corresponding stochastic queueing network, and weak stability implies rate stability of a corresponding stochastic network. These results have been established both for cases of specific scheduling policies and for the class of all work conserving policies. However, only partial converse results have been established and in certain cases converse statements do not hold. In this paper we close one of the existing gaps. For the case of networks with two stations we prove that if the fluid model is not weakly stable under the class of all work conserving policies, then a corresponding queueing network is not rate stable under the class of all work conserving policies. We establish the result by building a particular work conserving scheduling policy which makes the associated stochastic process transient. An important corollary of our result is that the condition $\rho^*\leq 1$, which was proven in \cite{daivan97} to be the exact condition for global weak stability of the fluid model, is also the exact global rate stability condition for an associated queueing network. Here $\rho^*$ is a certain computable parameter of the network involving virtual station and push start conditions.Comment: 30 pages, To appear in Annals of Applied Probabilit

Optimal Paths in Large Deviations of Symmetric Reflected Brownian Motion in the Octant

We study the variational problem that arises from consideration of large deviations for semimartingale reflected Brownian motion (SRBM) in the positive octant. Due to the difficulty of the general problem, we consider the case in which the SRBM has rotationally symmetric parameters. In this case, we are able to obtain conditions under which the optimal solutions to the variational problem are paths that are gradual (moving through faces of strictly increasing dimension) or that spiral around the boundary of the octant. Furthermore, these results allow us to provide an example for which it can be verified that a spiral path is optimal. For rotationally symmetric SRBM's, our results facilitate the simplification of computational methods for determining optimal solutions to variational problems and give insight into large deviations behavior of these processes

Ontogeny influences sensitivity to climate change stressors in an endangered fish.

Coastal ecosystems are among the most human-impacted habitats globally, and their management is often critically linked to recovery of declining native species. In the San Francisco Estuary, the Delta Smelt (Hypomesus transpacificus) is an endemic, endangered fish strongly tied to Californian conservation planning. The complex life history of Delta Smelt combined with dynamic seasonal and spatial abiotic conditions result in dissimilar environments experienced among ontogenetic stages, which may yield stage-specific susceptibility to abiotic stressors. Climate change is forecasted to increase San Francisco Estuary water temperature and salinity; therefore, understanding the influences of ontogeny and phenotypic plasticity on tolerance to these critical environmental parameters is particularly important for Delta Smelt and other San Francisco Estuary fishes. We assessed thermal and salinity limits in several ontogenetic stages and acclimation states of Delta Smelt, and paired these data with environmental data to evaluate sensitivity to climate-change stressors. Thermal tolerance decreased among successive stages, with larval fish exhibiting the highest tolerance and post-spawning adults having the lowest. Delta Smelt had limited capacity to increase tolerance through thermal acclimation, and comparisons with field temperature data revealed that juvenile tolerance limits are the closest to current environmental conditions, which may make this stage especially susceptible to future climate warming. Maximal water temperatures observed in situ exceeded tolerance limits of juveniles and adults. Although these temperature events are currently rare, if they increase in frequency as predicted, it could result in habitat loss at these locations despite other favourable conditions for Delta Smelt. In contrast, Delta Smelt tolerated salinities spanning the range of expected environmental conditions for each ontogenetic stage, but salinity did impact survival in juvenile and adult stages in exposures over acute time scales. Our results underscore the importance of considering ontogeny and phenotypic plasticity in assessing the impacts of climate change, particularly for species adapted to spatially and temporally heterogeneous environments

Konzeption und Evaluation des Distanzkurses "Basiskompetenz wissensorientiertes Management" der Volkswagen AutoUni

In the context of the Volkswagen AutoUni the distance course “Basic competence knowledge-oriented management” was designed and evaluated. The effect of the course was evaluated by the participants regarding acceptance, quality of the learning environment, case-based learning, motivation, group work, learning success and transfer. The acceptance, the quality of the learning environment, the case-based learning and the motivation were evaluated positively. However the usability of the learning platform and the virtual group work were evaluated less positively thus making a need of improvement apparent which should be taken into consideration in the further development of the course concept. Furthermore the learning success and the learning transfer were positively evaluated.Im Rahmen der Volkswagen AutoUni wurde der Distanzkurs „Basiskompetenz wissensorientiertes Management“ konzipiert und evaluiert. Die Wirkung des Kurses wurde von den Teilnehmern hinsichtlich der Akzeptanz, der Qualität der Lernumgebung, des fallbasierten Lernens, der Motivation und der Gruppenarbeit sowie des Lernerfolgs und Lerntransfers beurteilt. Die Ergebnisse der Untersuchung zeigen eine hohe Bewertung der Akzeptanz, der Qualität der Lernumgebung sowie des fallbasierten Lernens und der Motivation. Die Benutzerfreundlichkeit der Lernplattform und die virtuelle Gruppenarbeit wurden niedriger bewertet. Hier zeigt sich Optimierungsbedarf, der bei einer Weiterentwicklung des Kurskonzepts berücksichtigt werden sollte. Hoch eingeschätzt wurden zudem der Lernerfolg und Lerntransfer

A Hierarchical Approach to Robust Stability of Multiclass Queueing Networks

We re-visit the global - relative to control policies - stability of multiclass queueing networks. In these, as is known, it is generally insufficient that the nominal utilization at each server is below 100%. Certain policies, although work conserving, may destabilize a network that satisfies the nominal load conditions; additional conditions on the primitives are needed for global stability. The global-stability region was fully characterized for two-station networks in [13], but a general framework for networks with more than two stations remains elusive. In this paper, we offer progress on this front by considering a subset of non-idling control policies, namely queue-ratio (QR) policies. These include as special cases also all static-priority policies. With this restriction, we are able to introduce a complete framework that applies to networks of any size. Our framework breaks the analysis of QR-global stability into (i) global state-space collapse and (ii) global stability of the Skorohod problem (SP) representing the fluid workload. Sufficient conditions for both are specified in terms of simple optimization problems. We use these optimization problems to prove that the family of QR policies satisfies a weak form of convexity relative to policies. A direct implication of this convexity is that: if the SP is stable for all static-priority policies (the "extreme" QR policies), then it is also stable under any QR policy. While QR-global stability is weaker than global stability, our framework recovers necessary and sufficient conditions for global stability in specific networks

Semi-empirical model for the direct simulation of power plant with integrated post-combustion CO2 capture processes by wet chemical absorption

AbstractIn this work, a semi-empirical column model is developed to represent post-combustion CO2 capture processes with chemical solvents in coal-fired steam power plants. The solvents are represented by empirical correlations on the basis of fundamental measurement data (CO2 solubility, heat capacity, density). The model of a CO2 capture process including the column model is coupled to detailed models of a hard-coal-fired steam power plant and of a CO2 compressor to evaluate and compare the impact of CO2 capture on the overall power plant process using six different solvents

A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane

We present a stochastic programming model for informing the deployment of temporary flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.Comment: 35 pages, 12 figure