Concave Switching in Single and Multihop Networks

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a {($\alpha,g$)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.Comment: 28 page

Sensitivity analysis of simulation experiments: Tutorial on regression analysis and statistical design

Simulation;mathematische statistiek

Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis

A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis

Minimizing the externalities variance in a LCFS-PR M/G/1M/G/1 queue under various constraints

Consider a LCFS-PR $M/G/1$ queue and assume that at time $t = 0$, there are $n+2$ customers $c_1,c_2,...,c_{n+1},c$ who arrived in that order such that $t = 0$ is the arrival time of $c$. Then, the externalities which are generated by $c$ is the total waiting time that would be saved by $c_1,c_2,...,c_{n+1}$ if $c$ reduced his service requirement to zero. Motivated by some applications, this work is about the minimization of the externalities variance under various constraints

Modeling Evacuation Risk Using a Stochastic Process Formulation of Mesoscopic Dynamic Network Loading

One of the actions usually conducted to limit exposure to a hazardous event is the evacuation of the area that is subject to the effects of the event itself. This involves modifications both to demand (a large number of users all want to move together) and to supply (the transport network may experience changes in capacity, unusable roads, etc.). In order to forecast the traffic evolution in a network during an evacuation, a natural choice is to adopt an approach based on Dynamic Traffic Assignment (DTA) models. However, such models typically give a deterministic prediction of future conditions, whereas evacuations are subject to considerable uncertainty. The aim of the present paper is to describe an evacuation approach for decision support during emergencies that directly predicts the time-evolution of the probability of evacuating users from an area, formulated within a discrete-time stochastic process modelling framework. The approach is applied to a small artificial case as well as a real-life network, where we estimate users' probabilities to reach a desired safe destination and analyze time dependent risk factors in an evacuation scenario

Performance evaluation of warehouses with automated storage and retrieval technologies.

In this dissertation, we study the performance evaluation of two automated warehouse material handling (MH) technologies - automated storage/retrieval system (AS/RS) and autonomous vehicle storage/retrieval system (AVS/RS). AS/RS is a traditional automated warehouse MH technology and has been used for more than five decades. AVS/RS is a relatively new automated warehouse MH technology and an alternative to AS/RS. There are two possible configurations of AVS/RS: AVS/RS with tier-captive vehicles and AVS/RS with tier-to-tier vehicles. We model the AS/RS and both configurations of the AVS/RS as queueing networks. We analyze and develop approximate algorithms for these network models and use them to estimate performance of the two automated warehouse MH technologies. Chapter 2 contains two parts. The first part is a brief review of existing papers about AS/RS and AVS/RS. The second part is a methodological review of queueing network theory, which serves as a building block for our study. In Chapter 3, we model AS/RSs and AVS/RSs with tier-captive vehicles as open queueing networks (OQNs). We show how to analyze OQNs and estimate related performance measures. We then apply an existing OQN analyzer to compare the two MH technologies and answer various design questions. In Chapter 4 and Chapter 5, we present some efficient algorithms to solve SOQN. We show how to model AVS/RSs with tier-to-tier vehicles as SOQNs and evaluate performance of these designs in Chapter 6. AVS/RS is a relatively new automated warehouse design technology. Hence, there are few efficient analytical tools to evaluate performance measures of this technology. We developed some efficient algorithms based on SOQN to quickly and effectively evaluate performance of AVS/RS. Additionally, we present a tool that helps a warehouse designer during the concepting stage to determine the type of MH technology to use, analyze numerous alternate warehouse configurations and select one of these for final implementation

A Bayesian Approach to Parameter Inference in Queueing Networks

The application of queueing network models to real-world applications often involves the task of estimating the service demand placed by requests at queueing nodes. In this article, we propose a methodology to estimate service demands in closed multiclass queueing networks based on Gibbs sampling. Our methodology requires measurements of the number of jobs at resources and can accept prior probabilities on the demands. Gibbs sampling is challenging to apply to estimation problems for queueing networks since it requires one to efficiently evaluate a likelihood function on the measured data. This likelihood function depends on the equilibrium solution of the network, which is difficult to compute in closed models due to the presence of the normalizing constant of the equilibrium state probabilities. To tackle this obstacle, we define a novel iterative approximation of the normalizing constant and show the improved accuracy of this approach, compared to existing methods, for use in conjunction with Gibbs sampling. We also demonstrate that, as a demand estimation tool, Gibbs sampling outperforms other popular Markov Chain Monte Carlo approximations. Experimental validation based on traces from a cloud application demonstrates the effectiveness of Gibbs sampling for service demand estimation in real-world studies

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"