Christopher M. Rump

Advances in Active Queue Management (AQM) Based TCP Congestion Control

Current end-to-end Internet congestion control under tail-drop (TD) queue management experiences performance degradations such as multiple packet losses, high queueing delay and low link utilization. In this paper, we review recently proposed active queue management (AQM) algorithms for supporting end-to-end transmission control protocol (TCP) congestion control. We focus recently developed control theoretic design and analysis method for the AQM based TCP congestion control dynamics. In this context, we analyze the problems of existing AQM proposals in which congestion is detected and controlled reactively based on current and/or past congestion. Then we argue that AQM based TCP congestion control should be adaptive to the dynamically changing traffic situation in order to detect, control and avoid the current and the incipient congestion proactively. Finally, we survey two adaptive and proactive AQM algorithms, PID-controller and Pro-Active Queue Management (PAQM), designed using classical proportional-integral–derivative (PID) feedback control to overcome the reactive congestion control dynamics of existing AQM algorithms. A comparative study of these AQM algorithms with existing AQM algorithms is given. A simulation study under a wide range of realistic traffic conditions suggests that PID-controller and PAQM outperform other AQM algorithms such as random early detection (RED) [Floyd and Jacobson, 18] and proportional-integral (PI) controller [Hollot et al., 24].

A branch-and-price approach for operational aircraft maintenance routing

Abstract In recent years, considerable effort in the field of operations research has been paid to optimizing airline operations, including the logistics of an airline’s fleet of aircraft. We focus on the problem of aircraft routing, which involves generating and selecting a particular route for each aircraft of a sub-fleet that is already assigned to a set of feasible sequences of flight legs. Similar studies typically focus on long-term route planning. However, stochastic events such as severe weather changes, equipment failures, variable maintenance times, or even new regulations mandated by the Federal Aviation Administration (FAA) play havoc on these long-term plans. In addition, these long-term plans ignore detailed maintenance requirements by considering only one or two of the primary maintenance checks that must be performed on a regular, long-term basis. As a result, these plans are often ignored by personnel in airline operations who are forced on a daily basis to develop quick, ad hoc methods to address these maintenance requirements and other irregular events. To address this problem, we develop an operational aircraft maintenance routing problem formulation that includes maintenance resource availability constraints. We propose a branch-and-price algorithm for solving this problem, which, due to the resource constraints, entails a modification of the branch-on, follow-on branching rule typically used for solving similar problems. Through computational testing, we explore the efficiency of this solution approach under a combination of heuristic choices for column (route) generation and selection.

A predictive and robust active queue management for Internet congestion control

Recently many active queue management (AQM) algorithms have been proposed to address performance degradations of end-to-end congestion control. However, these AQM algorithms show weaknesses to detect and control congestion under dynamically changing network situations. In this paper, we propose a predictive and robust AQM algorithm, called proportional-integral-derivative (PID)-controller, using PID feedback control the incipient as well as current congestion adaptively and proactively to dynamically changing network environments. A simulation study over a wide range of IP traffic conditions shows that PID-controller outperforms other AQM algorithms such as random early detection (RED) and proportional-integral (PI) controller in terms of the queue length dynamics, the packet loss rates, and the link utilization.

Routing of a hazmat truck in the presence of weather systems

This paper focuses on the effects of weather systems on hazmat routing. We start by analyzing the effects of a weather system on a vehicle traversing a single link. This helps characterize the time-dependent attributes of a link due to movement of the weather systems. This analysis is used as a building block for the problem of finding a least risk path for hazmat transportation on a network exposed to such weather systems. Several methods are offered to solve the underlying problem, and computational results are reported. We draw two conclusions from this paper. First, it is possible to determine the time-dependent attributes for links on a network provided that some assumptions on the nature of the weather system are made. Second, heuristics can provide effective solutions for practical size problems while allowing for parking the vehicle to avoid weather system effects.

Data Clustering for Fitting Parameters of a Markov Chain Model of Multi-Game Playoff Series

We propose a Markov chain model of a best-of-7 game playoff series that involves game-to-game dependence on the current status of the series. To create a relatively parsimonious model, we seek to group transition probabilities of the Markov chain into clusters of similar game-winning frequency. To do so, we formulate a binary optimization problem to minimize several measures of cluster dissimilarity. We apply these techniques on Major League Baseball (MLB) data and test the goodness of fit to historical playoff outcomes. These state-dependent Markov models improve significantly on probability models based solely on home-away game dependence. It turns out that a better two-parameter model ignores where the games are played and instead focuses simply on, for each possible series status, whether or not the team with home-field advantage in the series has been the historical favorite - the more likely winner - in the next game of the series.

The Effects of Home-Away Sequencing on the Length of Best-of-Seven Game Playoff Series

We analyze the number of games played in a seven-game playoff series under various home-away sequences. In doing so, we employ a simple Bernoulli model of home-field advantage in which the outcome of each game in the series depends only on whether it is played at home or away with respect to a designated home team. Considering all such sequences that begin and end at home, we show that, in terms of the number of games played, there are four classes of stochastically different formats, including the popular 2-3 and 2-2 formats both currently used in National Basketball Association (NBA) playoffs. Characterizing the regions in parametric space that give rise to distinct stochastic and expected value orderings of series length among these four format classes, we then investigate where in this parametric space that teams actually play. An extensive analysis of historical 7-game playoff series data from the NBA reveals that this home-away model is preferable to the simpler, well-studied but ill-fitting binomial model that ignores home-field advantage. The model suggests that switching from the 2-2 series format used for most of the playoffs to the 2-3 format that has been used in the NBA Finals since a switch in 1985 would stochastically lengthen these playoff series, creating an expectation of approximately one extra game per playoff season. Such evidence should encourage television sponsors to lobby for a change of playoff format in order to garner additional television advertising revenues while reducing team and media travel costs.

Andrei Markov in the Stanley Cup Playoffs

A Markov is a young Russian defenseman for the Montreal Canadiens of the National Hockey League (NHL). The title of this article, however, refers to the Russian mathematician of the same name born more than a century earlier. For, unlike the hockey player, the mathematician appears to be at play in every Stanley Cup playoff series. This article studies the application of a Markov chain model to sevengame playoff series in the NHL. Each of these series of games ends when one of the team garners four wins. With few exceptions, these series are played in a so-called 2–2 format (HHAAHAH), in which the team favored with a homeThe Stanley Cup playoffs appear to be well-modeled by a Markov Chain. This article describes the model and the fit using data from 1939–2004.

Capital Growth and the St. Petersburg Game

We are forced to quell the mistaken notion that William A. Whitworth discovered the famous Kelly formula for proportionate betting as put forth in a recent note by Székely and Richards. In his analysis of gambling, Whitworth, like Daniel Bernoulli before him, sought a “fair” valuation of a risky venture for a gambler with limited wealth. A “fair” valuation was one that would yield zero capital growth, that is, a geometric mean return of zero. In contrast, the Kelly criterion seeks a fixed proportion of a gamblers wealth that should be wagered to maximize capital growth. We compare and contrast these similar problems in the context of the famous St. Petersburg wager.

Application of a PID feedback control algorithm for adaptive queue management to support TCP congestion control

Recently, many active queue management (AQM) algorithms have been proposed to address the performance degradation of end-to-end congestion control under tail-drop (TD) queue management at Internet routers. However, these AQM algorithms show performance improvement only for limited network environments, and are insensitive to dynamically changing network situations. In this paper, we propose an adaptive queue management algorithm, called PID-controller, that uses proportionalintegral-derivative (PID) feedback control to remedy these weaknesses of existing AQM proposals. The PID-controller is able to detect and control congestion adaptively and proactively to dynamically changing network environments using incipient as well as current congestion indications. A simulation study over a wide range of IP traffic conditions shows that PID-controller outperforms other AQM algorithms such as Random Early Detection (RED) [3] and Proportional-Integral (PI) controller [9] in terms of queue length dynamics, packet loss rates, and link utilization.