The MVA Priority Approximation

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation

FAST TCP: Motivation, Architecture, Algorithms, Performance

We describe FAST TCP, a new TCP congestion control algorithm for high-speed long-latency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties which the current TCP implementation has at large windows. We describe the architecture and summarize some of the algorithms implemented in our prototype. We characterize its equilibrium and stability properties. We evaluate it experimentally in terms of throughput, fairness, stability, and responsiveness

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

Modelling and stability of FAST TCP

We introduce a discrete-time model of FAST TCP that fully captures the effect of self-clocking and compare it with the traditional continuous-time model. While the continuous-time model predicts instability for homogeneous sources sharing a single link when feedback delay is large, experiments suggest otherwise. Using the discrete-time model, we prove that FAST TCP is locally asymptotically stable in general networks when all sources have a common round-trip feedback delay, no matter how large the delay is. We also prove global stability for a single bottleneck link in the absence of feedback delay. The techniques developed here are new and applicable to other protocols

Analysis of a class of distributed queues with application

Recently we have developed a class of media access control algorithms for different types of Local Area Networks. A common feature of these LAN algorithms is that they represent various strategies by which the processors in the LAN can simulate the availability of a centralized packet transport facility, but whose service incorporates a particular type of change over time known as 'moving sever' overhead. First we describe the operation of moving server systems in general, for both First-Come - First-Served and Head-of-the-Line orders of service, together with an approach for their delay analysis in which we transform the moving server queueing system into a conventional queueing system having proportional waiting times. Then we describe how the various LAN algorithms may be obtained from the ideal moving server system, and how a significant component of their performance characteristics is determined by the performance characteristics of that ideal system. Finally, we evaluate the compatibility of such LAN algorithms with separable queueing network models of distributed systems by computing the interdeparture time distribution for M/M/1 in the presence of moving server overhead. Although it is not exponential, except in the limits of low server utilization or low overhead, the interdeparture time distribution is a weighted sum of exponential terms with a coefficient of variation not much smaller than unity. Thus, we conjecture that a service centre with moving server overhead could be used to represent one of these LAN algorithms in a product form queueing network model of a distributed system without introducing significant approximation errors

Unbounded Human Learning: Optimal Scheduling for Spaced Repetition

In the study of human learning, there is broad evidence that our ability to retain information improves with repeated exposure and decays with delay since last exposure. This plays a crucial role in the design of educational software, leading to a trade-off between teaching new material and reviewing what has already been taught. A common way to balance this trade-off is spaced repetition, which uses periodic review of content to improve long-term retention. Though spaced repetition is widely used in practice, e.g., in electronic flashcard software, there is little formal understanding of the design of these systems. Our paper addresses this gap in three ways. First, we mine log data from spaced repetition software to establish the functional dependence of retention on reinforcement and delay. Second, we use this memory model to develop a stochastic model for spaced repetition systems. We propose a queueing network model of the Leitner system for reviewing flashcards, along with a heuristic approximation that admits a tractable optimization problem for review scheduling. Finally, we empirically evaluate our queueing model through a Mechanical Turk experiment, verifying a key qualitative prediction of our model: the existence of a sharp phase transition in learning outcomes upon increasing the rate of new item introductions.Comment: Accepted to the ACM SIGKDD Conference on Knowledge Discovery and Data Mining 201

Queue Dynamics With Window Flow Control

This paper develops a new model that describes the queueing process of a communication network when data sources use window flow control. The model takes into account the burstiness in sub-round-trip time (RTT) timescales and the instantaneous rate differences of a flow at different links. It is generic and independent of actual source flow control algorithms. Basic properties of the model and its relation to existing work are discussed. In particular, for a general network with multiple links, it is demonstrated that spatial interaction of oscillations allows queue instability to occur even when all flows have the same RTTs and maintain constant windows. The model is used to study the dynamics of delay-based congestion control algorithms. It is found that the ratios of RTTs are critical to the stability of such systems, and previously unknown modes of instability are identified. Packet-level simulations and testbed measurements are provided to verify the model and its predictions