Cathy H. Xia

Fleet-sizing and service availability for a vehicle rental system via closed queueing networks

In this paper, we address the problem of determining the optimal fleet size for a vehicle rental company and derive analytical results for its relationship to vehicle availability at each rental station in the companys network of locations. This work is motivated by the recent surge in interest for bicycle and electric car sharing systems, one example being the French program Velib (2010). We first formulate a closed queueing network model of the system, obtained by viewing the system from the vehicles perspective. Using this framework, we are able to derive the asymptotic behavior of vehicle availability at an arbitrary rental station with respect to fleet size. These results allow us to analyze imbalances in the system and propose some basic principles for the design of system balancing methods. We then develop a profit-maximizing optimization problem for determining optimal fleet size. The large-scale nature of real-world systems results in computational difficulties in obtaining this exact solution, and so we provide an approximate formulation that is easier to solve and which becomes exact as the fleet size becomes large. To illustrate our findings and validate our solution methods, we provide numerical results on some sample networks.

A smart hill-climbing algorithm for application server configuration

The overwhelming success of the Web as a mechanism for facilitating information retrieval and for conducting business transactions has ledto an increase in the deployment of complex enterprise applications. These applications typically run on Web Application Servers, which assume the burden of managing many tasks, such as concurrency, memory management, database access, etc., required by these applications. The performance of an Application Server depends heavily on appropriate configuration. Configuration is a difficult and error-prone task dueto the large number of configuration parameters and complex interactions between them. We formulate the problem of finding an optimal configuration for a given application as a black-box optimization problem. We propose a smart hill-climbing algorithm using ideas of importance sampling and Latin Hypercube Sampling (LHS). The algorithm is efficient in both searching and random sampling. It consists of estimating a local function, and then, hill-climbing in the steepest descent direction. The algorithm also learns from past searches and restarts in a smart and selective fashion using the idea of importance sampling. We have carried out extensive experiments with an on-line brokerage application running in a WebSphere environment. Empirical results demonstrate that our algorithm is more efficient than and superior to traditional heuristic methods.

Parameter inference of queueing models for IT systems using end-to-end measurements

Performance modeling has become increasingly important in the design, engineering and optimization of information technology (IT) infrastructures and applications. However, modeling work itself is time consuming and requires a good knowledge not only of the system, but also of modeling techniques. One of the biggest challenges in modeling complex IT systems consists in the calibration of model parameters, such as the service requirements of various job classes. We present an approach for solving this problem in the queueing network framework using inference techniques. This is done through a mathematical programming formulation, for which we propose an efficient and robust solution method. The necessary input data are end-to-end measurements which are usually easy to obtain. The robustness of our method means that the inferred model performs well in the presence of noisy data and further, is able to detect and remove outlying data sets. We present numerical experiments using data from real IT practice to demonstrate the promise of our framework and algorithm.

Distributed Operator Placement and Data Caching in Large-Scale Sensor Networks

Recent advances in computer technology and wireless communications have enabled the emergence of stream-based sensor networks. In such sensor networks, real-time data are generated by a large number of distributed sources. Queries are made that may require sophisticated processing and filtering of the data. A query is represented by a query graph. In order to reduce the data transmission and to better utilize resources, it is desirable to place operators of the query graph inside the network, and thus to perform in-network processing. Moreover, given that various queries occur with different frequencies and that only a subset of sensor data may actually be queried, caching intermediate data objects inside the network can help improve query efficiency. In this paper, we consider the problem of placing both operators and intermediate data objects inside the network for a set of queries so as to minimize the total cost of storage, computation, and data transmission. We propose distributed algorithms that achieve optimal solutions for tree-structured query graph topologies and general network topologies. The algorithms converge in Lmax(.HQ + 1) iterations, where Lmax is the order of the diameter of the sensor network, and Hq represents the depth of the query graph, defined as the maximum number of operations needed for a raw data to become a final data. For a regular grid network and complete binary tree query graph, the complexity is 0(radic(N)log2 M), where N is the number of nodes in the sensor network and M is the number of data objects in a query graph. The most attractive features of these algorithms are that they require only information exchanges between neighbors, can be executed asynchronously, are adaptive to cost change and topology change, and are resilient to node or link failures.

Distributed source coding in dense sensor networks

We study the problem of the reconstruction of a Gaussian field defined in [0,1] using N sensors deployed at regular intervals. The goal is to quantify the total data rate required for the reconstruction of the field with a given mean square distortion. We consider a class of two-stage mechanisms which (a) send information to allow the reconstruction of the sensors samples within sufficient accuracy, and then (b) use these reconstructions to estimate the entire field. To implement the first stage, the heavy correlation between the sensor samples suggests the use of distributed coding schemes to reduce the total rate. Our main contribution is to demonstrate the existence of a distributed block coding scheme that achieves, for a given fidelity criterion for the sensors measurements, a total information rate that is within a constant, independent of N, of the minimum information rate required by an encoder that has access to all the sensor measurements simultaneously. The constant in general depends on the autocorrelation function of the field and the desired distortion criterion for the sensor samples.

A unified modeling framework for distributed resource allocation of general fork and join processing networks

This paper addresses the problem of distributed resource allocation in general fork and join processing networks. The problem is motivated by the complicated processing requirements arising from distributed data intensive computing. In such applications, the underlying data processing software consists of a rich set of semantics that include synchronous and asynchronous data fork and data join. The different types of semantics and processing requirements introduce complex interdependence between various data flows within the network. We study the distributed resource allocation problem in such systems with the goal of achieving the maximum total utility of output streams. Past research has dealt with networks with specific types of fork/join semantics, but none of them included all four types. We propose a novel modeling framework that can represent all combinations of fork and join semantics, and formulate the resource allocation problem as a convex optimization problem on this model. We propose a shadow-queue based decentralized iterative algorithm to solve the resource allocation problem. We show that the algorithm guarantees optimality and demonstrate through simulation that it can adapt quickly to dynamically changing environments.

A hidden semi-Markov model for web workload self-similarity

Hidden semi-Markov models (HSMMs) have been well studied and successfully applied to many engineering and scientific problems. The advantage of using a HSMM is its efficient forward-backward algorithms for estimating model parameters to account for an observed sequence. In this paper, we propose a HSMM for modeling Web workloads. We show that this model asymptotically characterizes second order self-similar workloads when some duration distributions of the hidden states are heavy-tailed. A recursive formula is developed for estimating the Hurst parameter of self-similarity. We validate our model and estimation methods with respect to two sets of empirical data (requests per second) collected from two different Web servers. We then use this model to generate self-similar workloads that exhibit the same statistical properties. These measurements show that we can use as few as 4 states together with a simple Poisson process and heavy-tailed Pareto holding time distributions to accurately model the Web workloads considered in this study.

On the Asymptotic Optimality of the SPT Rule for the Flow Shop Average Completion Time Problem

Consider a flow shop withM machines in series, through which a set of jobs are to be processed. All jobs have the same routing, and they have to be processed in the same order on each of the machines. The objective is to determine such an order of the jobs, often referred to as a permutation schedule, so as to minimize the total completion time of all jobs on the final machine. We show that when the processing times are statistically exchangeable across machines and independent across jobs, the Shortest ProcessingTime first (SPT) scheduling rule, based on the total service requirement of each job on allM machines, is asymptotically optimal as the total number of jobs goes to infinity. This extends a recent result of Kaminsky and Simchi-Levi (1996), in which a crucial assumption is that the processing times on allM machines for all jobs must be i.i.d.. Our work provides an alternative proof using martingales, which can also be carried out directly to show the asymptotic optimality of the weighted SPT rule for the Flow Shop Weighted Completion Time Problem.

EMS: Encoded Multipath Streaming for real-time live streaming applications

Multipath streaming protocols have recently attracted much attention because they provide an effective means to provide high-quality streaming over the Internet. However, many existing schemes require a long start-up delay and thus are not suitable for interactive applications such as video conferencing and tele-presence. In this paper, we focus on real-time live streaming applications with stringent end-to-end latency requirement, say several hundreds of milliseconds. To address these challenges, we take a joint multipath and FEC approach that intelligently splits the FEC-encoded stream among multiple available paths. We develop an analytical model and use asymptotic analysis to derive closed-form, optimal load splitting solutions, which are surprisingly simple yet insightful. To our best knowledge, this is the first work that provides such closed-form optimal solutions. Based on the analytical insights, we have designed and implemented a novel Encoded Multipath Streaming (EMS) scheme for real-time live streaming. EMS strives to continuously satisfy the applications QoS requirements by dynamically adjusting the load splitting decisions and the FEC settings. Our simulation results have shown that EMS can not only outperform the existing multipath streaming schemes, but also adapt to the dynamic loss and delay characteristics of the network with minimal overhead.

Performance Modeling and Engineering

This book presents the latest advances in methodology and techniques of performance modeling and engineering, ranging from theoretical advances to system and architecture developments, from technology to economics, from academic innovations to engineering processes, from statistical analysis to system control, and from enterprise systems to computer networks. The collection promotes innovative research in these emerging topics, bridging the gap between theory and practice, and stimulating the use of these new developments. Part I focuses on performance design and engineering, introducing new methodologies and considerations including machine learning, network economics, online advertising and performance engineering. Part II concentrates on scheduling and control, covering new developments in Internet traffic routing, network scheduling, and modeling and control of computer systems. Each chapter is self-contained, including both a broad survey of the topic and the technical challenges and solutions.