Bruce Hillyer

How to turn loaded dice into fair coins

We present a new technique for simulating fair coin flips using a biased, stationary source of randomness. Sequences of random numbers are of pervasive importance in cryptography and vital to many other computing applications. Many sources of randomness, such as radioactive or quantum-mechanical sources, possess the property of stationarity. In other words, they produce independent outputs over fixed probability distributions. The output of such sources may be viewed as the result of rolling a biased or loaded die. While a biased die may be a good source of entropy, many applications require input in the form of unbiased bits, rather than biased ones. For this reason, von Neumann (1951) presented a now well-known and extensively investigated technique for using a biased coin to simulate a fair coin. We describe a new generalization of von Neumanns algorithm distinguished by its high level of practicality and amenability to analysis. In contrast to previous efforts, we are able to prove our algorithm optimally efficient, in the sense that it simulates the maximum possible number of fair coin flips for a given number of die rolls. In fact, we are able to prove that in an asymptotic sense our algorithm extracts the full entropy of its input. Moreover, we demonstrate experimentally that our algorithm achieves a high level of computational and output efficiency in a practical setting.

Random I/O scheduling in online tertiary storage systems

New database applications that require the storage and retrieval of many terabytes of data are reaching the limits for disk-based storage systems, in terms of both cost and scalability. These limits provide a strong incentive for the development of databases that augment disk storage with technologies better suited to large volumes of data. In particular, the seamless incorporation of tape storage into database systems would be of great value. Tape storage is two orders of magnitude more efficient than disk in terms of cost per terabyte and physical volume per terabyte; however, a key problem is that the random access latency of tape is three to four orders of magnitude slower than disk. Thus, to incorporate a tape bulk store in an online storage system, the problem of tape access latency must be solved. One approach to reducing the latency is careful I/O scheduling. The focus of this paper is on efficient random I/O scheduling for tape drives that use a serpentine track layout, such as the Quantum DLT and the IBM 3480 and 3590. For serpentine tape, I/O scheduling is problematic because of the complex relationships between logical block numbers, their physical positions on tape, and the time required for tape positioning between these physical positions. The results in this paper show that our scheduling schemes provide a significant improvement in the latency of random access to serpentine tape.

On the modeling and performance characteristics of a serpentine tape drive

New applications require online access to many terabytes of data, but a magnetic disk storage system this large requires thousands of drives. Magnetic tape is be a good alternative, except that the application demand for transparent data retrieval is not met by current tape systems because of their high access latency. This latency can be significantly improved by good retrieval scheduling. A fundamental prerequisite to efficient scheduling is the ability to estimate the amount of time required for tape positioning operations (the locate time). For serpentine tape, which is the most common mass storage tape technology, this estimation is subtle and complex. The main contribution of this paper is a locate-time model for a DLT4000 tape drive. The accuracy of the model is evaluated by measurements, and the utility of the model is demonstrated through a model-driven simulation of retrieval scheduling, validated by measurements and sensitivity testing. In brief, the locate-time model is accurate to within a few percent, which enables the production of efficient schedules.

Modeling and optimizing I/O throughput of multiple disks on a bus

In modern I O architectures multiple disk drives are at tached to each I O controller A study of the performance of such architectures under I O intensive workloads has re vealed a performance impairment that results from a pre viously unknown form of convoy behavior in disk I O In this paper we describe measurements of the read perfor mance of multiple disks that share a SCSI bus under a heavy workload and develop and validate formulas that accurately characterize the observed performance to within on several platforms for I O sizes in the range KB Two terms in the formula clearly characterize the lost perfor mance seen in our experiments We describe techniques to deal with the performance impairment via user level work arounds that achieve greater overlap of bus transfers with disk seeks and that increase the percentage of transfers that occur at the full bus bandwidth rather than at the lower bandwidth of a disk head Experiments show bandwidth improvements of when using these user level tech niques but only in the case of large I Os

A practical secure physical random bit generator

We sugg=t a practical and economical way to generate random bits using a computer disk drive * a source of randomn-. It requirw no additiond hardware (given a system with a disk), and no user involvement. As a concrete example of performance, on a Sun Wtra-1 with a Seagate Cheetah disk, it generatw bits at a rate of either 5 bits per minute or 577 bits per minute depending on the physical phenomena that we use = a source of randomness. The generated bits are random by a theoretical argument, and *O pass a severe battery of statiaticrd twts.

Simulation of power evolution and control dynamics in optical transport systems

The design and analysis of control strategies for high-capacity, reconfigurable optical transmission systems require an understanding of optical system dynamics involving the time-dependent interaction of many components. This paper describes system simulation software that couples continuous physical-layer models of optical transmission components with discrete models for events such as channel add/drops. The simulator computes detailed time traces of signal and noise power propagation along a line system consisting of multiple controlled transmission elements and monitoring devices in response to a particular discrete event. Examples are given illustrating the rich variety of experimentation modes the software supports, including the evaluation of control algorithms, systematic exploration of design parameters, and investigation of cost reduction plans. Details of the development effort are presented, illustrating the contributions of the optical physicists, applied mathematicians, system engineers, and computer scientists who were involved in this collaborative project.

Obtaining high performance for storage outsourcing

The viability of storage outsourcing is critically dependent on the access performance of remote storage. We study this issue by measuring the behavior of a broad variety of I/O-intensive benchmarks as they access remote storage over an IP network. We measure the effect of network latencies that correspond to distances ranging from a local neighborhood to halfway across a continent. We then measure the effect of latency-hiding mechanisms. Our results indicate that, in many cases, the adverse effects of network delay can be rendered inconsequential by clever file system and operating system techniques.

Modeling and optimizing I/O throughput of multiple disks on a bus (summary)

For a wide variety of computational tasks, disk I/O continues to be a serious obstacle to high performance. The focus of the present paper is on systems that use multiple disks per SCSI bus. We measured the performance of concurrent random I/Os, and observed bus-related phenomena that impair performance. We describe these phenomena, and present a new I/O performance model that accurately predicts the average bandwidth achieved by a heavy workload of random reads from disks on a SCSI bus. This model, although relatively simple, predicts performance on several platforms to within 12% for I/O sizes in the range 16-128 KB. We describe a technique to improve the I/O bandwidth by 10-20% for random-access workloads that have large I/Os and high concurrency. This technique increases the percentage of disk head positioning time that is overlapped with data transfers, and increases the percentage of transfers that occur at bus bandwidth, rather than at disk-head bandwidth.

Performance Analysis of Storage Systems

By “performance analysis of a storage system,” we mean the application of a variety of approaches to predict, assess, evaluate, and explain the system’s performance characteristics, along dimensions such as throughput, latency, and bandwidth. Several approaches are commonly used. One approach is analytical modeling, which is the writing of equations that predict performance variables as a function of parameters of the workload, equipment, and system configuration. Another approach is to collect measurements of a running system, and to observe the relationship between characteristics of the workload and the system components, and the resulting performance measurements. A third approach is simulation, in which a computer program implements a simplified representation of the behavior of the components of the storage system, and then a synthetic or actual workload is applied to the simulation program, so that the performance of the simulated components and system can be measured. Trace-driven simulation is an approach that controls a simulation model by feeding in a trace—a sequence of specific events at specific time intervals. The trace is typically obtained by collecting measurements from an actual running system.

Round-like behavior in multiple disks on a bus

In modern I/O architectures, multiple disk drives are attached to each I/O bus. Under I/O-intensive workloads, the disk latency for a request can be overlapped with the disk latency and data transfers of requests to other disks, potentidly resulting in an aggregate I/O throughput at nearly bus bandwidth. This paper reports on a performance impairment that results from a previously unknown form of convoy behavior in disk I/O, which we call munds. In rounds, independent requests to distinct disks convoy, so that each disk services one request before any disk services its next re quest. We analyze log tiles to describe read performance of multiple Seagate Wren-7 disks that share a SCSI bus under a heavy workload, demonstrating the rounds behavior and quantifying its performance impact.