Papers by Randolph Nelson
Fearful Symmetry
Springer eBooks, 2020
Journal of the ACM, Jan 3, 1995
Analysis of Contention in Multiprocessor Scheduling
International Symposium on Computer Modeling, Measurement and Evaluation, Sep 12, 1990
Performance evaluation review, Apr 2, 1991
In shared-memory multiprocessor systems it may be more efficient to schedule a task on one proces... more In shared-memory multiprocessor systems it may be more efficient to schedule a task on one processor than on mother, Due to the inevitability of idle processors in these environments, there exists en important tradeoff between keeping the workload balanced and scheduling tasks where they run most efficiently. The purpose of an adaptive task migration policy is to cleterrninc the appropriate balance between the extremes of this load sharing tradeoff. We make the observation that there are considerable differences between this load sharing problem in distributed and
Performance analysis of parallel processing systems
IEEE Computer Society Press eBooks, 1995
... 2459, Volume 2, Issue 3, March 2012) 366 Performance Analysis of Parallel Processing Systems ... more ... 2459, Volume 2, Issue 3, March 2012) 366 Performance Analysis of Parallel Processing Systems B Rajesh1, J Sarath Chandra2, N Gopalakrishna Kini3, Deepthi TS4 Dept of Computer Science and Engineering, Manipal Institute ...
Annals of Operations Research, Dec 1, 1987
This paper will describe the application of an interactive queueing network analyzer and an inter... more This paper will describe the application of an interactive queueing network analyzer and an interactive graphics system to the analysis of a multiple processor computer system. The application of these tools greatly increased the productivity of the modelers and resulted in insights which would have otherwise been difficult, if not impossible, to obtain. With this experience as background, we discuss how the increasing availability of computing resources, especially high resolution interactive computer graphics and sophisticated modeling packages, is likely to have a profound influence on the applied stochastic modeler.
Heavy Traffic Response Times for a Priority Queue with Linear Priorities
Operations Research, Jun 1, 1990
This paper analyzes a queueing system consisting of a single server which dispenses service to jo... more This paper analyzes a queueing system consisting of a single server which dispenses service to jobs of K ≥ 1 priority classes. Jobs are assumed to arrive to the queue according to a Poisson point process with a class dependent rate and to have class dependent service demands that are generally distributed. A linear priority function of the time spent in the system is specified for each job class and is used to schedule jobs. Specifically, the server, when available for service, nonpreemptively selects the job having the highest priority value to be the next job scheduled. Previous work in analyzing a system of this type has concentrated on providing bounds on the expected class response time. We extend these results by providing a closed form expression for the mean class response time and an expression for the ratio of expected response times in the limiting case of heavy traffic. We also provide a closed form expression for the mean class response time under certain light load conditions.
Heads I Win, Tails You Lose
Springer eBooks, 2020
Consider a game where two players toss a coin. If the coin lands heads up, player 1 wins a dollar... more Consider a game where two players toss a coin. If the coin lands heads up, player 1 wins a dollar. Otherwise player 2 wins a dollar. If the coin is fair, then each player has the same chance of winning. A few things about the game are obvious from the outset. Since neither player has an edge over the other, there is little chance that one of them will win a lot of money. Thus, the game should hover around break even most of the time. Additionally, each player should be ahead of the other about half of the time. Another feature of the game concerns its duration if there is an agreed stopping event. For example, suppose the game stops the first time heads is ahead of tails. Then, clearly, the game should end fairly quickly. These observations are all straightforward which suggests that coin tossing does not have much to offer in terms of mathematical results. To show this, and move on to a more interesting topic, let us quickly dispense with the mathematical analysis that establishes these obvious, intuitive, observations.
All That Glitters Is Not Gold
Springer eBooks, 2020
Despite the temptations of gold alluded to in Shakespeare’s verse above from The Merchant of Veni... more Despite the temptations of gold alluded to in Shakespeare’s verse above from The Merchant of Venice, the pursuit of mathematical gold leads not to gilded tombs but to the paradise of the Elysian fields of ancient Greece. Our journey in this chapter takes us back to the days of Phidias (480–430 BC), a Greek sculptor and mathematician who is said to have helped with the design of the Parthenon. The approach in this chapter uses a simple artifice—the ratio of two line segments.
Journal of the ACM, Jul 1, 1987
In this paper catastrophic behavior found in computer systems is investigated. Deterministic Cata... more In this paper catastrophic behavior found in computer systems is investigated. Deterministic Catastrophe theory is introduced first. Then it is shown how the theory can be applied in a stochastic framework, which is useful for understanding computer system performance models. Computer system models that exhibit stochastic cusp catastrophe behavior are then analyzed. These models include slotted ALOHA, multiprogramming in computer systems, and buffer flow control in computer networks.
Expectation and Fundamental Theorems
Springer eBooks, 1995
In the previous chapter we defined random variables and established some of their properties. Lik... more In the previous chapter we defined random variables and established some of their properties. Like variables in algebra, random variables have values but these values can only be determined from random experiments. To characterize all possible outcomes from such an experiment we use distribution functions, which provide a complete specification of a random variable without the necessity of defining an underlying probability space. Specifying distribution functions poses no inherent mathematical difficulties. However, in applications it is frequently not possible to determine the complete distribution function. Often a simpler representation is possible; instead of specifying the entire function we specify a set of statistical values. A statistical value is the average of a function of a random variable. This can be thought of as the value that is obtained from averaging the outcomes of a large number of random experiments as discussed in the frequency-based approach to probability of Section 2.1. In the axiomatic framework of Section 2.2 such an average corresponds to the operation of expectation applied to a function of a random variable.
Randomness and Probability
What do we mean by saying that an event occurs randomly with a certain probability? Answering thi... more What do we mean by saying that an event occurs randomly with a certain probability? Answering this simple question is the objective of this chapter and our answer forms the foundation for all of the material presented in the text. The existence of randomness is often taken for granted, much like the existence of straight lines in geometry, and the assignment of probabilities to events is often assumed axiomatically. The pervasive use of the word “probability” seems to imply that randomness is the rule rather than the exception. One hears of probabilities being ascribed to such diverse things as the weather, the electability of a presidential candidate, the genetic makeup of a child, the outcome of a sporting event, the chance of winning at blackjack, the behavior of elementary particles, the future marriage prospects of two friends, quantum physics, and the wonderfully incessant gyrations of the stock market.
Journal of the American Statistical Association, Jun 1, 1996
Finally, I would like to acknowledge my thesis advisor, Leonard Kleinrock, for the thrill of firs... more Finally, I would like to acknowledge my thesis advisor, Leonard Kleinrock, for the thrill of first seeing the beauty of applied probability through his eyes.
Matrix Geometric Solutions
Springer eBooks, 1995
In Example 8.12 we analyzed a scalar state process that was a modification of the M/M/1 queue. In... more In Example 8.12 we analyzed a scalar state process that was a modification of the M/M/1 queue. In the example, we classified two sets of states: boundary states and repeating states. Transitions between the repeating states had the property that rates from states 2, 3,..., were congruent to rates between states j, j + 1,... for all j ≥ 2. We noted in the example that this implied that the stationary distribution for the repeating portion of the process satisfied a geometric form. In this chapter we generalize this result to vector state processes that also have a repetitive structure. The technique we develop in this chapter to solve for the stationary state probabilities for such vector state Markov processes is called the matrix geometric method. (The theory of matrix geometric solutions was pioneered by Marcel Neuts; see [86] for a full development of the theory.) In much the same way that the repetition of the state transitions for this variation of the M/M/1 queue considered in Example 8.12 implied a geometric solution (with modifications made to account for boundary states), the repetition of the state transitions for vector processes implies a geometric form where scalars are replaced by matrices. We term such Markov processes matrix geometric processes.
Communications in statistics, 1993
Springer eBooks, 1995
Finally, I would like to acknowledge my thesis advisor, Leonard Kleinrock, for the thrill of firs... more Finally, I would like to acknowledge my thesis advisor, Leonard Kleinrock, for the thrill of first seeing the beauty of applied probability through his eyes.
Random Variables and Distributions
Springer eBooks, 1995
This chapter continues developing the theory of probability by defining random variables that are... more This chapter continues developing the theory of probability by defining random variables that are functions defined on the sample space of a probability space. Most stochastic models are expressed in terms of random variables: the number of customers in a queue, the fraction of time a processor is busy, and the amount of time there are fewer than k customers in the network are all examples of random variables. It is typically more convenient to work with random variables than with the underlying basic events of a sample space. Unlike a variable in algebra, which represents a deterministic value, a random variable represents the outcome of a random experiment and can thus only be characterized by its probabilistic outcome. To characterize these possibilities, we specify a distribution function that expresses the probability that a random variable has a value within a certain range. For example, if we let X k be the number of heads obtained in k tosses of a fair coin, then the value of X k is random and can range from 0 to k. The probability that there are less than or equal to l heads, denoted by P [X k ≤ l], can be calculated by enumerating all possible outcomes and is given by $$P[{X_k} \leqslant \ell ] = {2^{ - k}}\sum\limits_{i = 0}^\ell {\left( \begin{gathered} k \hfill \\ i \hfill \\ \end{gathered} \right)}$$ (4.1) (notice that this is the enigmatic summation of (3.36)). The set of values of P [X k ≤ l] for all l is called the distribution function of the random variable X k . In this chapter we will show that a distribution function can be used in place of a probability space when specifying the outcome of a random experiment. This is the basis for most probabilistic models that specify the distributions of random variables of interest but do not specify the underlying probability space. In fact, it is very rare in models to find a specification of a probability space since this is usually understood from the context of the model.
Operations Research, Jun 1, 1987
Subject classifcation: 684 mean time in system, 696 threshold scheduling.
IBM journal of research and development, May 1, 1995
We consider properties of time-sharing schedulers with operations based on an economic measure te... more We consider properties of time-sharing schedulers with operations based on an economic measure termed the delay cost, and reiate these to scheduling policies such as those used in VIM and IMVS. One of these policies, deadline scheduling, is shown to be potentially unstable. We develop delay-cost schedulers that meet similar performance objectives under quasi-equilibrium conditions but which are stable under rapidly varying loads.
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Papers by Randolph Nelson