| Stochastic Models in Reliability |
30 SEP 91 |
15 pages |
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEAR CH
|
 | Two approaches for simulating the reliability function are considered - one using the total hazard estimator and the other using importance sampling. It is shown both for the Wheatstone Bridge system and also for a triangular system that the total hazard estimator has significantly smaller variance when compared both to the standard importance sampling estimator and also to an improved version of it. |
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| Stochastic Models in Reliability |
30 JUN 90 |
5 pages |
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEAR CH
|
| There were two principal accomplishments during the grant period. The first gives a new more effective reordering role for processing jobs (that may not complete) on a multiprocessor system. This is shown to improve on the previously known MF (move to front) and MB (move to back) ordering rules. The other accomplishment was a new variance reduction method in simulation, using 'random hazards' in a Markov process. |
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| Stochastic Models in Reliability |
NOV 89 |
11 pages |
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEAR CH
|
| A variety of stochastic models in reliability were studied. Approximations in renewal theory and continuous time Markov chains were obtained by analyzing the relevant stochastic process at a gamma distributed rather than a fixed time. Some statistical problems related to software reliability were considered. Keywords: Reliability, Simulation, Continuous time markov chains, Renewal processes, Stochastic models. |
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| Are Mass Extinctions Really Periodic? |
OCT 86 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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 | It is argued that the analysis of family extinction data that resulted in the claim of a 26 Myr periodicity of mass extinctions was flawed in that it did not allow for the possibility of a symmetric random walk model, which is shown to be perfectly consistent with the data. (Author) |
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| Peaks from Random Data |
OCT 86 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| In an influential and controversial paper, Raup and Sepkoski defined an event of mass extinction to have occurred in any time period (of roughly 6.4 million years) for which the data value for that time period (equal to the proportion of the families existing at the beginning of that period that went extinct during the period) exceeded that of its immediate neighbors. This note analyzes the data are randomly generated ... |
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| Reliability Analysis |
31 AUG 86 |
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| Authors:
Richard E. Barlow; William S. Jewell; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| The operations research accomplishments of three principal investigators are described. Areas with results are system reliability, combination of opinions, Bayesian applications to data analysis and quality assurance, reliability growth and software reliability, Bayesian approximation methods, risk portfolio problems, hierarchical models, simulation, estimation and testing, reliability models, and peaks from random data. |
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| A Random Walk Subject to a Randomly Changing Environment |
SEP 1983 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| A common model for the changes over time of the price (or sometimes the logarithm of the price) of a commodity is the random walk model. This is a Markov model which supposes that the change in price in any time period is a random variable, independent of the past, and having a given distribution F. In this note, we propose a generalized model in which the distribution of price ... |
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| On the Use of Replacements to Extend System Life |
JUN 1983 |
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| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| This paper is concerned with the following question. A system has one vital component for which there are n spares. Whenever the vital component fails, the system fails. The authors like to schedule the replacement of the vital component with the spares so as to prolong the life of the system as much as possible. This problem can be generalized to where there are several components in the system and ... |
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| Using Simulation to Estimate First Passage Distributions |
JAN 1983 |
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| Authors:
Sheldon M. Ross; Zvi Schechner; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| Consider a discrete time Markov process (X sub n, n > or = 0). For a given subset A of the state space consider the problem of using simulation to estimate the number of transitions it takes the process to enter A. Using estimators based on the 'observed hazard', we are able to improve on the usual Monte Carlo estimator. We also consider the problem of estimating the distribution of ... |
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| A Model in Which Component Failure Rates Depend on the Working Set |
SEP 1982 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| The authors consider a multicomponent system in which the failure rate of given component at any time depends on the set of working components at that time. Sufficient conditions are presented under which such a system has a new better then used life distribution. When the failed components are allowed to be repaired, they present conditions under which the resulting process is time reversible. |
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| Some Reliability Applications of the Variability Ordering |
MAY 1982 |
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| Authors:
Sheldon M. Ross; Zvi Schechner; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| The random variable X is said to be more variable than Y if E(f(x)) = or > E(f(Y)) for all increasing convex functions f. We prove a preservation, under random sized sums, property of this ordering and then applying it to branching processes and shock models. Other applications of this order--to a population survival and to a Poisson shock model--are also given. (Author) |
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| A Simple Heuristic Approach to Simplex Efficiency |
AUG 1981 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| Consider the standard linear program: Minimize c x--subject to: A x = b, x greater than or equal to 0, where A is an m x n matrix. The simplex algorithm solves this linear program by moving from extreme point of the feasibility region to a better (in terms of the objective function c x) extreme point (via the pivot operation) until the optimal is reached. In order to obtain ... |
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| Minimizing Expected Makespan in Stochastic Open Shops |
JUL 1981 |
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| Authors:
Michael L. Pinedo; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| Suppose that two machines are available to process n tasks. Each task has to be processed on both machines, the order in which this happens is immaterial. Task j has to be processed on machine 1 (2) for random time X sub j (Y sub j) with distribution F sub j (G sub j). This kind of model is usually called an Open Shop. The time that it takes to ... |
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| Some Applications of a Result Concerning Variability Orderings |
JUN 1981 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| We say that the random variable X is more variable than Y if E(f(X)) greater than or equal to E(f(Y)) for all increasing convex functions f. We prove a preservation, under random sized sums, property of this ordering and then apply it to branching processes and shock models. |
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| Multi-Server Queues |
JUN 1981 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| We will survey a variety of multiserver models in which the arrival stream is a Poisson process. In particular, we will consider the Erlang loss model in which arrivals finding all servers busy are lost. In this system, we assume a general service distribution. We will also consider finite and infinite capacity versions of this model. Another model of this type is the shared processor system in which service is ... |
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| Multi-Valued Component Systems |
31 JAN 1981 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| A large number of reliability models have been considered under the AFOSR Grant AFOSR77-3213. |
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| On the Consecutive k-of-n System. |
DEC 1980 |
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| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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| The consecutive k-of-n system is considered in which there are n components linearly ordered. Each component either functions or fails and the system is said to be failed if any k consecutive components are failed. Let r(p) = r(p sub 1, ..., p sub n) denote the probability that the system does not fail given that the components are independent, component i functions with probability p sub i, i = ... |
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| On the Consecutive k-of-n System. |
NOV 1980 |
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| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| We consider the consecutive k-of-n system in which there are n components linearly ordered. Each component either functions or fails and the system is said to be failed if any k consecutive components are failed. Let r(p) = r(p(1), ..., p(n)) denote the probability that the system does not fail given that the components are independent, component i functions with probability p(i), i = 1, ..., n. The function r(p) ... |
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| Waiting Line and Queueing Models. |
OCT 1980 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| A large number of waiting line and scheduling models have been considered under the support of the ONR contract N00014-77-C-0299. (Author) |
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| The Observed Hazard and Multicomponent Systems. |
JAN 1980 |
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| Authors:
Mark Brown; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| Let X denote the life of some system. We define the observed hazard rate at time t, call it R(t), as the instantaneous probability (density) of failure of X at time t given survival up to t and given a complete description of the system state at t. We conjecture that the total observed hazard--namely, the integral of R(t)dt from the limits of 0 to x--is an exponential random variable ... |
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| A Note on First Passage Times in Birth and Death and Nonnegative Diffusion Processes. |
NOV 1979 |
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| Authors:
Cyrus Derman; Sheldon M. Ross; Zvi Schechner; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Consider a birth and death process starting in state 0. Analytical arguments were shown earlier that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR. |
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| Scheduling Jobs Subject to Nonhomogeneous Poisson Shocks. |
NOV 1979 |
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| Authors:
Michael L. Pinedo; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Consider n jobs which have to be performed sequentially in time. There are external shocks which occur according to a nonhomogenous Poisson process. If a shock occurs during the performance of a job, then work on that job ends and work on the next one commences. A job is successfully performed if no shocks occur during its execution time. We consider such problems as maximizing: (1) The expected number of ... |
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| On the Candidate Problem with a Random Number of Candidates. |
AUG 1979 |
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| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| In the problem under consideration a decision maker has a total of M candidates to interview sequentially. The decision maker must either accept or reject the candidate being interviewed after he has been ranked with respect to his predecessors. Once rejected a candidate cannot be reconsidered; once a candidate is accepted no futher interviews are carried out. The objective is to select the candidate in such a way as to ... |
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| A Random Graph. |
APR 1979 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Let X(1),X(2), ..., X(n) be independent random variables such that P(X(i) = j) = P sub j , j = 1,2, ..., n, sum from j = 1 to n of P sub j = 1 and consider a graph with n nodes numbered 1,2, ..., n and the arcs (i,X(i)), i = 1,2, ..., n. We determine the probability that the above so-called random graph is connected and then ... |
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| Optimal List Order under Partial Memory Constraints. |
MAR 1979 |
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| Authors:
Yi C. Kan ; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| The problem of interest is to determine the optimal ordering so as to minimize the long run average cost. Clearly if the P sub i were known the optimal ordering would simply be to order the elements in decreasing order of the P sub i's. In fact even if the P sub i's were unknown we could do as well asymptotically by ordering the elements at each unit of time ... |
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| On the Optimal Assignment of Servers and Repairman. |
NOV 1978 |
|
| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Consider an N server queuing system in which service times of server i are exponentially distributed random variables with rate lambda sub i. Customers arrive in accordance with some arbitrary arrival process. If a customer arrives when all servers are busy, then he is lost to the system; otherwise, he is assigned to one of the free servers according to some policy. Once a customer is assigned to a server ... |
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| On the Duration of the Problem of the Points. |
NOV 1978 |
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| Authors:
Sheldon M. Ross; Mehrdad Shahshahani; Gideon Weiss; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| We consider an r-player version of the famous problem of the points which was the stimulus for the correspondence between Pascal and Fermat in the seventeenth century. At each play of a game, exactly one of the players wins a point - player i winning with probability p sub i. The game ends the first time a player has accumulated his required number of points - this requirement being n ... |
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| On the Number of Component Failures in System Whose Component Lives are Exchangeable. |
OCT 1978 |
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| Authors:
Sheldon M. Ross; Mehrdad Shahshahani; Gideon Weiss; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
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| On the First Time a Separately Maintained Parallel System has been Down for a Fixed Time. |
APR 1978 |
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| Authors:
Sheldon M. Ross; Jack Schechtman; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| In considering a system that works for a random time and when failed is fixed in a length of time that is also random an important question is the study of the first time the system is not working for an interval of time longer than some prespecified value. For instance in a nuclear reactor, when the safety system is out for some critical time it is necessary to shut ... |
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| Generalized Poisson Shock Models. |
APR 1978 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Suppose that shocks hit a device in accordance with a nonhomogeneous Poisson process with intensity function lambda(t). The ith shock causes a damage X sub i. The X sub i are assumed to be independent and identically distributed positive random variables, and are also assumed independent of the counting process of shocks. Let D(x sub 1, ..., x sub n) denote the total damage when n shocks having damages x ... |
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| Approximations in Finite Capacity Multi-Server Queues with Poisson Arrivals. |
DEC 1977 |
|
| Authors:
Shirley A. Nozaki; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| This paper considers an M/G/K queueing model having finite capacity N. That is, a model in which customers, arriving in accordance with a Poisson process having rate lambda, enter the system if there are less than N others present when they arrive, and are then serviced by one of k servers, each of whom has service distribution G. Upon entering, a customer will either immediately enter service if at least ... |
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| Multi-Valued State Component Reliability Systems. |
JUN 1977 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Consider a reliability system that is composed of n components each of which is operating at some performance level. And suppose that there exists a nondecreasing function phi, called the structure function, such that phi (x sub 1, ..., x sub n) denotes the performance level of the system when the ith component's performance level is x sub i , i = 1, ..., n. Whereas almost all previous work ... |
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| Average Delay in Queues with Nonstationary Poisson Arrivals. |
MAY 1977 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| One of the major difficulties in attempting to apply known queueing theory results to real problems is that almost always these results assume a time stationary Poisson arrival process, whereas in practice the actual process is almost invariably nonstationary. This paper considers single server infinite capacity queueing models in which the arrival process is a nonstationary process with an intensity function Lambda(t), t > or = 0, which is itself ... |
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| A Heterogeneous Arrival and Service Queueing Loss Model. |
MAY 1977 |
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| Authors:
Simson Fond; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| It can be shown that if all arrivals finding the server busy are lost then the percentage of arrivals lost is a decreasing function of c. This is in line with a general conjecture to the effect that the more nonstationary a Poisson arrival process is then the greater the average customer delay (in infinite capacity models) or the greater the percentage of lost customers (in finite capacity models). |
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| Queuing Models for Multiple Chamber Locks. |
SEP 1976 |
32 pages |
| Authors:
C. Roger Glassey; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Several models for predicting mean waiting time of river traffic at a multiple chamber lock were developed and tested. Mean waiting time predicted by the M/G/1 model differed significantly from observed times. Analysis of possible causes of failure of this model suggested a limited queue length M/G/1 model for one chamber, from which more accurate predictions were derived. For the two chamber system, an M/G/1 model with random batch size ... |
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| Approximations in Multi-Server Poisson Queues. |
APR 1976 |
|
| Authors:
Shirley A. Nozaki; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Our major objective is to obtain an approximation for the average time spent waiting in queue by a customer in an M/G/k queueing system--call it W sub Q. This is done by means of an approximation assumption presented, which is shown to be asymptotically valid both in heavy and in light traffic. The approximation assumption is used to derive an approximation for W sub Q. Numerical comparison with tables given ... |
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| Optimal System Allocations with Penalty Costs. |
SEP 1975 |
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| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| There are N stages to sequentially construct I successful components. At each stage, one allocates a certain amount of money for the construction of a component. If y is the amount allocated, then the component constructed will be a success with probability P(y), where P is a continuous nondecreasing function satisfying P(0) = 0. After each component is constructed, one is informed as to whether or not it is successful. ... |
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| A Note on Optimal Stopping for Success Runs. |
NOV 1974 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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| The following model is considered by Starr (1972): At most n tosses of a coin, having a constant probability p of coming up heads, are made. After each toss one has the option of either stopping and receiving an amount equal to the length of the terminal run of heads (that is, if one was on a streak of k heads in the last k tosses, then one could stop ... |
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| Planning and Control under Risk. |
30 JUN 1974 |
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| Authors:
William S. Jewell; Robert M. Oliver; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| A variety of different research efforts have been supported in the past three years. This research falls in the following areas: (1) Theory and computation of optimal policies in dynamic programming risk problems; (2) Applied stochastic processes; (3) Development of models for institutional operating policies; and, (4) Linearized Bayesian estimation models. A summary of the research effort in each of the above areas is presented. |
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| On Time to First Failure in Multicomponent Exponential Reliability Systems. |
MAR 1974 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Consider an n component reliability system having the property that at any time each of its components is either up (i.e., working) or down (i.e., being repaired). Each component acts independently and it is supposed that each time the ith component goes up it remains up for an exponentially distributed time having mean (mu sub i), and each time it goes down it remains down for an exponentially distributed time ... |
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| Multicomponent Reliability Systems. |
FEB 1974 |
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| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| A multicomponent reliability system in which each component is either up (i.e., working) or down (i.e., failed) in accordance with an alternating renewal process is considered. For arbitrary structures the following quantities are derived: The average rate of system failure; the average uptime of the system; and, the average downtime of the system. Further results are also obtained in the special case where the system structure is either series or ... |
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| Optimal Allocations in the Construction of k-Out-of-n Reliability Systems. |
SEP 1973 |
|
| Authors:
Sheldon M. Ross; Cyrus Derman; Gerald J. Lieberman; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| The authors want to build n components so as to form an n component system which will function if at least k of the components function. If x dollars is invested in building a component, then this component will function with probability P(x). Given a total income of A dollars, the problem of interest is to determine how much money should be invested in each component so as to maximize ... |
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| Bounds on the Delay Distribution in GI/G/1 Queues, |
JAN 1973 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| Bounds are obtained for the limiting distribution of the delay in queue for a GI/G/1 system via Martingale theory. These bounds are somewhat stronger than similar bounds recently obtained by Kingman. Simplifications of the bounds are obtained in the special cases where the service distribution is either IFR, DFR, NBU or NWU. (Author) |
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| Assembly of Systems Having Maximum Reliability. |
29 SEP 1972 |
|
| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; STANFORD UNIV CALIF
|
| The first problem considered in the paper is concerned with the assembly of independent components into parallel systems so as to maximize the expected number of system that perform satisfactorily. Associated with each component is a probability of it performing successfully. It is shown that an optimal assembly is obtained if the reliability of each assembled system can be made equal. If such equality is not attainable, then bounds are ... |
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| Dynamic Programming and Gambling Models, |
SEP 1972 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| In the paper the author formulates and obtains optimal gambling strategies for certain gambling models. This is done by setting these models within the framework of dynamic programming (also referred to as Markovian decision processes) and then using results in this field. (Author) |
|
| On the Maximum of a Stationary Independent Increment Process. |
NOV 1971 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| A stationary independent increment process is the continuous time analogue of the discrete random walk, and, as such, has a wide variety of applications. In this paper the author considers M(t) , the maximum value that such a process attains by time t . By using renewal theoretic methods the author obtains results about M(t) . In particular the author shows that if mu, the mean drift of the process, ... |
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| On Optimal Assembly of Systems. |
25 AUG 1971 |
|
| Authors:
Cyrus Derman; Gerald J. Lieberman; Sheldon M. Ross; STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
|
| The paper discusses the following reliability problem: A system has k different types of components. Associated with each component is a numerical value. Let the set(a sup j) (j = 1,...,k) denote the set of numerical values of the k components. Let R(a(sup 1),...,a(sup k) denote the probability that the system will perform satisfactorily (i.e. R(a(sup 1),...,a(sup k) is the reliability of the system) and assume R(a(sup 1),...,a(sup k) has ... |
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| Optimal Issuing Policies. |
APR 1971 |
|
| Authors:
Mark Brown; Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| The document considers a stockpile consisting of n items where the ith item has a rating r sub i, where i = 1, ..., n . An item with rating r, if kept in stockpile until time t and then released to the field, is considered to have a field life of L(r)d(t). Thus it is assumed that for any t, the field life for issuance at time t is ... |
|
| Some Results in Dynamic Programming. |
APR 1971 |
|
| Authors:
Sheldon M. Ross; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| The first part of the report discusses a dynamic programming model in which all rewards obtained by the decision maker are assumed nonnegative. The decision maker's objective is to successively choose actions so as to maximize his expected reward earned over an infinite time span. It follows from known results that the decision maker's choice need only depend upon the outcome of a randomization that depends on the model only ... |
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| ASYMPTOTIC PROPERTIES OF CUMULATIVE PROCESSES. |
SEP 1970 |
|
| Authors:
Sheldon M. Ross; Mark Brown; CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
|
| The theory of cumulative processes, introduced and developed by W. L. Smith, provides a significant generalization of the renewal counting process. One examines the question of extending the Blackwell and key renewal theorems to cumulative processes. For a subclass of cumulative processes, which one calls strongly cumulative, the Blackwell and key renewal theorems hold under very general conditions. This class of cumulative processes includes all the standard examples of cumulative ... |
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Reports by Author
