Whitt, Ward
Overview
Works:  54 works in 91 publications in 1 language and 879 library holdings 

Roles:  Author 
Publication Timeline
.
Most widely held works by
Ward Whitt
Stochasticprocess limits : an introduction to stochasticprocess limits and their application to queues by
Ward Whitt(
)
25 editions published between 2001 and 2011 in English and held by 824 WorldCat member libraries worldwide
This book is about stochasticprocess limits  limits in which a sequence of stochastic processes converges to another stochastic process. These are useful and interesting because they generate simple approximations for complicated stochastic processes and also help explain the statistical regularity associated with a macroscopic view of uncertainty. This book emphasizes the continuousmapping approach to obtain new stochasticprocess limits from previously established stochasticprocess limits. The continuousmapping approach is applied to obtain heavytrafficstochasticprocess limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavytraffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance. This book was the recipient of the 2003 INFORMS Frederick W. Lanchester Prize, awarded annually by the Institute for Operations Research and the Management Sciences (INFORMS) for the best contribution to operations research and the management sciences published in English
25 editions published between 2001 and 2011 in English and held by 824 WorldCat member libraries worldwide
This book is about stochasticprocess limits  limits in which a sequence of stochastic processes converges to another stochastic process. These are useful and interesting because they generate simple approximations for complicated stochastic processes and also help explain the statistical regularity associated with a macroscopic view of uncertainty. This book emphasizes the continuousmapping approach to obtain new stochasticprocess limits from previously established stochasticprocess limits. The continuousmapping approach is applied to obtain heavytrafficstochasticprocess limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavytraffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance. This book was the recipient of the 2003 INFORMS Frederick W. Lanchester Prize, awarded annually by the Institute for Operations Research and the Management Sciences (INFORMS) for the best contribution to operations research and the management sciences published in English
A new view of the heavytraffic limit theorem for manyserver queues by
Peter W Glynn(
Book
)
2 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
The asymptotic efficiency of simulation estimators by
Peter W Glynn(
Book
)
4 editions published in 1989 in English and held by 6 WorldCat member libraries worldwide
A decisiontheoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes. In this context, the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk (the overall expected cost). This framework is appealing philosophically, but it is difficult to apply in practice (e.g., to compare the efficiency of two different estimators) because only rarely can the efficiency associated with a given computational budget be calculated. However, a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases. A limit theorem established for this model supports and extends a fairly well known efficiency principle, proposed by Hammersley and Handscomb (1964), p. 22: The efficiency of a Monte Carlo process may be taken as inversely proportional to the product of the sampling variance and the amount of labour expended in obtaining this estimate. (KR)
4 editions published in 1989 in English and held by 6 WorldCat member libraries worldwide
A decisiontheoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes. In this context, the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk (the overall expected cost). This framework is appealing philosophically, but it is difficult to apply in practice (e.g., to compare the efficiency of two different estimators) because only rarely can the efficiency associated with a given computational budget be calculated. However, a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases. A limit theorem established for this model supports and extends a fairly well known efficiency principle, proposed by Hammersley and Handscomb (1964), p. 22: The efficiency of a Monte Carlo process may be taken as inversely proportional to the product of the sampling variance and the amount of labour expended in obtaining this estimate. (KR)
Portfolio choice and the Bayesian Kelly criterion by
Sid Browne(
Book
)
1 edition published in 1995 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 5 WorldCat member libraries worldwide
Weak convergence theorems for queues in heavy traffic by
Ward Whitt(
Book
)
4 editions published between 1968 and 1969 in English and held by 4 WorldCat member libraries worldwide
Limit theorems are proved for unstable queueing systems. The GI/G/1 queue is the primary concern, but the theorems apply to more general systems in which the various independence assumptions are relaxed. Bulk queues, queues with several servers (GI/M/s), queues with a finite waiting room, and dams are also discussed. (Author)
4 editions published between 1968 and 1969 in English and held by 4 WorldCat member libraries worldwide
Limit theorems are proved for unstable queueing systems. The GI/G/1 queue is the primary concern, but the theorems apply to more general systems in which the various independence assumptions are relaxed. Bulk queues, queues with several servers (GI/M/s), queues with a finite waiting room, and dams are also discussed. (Author)
Multiple channel queues in heavy traffic by
Donald L Iglehart(
Book
)
2 editions published in 1969 in English and held by 4 WorldCat member libraries worldwide
Queueing systems with r arrival channels and s service channels are studied under the condition of heavy traffic: traffic intensity greater than or equal to one. Limit theorems are obtained for the random functions induced in D(0,1) by the following processes: total queue length, queue length at the ith server, total load, load at the ith server, virtual waiting time, waiting time of the nth arrival, number of departures, time of the nth arrival, and the time of the nth departure. Also limit theorems for certain functionals of the above processes are obtained as an immediate consequence of weak convergence
2 editions published in 1969 in English and held by 4 WorldCat member libraries worldwide
Queueing systems with r arrival channels and s service channels are studied under the condition of heavy traffic: traffic intensity greater than or equal to one. Limit theorems are obtained for the random functions induced in D(0,1) by the following processes: total queue length, queue length at the ith server, total load, load at the ith server, virtual waiting time, waiting time of the nth arrival, number of departures, time of the nth arrival, and the time of the nth departure. Also limit theorems for certain functionals of the above processes are obtained as an immediate consequence of weak convergence
The equivalence of functional central limit theorems for counting processes and associated partial sums by
Donald L Iglehart(
Book
)
3 editions published in 1969 in English and held by 3 WorldCat member libraries worldwide
Let (u sub n, n = or> 1) be a sequence of nonnegative random variables, not necessarily independent or identically distributed, with an associated counting process (N(t), t = or>), defined by N(t) = max (k: u sub 1 + ... + u sub k = or <t), u sub 1 = or <t; N(t) = 0, u sub 1> t. It is shown that functional central limit theorems (invariance principles) for N(t) are equivalent to corresponding statements for the sequence of partial sums of the u sub n's. (Author)
3 editions published in 1969 in English and held by 3 WorldCat member libraries worldwide
Let (u sub n, n = or> 1) be a sequence of nonnegative random variables, not necessarily independent or identically distributed, with an associated counting process (N(t), t = or>), defined by N(t) = max (k: u sub 1 + ... + u sub k = or <t), u sub 1 = or <t; N(t) = 0, u sub 1> t. It is shown that functional central limit theorems (invariance principles) for N(t) are equivalent to corresponding statements for the sequence of partial sums of the u sub n's. (Author)
Multiple channel queues in heavy traffic, II: sequences, networks, and batches by
Stanford University(
Book
)
2 editions published in 1969 in English and held by 2 WorldCat member libraries worldwide
Sequences of queueing facilities with r parallel arrival channels and s parallel service channels are studied under the conditions of heavy traffic: the associated sequences of traffic intensities approaching a limit greater than or equal to one. Weak convergence is obtained for sequences of random functions induced in D(0,1) by the basic queueing processes. Sequences of queueing systems in heavy traffic which are networks of the facilities described above are also investigated. Furthermore, customers are allowed to arrive and be served in batches
2 editions published in 1969 in English and held by 2 WorldCat member libraries worldwide
Sequences of queueing facilities with r parallel arrival channels and s parallel service channels are studied under the conditions of heavy traffic: the associated sequences of traffic intensities approaching a limit greater than or equal to one. Weak convergence is obtained for sequences of random functions induced in D(0,1) by the basic queueing processes. Sequences of queueing systems in heavy traffic which are networks of the facilities described above are also investigated. Furthermore, customers are allowed to arrive and be served in batches
Fiat Money in an Economy with One Nondurable Good and No Credit (A Noncooperative Sequential Game) by
Martin Shubik(
Book
)
2 editions published in 1973 in English and held by 2 WorldCat member libraries worldwide
The purpose of the report is to provide satisfactory connections between current theories in macroeconomics and microeconomics. This study differs from the majority of past efforts in this direction because in a microeconomic context it focuses on money, credit, and financial institutions. From the point of view of monetary theory, the novelty lies in the efforts to connect individual economic behavior with the behavior of the economy as a whole and to apply mathematical models for this purpose. From the point of view of the more closely related mathematical literature on nperson games and competitive equilibrium analysis, the novelty lies in the efforts to explicitly consider money, credit, and financial institutions. The authors believe that an explicit treatment of money, credit, and financial institutions is necessary for forging links between macroeconomics and microeconomics. (Author)
2 editions published in 1973 in English and held by 2 WorldCat member libraries worldwide
The purpose of the report is to provide satisfactory connections between current theories in macroeconomics and microeconomics. This study differs from the majority of past efforts in this direction because in a microeconomic context it focuses on money, credit, and financial institutions. From the point of view of monetary theory, the novelty lies in the efforts to connect individual economic behavior with the behavior of the economy as a whole and to apply mathematical models for this purpose. From the point of view of the more closely related mathematical literature on nperson games and competitive equilibrium analysis, the novelty lies in the efforts to explicitly consider money, credit, and financial institutions. The authors believe that an explicit treatment of money, credit, and financial institutions is necessary for forging links between macroeconomics and microeconomics. (Author)
Functional large deviation principles for waiting and departure processes by
Anatolii Puhalskii(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
Measurements and approximations to describe the offered traffic and predict the average workload in a singleserver queue by K. W Fendick(
)
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
Estimating the Asymptotic Variance with Batch Means(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
In this paper it is shown that there does not exist a procedure to consistently estimate the asymptotic variance constant in a stochastic simulation using batch means when the number of batches is held fixed as the run length increases. Thus, if consistency is desired, then the number of batches must increase as the run length increases. To be precise, we must first specify what we mean by an estimation procedure. To be interesting, an estimation procedure should apply to a large family of stochastic processes
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
In this paper it is shown that there does not exist a procedure to consistently estimate the asymptotic variance constant in a stochastic simulation using batch means when the number of batches is held fixed as the run length increases. Thus, if consistency is desired, then the number of batches must increase as the run length increases. To be precise, we must first specify what we mean by an estimation procedure. To be interesting, an estimation procedure should apply to a large family of stochastic processes
Large Deviations Behavior of Counting Processes and Their Inverses(
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
We show, under regularity conditions, that a counting process satisfies a large deviations principle in R, a samplepath large deviations principle in the function space D, or the GartnerEllis condition (convergence of the normalized logarithmic moment generating functions) if and only if its inverse process does. We show, again under regularity conditions, that embedded regenerative structure is sufficient for the counting process or its inverse process to have exponential asymptotics, and thus satisfy the GartnerEllis condition. These results help characterize the smalltail asymptotic behavior of steadystate distributions in queueing models, e.g., the waiting time, workload, and queue length. Large deviations, GartnerEllis theorem, Counting processes, Point processes, Cumulant generating function, Waitingtime distribution, Small tail asymptotics
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
We show, under regularity conditions, that a counting process satisfies a large deviations principle in R, a samplepath large deviations principle in the function space D, or the GartnerEllis condition (convergence of the normalized logarithmic moment generating functions) if and only if its inverse process does. We show, again under regularity conditions, that embedded regenerative structure is sufficient for the counting process or its inverse process to have exponential asymptotics, and thus satisfy the GartnerEllis condition. These results help characterize the smalltail asymptotic behavior of steadystate distributions in queueing models, e.g., the waiting time, workload, and queue length. Large deviations, GartnerEllis theorem, Counting processes, Point processes, Cumulant generating function, Waitingtime distribution, Small tail asymptotics
Logarithmic Asymptotics for SteadyState Tail Probabilities in a SingleServer Queue(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
We consider the standard singleserver queue with unlimited waiting space and the firstout service discipline. We find conditions for the steadystate waitingtime distribution to have smalltail asymptotics of a certain form. We require only stationarity of the basic sequence of service times minus interarrival times and a GartnerEllis condition for the cumulant generating function of the associated partial sums
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
We consider the standard singleserver queue with unlimited waiting space and the firstout service discipline. We find conditions for the steadystate waitingtime distribution to have smalltail asymptotics of a certain form. We require only stationarity of the basic sequence of service times minus interarrival times and a GartnerEllis condition for the cumulant generating function of the associated partial sums
Representation and convergence of point processes on the line : (point processes.) by
Ward Whitt(
Book
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
Computer engineering in applied electromagnetism by
Ward Whitt(
Book
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
The pros and cons of a job buffer in a tokenbank ratecontrol throttle by Arthur W Berger(
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Departures from Many Queues in Series(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
This paper considers a queueing model that could be used to represent the startup behavior of a long production line or the transient flow of messages over a long path in a communication network. In particular, we consider a series of n singleserver queues, each with unlimited waiting space and the firstin firstout service discipline. Initially, the system is empty; then k sub n customers are placed in the first queue. The service times of all the customers at all queuses are i.i.d. with a general distribution having mean 1 and finite positive variance delta squared. Our object is to describe the departure process from the n to the th power queue as n gets large. (Equivalently, since customers are served in order of arrival, we can consider infinitely many queues in series with infinitely many customers in the first queue; we are still interested in the departure times of the first k sub n customers from the n to the th power queue as n yields infinity.) We may have k sub n constant, independent of n, or k sub n yields infinity as n yields infinity
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
This paper considers a queueing model that could be used to represent the startup behavior of a long production line or the transient flow of messages over a long path in a communication network. In particular, we consider a series of n singleserver queues, each with unlimited waiting space and the firstin firstout service discipline. Initially, the system is empty; then k sub n customers are placed in the first queue. The service times of all the customers at all queuses are i.i.d. with a general distribution having mean 1 and finite positive variance delta squared. Our object is to describe the departure process from the n to the th power queue as n gets large. (Equivalently, since customers are served in order of arrival, we can consider infinitely many queues in series with infinitely many customers in the first queue; we are still interested in the departure times of the first k sub n customers from the n to the th power queue as n yields infinity.) We may have k sub n constant, independent of n, or k sub n yields infinity as n yields infinity
Continuity of several functions on the function space D. (continuity of functions on D.) by
Ward Whitt(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
The Asymptotic Validity of Sequential Stopping Rules for Stochastic Simulations(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
We establish general conditions for the asymptotic validity of sequential stopping rules to achieve fixedvolume confidence sets for simulation estimators of vectorvalued parameters. The asymptotic validity occurs as the prescribed volume of the confidences set approaches zero. There are two requirements: a functional central limit theorem for the estimation process and strong consistency (withprobabilityone convergence) for the variance or scaling matrix estimator. Applications are given for: sample means of i.i.d. random variables and random vectors, nonlinear functions of such sample means, jackknifing, KieferWolfowitz and RobbinsMonro stochastic approximation, and both regenerative and nonregenerative steadystate simulation. Keywords: Stochastic simulation, Variance estimators
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
We establish general conditions for the asymptotic validity of sequential stopping rules to achieve fixedvolume confidence sets for simulation estimators of vectorvalued parameters. The asymptotic validity occurs as the prescribed volume of the confidences set approaches zero. There are two requirements: a functional central limit theorem for the estimation process and strong consistency (withprobabilityone convergence) for the variance or scaling matrix estimator. Applications are given for: sample means of i.i.d. random variables and random vectors, nonlinear functions of such sample means, jackknifing, KieferWolfowitz and RobbinsMonro stochastic approximation, and both regenerative and nonregenerative steadystate simulation. Keywords: Stochastic simulation, Variance estimators
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 Carleton University Laboratory for Research in Statistics and Probability
 Iglehart, Donald L. 1933 Author
 STANFORD UNIV CA Dept. of OPERATIONS RESEARCH
 Stanford University Department of Statistics
 Glynn, Peter W. Author
 Glynn, Peter W. Author
 Browne, Sid Author
 Glynn, Peter W. Author
 Stanford University Department of Operations Research
 STANFORD UNIV CALIF Dept. of OPERATIONS RESEARCH
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Asymptotic efficiencies (Statistics) Bayesian statistical decision theory Canada Distribution (Probability theory) Estimation theoryAsymptotic theory Large deviations Limit theorems (Probability theory) Mathematical statistics Mathematics Operations research Portfolio managementMathematical models Queuing theory Scientists Stochastic processes Traffic engineeringMathematical models Traffic flowMathematical models United States
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Ward Whitt American academic
Ward Whitt Amerikaans actuaris
Ward Whitt mathématicien américain
Ward Whitt USamerikanischer Mathematiker
Whitt, W.
Whitt, W. (Ward)
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