STANFORD UNIV CALIF Dept. of OPERATIONS RESEARCH
Overview
Works:  187 works in 190 publications in 1 language and 192 library holdings 

Genres:  Lectures 
Classifications:  QA7, 
Publication Timeline
.
Most widely held works by
STANFORD UNIV CALIF Dept. of OPERATIONS RESEARCH
Computation of the Reliability of a Stochastic Network by
Andrew W Shogan(
Book
)
1 edition published in 1974 in English and held by 2 WorldCat member libraries worldwide
Given a directed network whose arcs either function or fail with known probabilities, define the reliability of a node as the probability that there exists a path from the network's source to the node composed only of functioning arcs. An algorithm is presented that recursively computes the reliabilities of nodes of the network until the reliability of the sink is obtained. Furthermore, algorithms are presented to recursively bound the reliabilities of nodes until upper and lower bounds on the reliability of the sink are obtained. These bounds are shown analytically to be tighter than the existing EsaryProschan bounds. (Author)
1 edition published in 1974 in English and held by 2 WorldCat member libraries worldwide
Given a directed network whose arcs either function or fail with known probabilities, define the reliability of a node as the probability that there exists a path from the network's source to the node composed only of functioning arcs. An algorithm is presented that recursively computes the reliabilities of nodes of the network until the reliability of the sink is obtained. Furthermore, algorithms are presented to recursively bound the reliabilities of nodes until upper and lower bounds on the reliability of the sink are obtained. These bounds are shown analytically to be tighter than the existing EsaryProschan bounds. (Author)
Regenerative Simulation of Response Times in Networks of Queues, II: Multiple Job Types by
Donald L Iglehart(
Book
)
1 edition published in 1978 in English and held by 2 WorldCat member libraries worldwide
The writers have previously discussed the simulation of networks of queues for general characteristics of passage times of a single job type, using the regenerative method for simulation and the idea of tracking a distinguished job through the network. In this paper, they consider from a somewhat different point of view passage time simulation in closed networks for queues having multiple job types. Their results provide a means of obtaining, from a single replication, point and interval estimates for passage times of the several job types. They also yield a statistically more efficient estimation procedure for passage times of a single job type
1 edition published in 1978 in English and held by 2 WorldCat member libraries worldwide
The writers have previously discussed the simulation of networks of queues for general characteristics of passage times of a single job type, using the regenerative method for simulation and the idea of tracking a distinguished job through the network. In this paper, they consider from a somewhat different point of view passage time simulation in closed networks for queues having multiple job types. Their results provide a means of obtaining, from a single replication, point and interval estimates for passage times of the several job types. They also yield a statistically more efficient estimation procedure for passage times of a single job type
TimeDependent Mathematical Programs by
B. Curtis Eaves(
Book
)
2 editions published between 1974 and 1977 in English and held by 2 WorldCat member libraries worldwide
The research supported under this contract has led, in conjunction with results of others, to a general new tool for solving systems of equations (e.g., differential equations). (Author)
2 editions published between 1974 and 1977 in English and held by 2 WorldCat member libraries worldwide
The research supported under this contract has led, in conjunction with results of others, to a general new tool for solving systems of equations (e.g., differential equations). (Author)
Weak convergence theorems for queues in heavy traffic by
Ward Whitt(
Book
)
2 editions published in 1968 in English and held by 1 WorldCat member library 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)
2 editions published in 1968 in English and held by 1 WorldCat member library 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)
Bilinear Programming: Part I. Algorithm for Solving Bilinear Programs(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
The paper deals with an algorithm for determining a global optimum of a structured nonconcave quadratic programming problem called the bilinear programming problem (BLP): maximize c supt x + d supt y + x supt Cy subject to Ex <or = e, x> or = 0 Fy <or = f, y> or = 0 This algorithm is an elaboration of the cutting plane algorithm proposed by K. Ritter. It is established that the authors algorithm generates and epsilonoptimal solution (with respect to the objective functional value) in finitely many steps for any given epsilon> 0 provided the constraint set is nonempty and compact. It must be noted that the BLP algorithm exclusively uses the simplex algorithm and that no elaborate subproblem needs be solved. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
The paper deals with an algorithm for determining a global optimum of a structured nonconcave quadratic programming problem called the bilinear programming problem (BLP): maximize c supt x + d supt y + x supt Cy subject to Ex <or = e, x> or = 0 Fy <or = f, y> or = 0 This algorithm is an elaboration of the cutting plane algorithm proposed by K. Ritter. It is established that the authors algorithm generates and epsilonoptimal solution (with respect to the objective functional value) in finitely many steps for any given epsilon> 0 provided the constraint set is nonempty and compact. It must be noted that the BLP algorithm exclusively uses the simplex algorithm and that no elaborate subproblem needs be solved. (Author)
Lectures on controllability and observability by
R. E Kalman(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
The lectures, delivered at the seminar of Centro Internazionale Matimatico Estivo on controllability and observability in Bologna, Italy, constitute an authoritative review of the main results of the theory of controllability with observability together with a very modern introduction to algebraic system theory. The notes also contain a historical appendix comparing the contributions of the Russian and American school. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
The lectures, delivered at the seminar of Centro Internazionale Matimatico Estivo on controllability and observability in Bologna, Italy, constitute an authoritative review of the main results of the theory of controllability with observability together with a very modern introduction to algebraic system theory. The notes also contain a historical appendix comparing the contributions of the Russian and American school. (Author)
Functionals of Brownian Meander and Brownian Excursion(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Brownian meander and Brownian excursion processes arise as the limit process of a number of conditional functional central limit theorems. To reap the full benefit of such limit theorems one needs to know the distribution of functionals of the limit process. In this paper the distribution of the maxima, first entrance times, and expected occupation time densities are computed for the two limit processes. This is done by using the methods of weak convergence
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Brownian meander and Brownian excursion processes arise as the limit process of a number of conditional functional central limit theorems. To reap the full benefit of such limit theorems one needs to know the distribution of functionals of the limit process. In this paper the distribution of the maxima, first entrance times, and expected occupation time densities are computed for the two limit processes. This is done by using the methods of weak convergence
Least dmajorized network flows with inventory and statistical applications by
Stanford University(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
It is shown that for any feasible network flow model, there is a flow which simultaneously minimizes every dSchur convex function of the flows emanating from a single distinguished node called the source. The vector of flows emanating from the source in the minimizing flow is unique and is the least dmajorized flow. This flow can be found by solving the problem for the special case where the dSchur convex function is separable and quadratic. Once this flow is found, the solution of the dual problem is reduced to evaluating the conjugate of a function appearing in the dual objective function at the above flow. The computation is extremely simple when the function is separable. These results are extended to situations in which the variables must be integers. An important special case of the problem can be solved geometrically by choosing, from among all paths joining two points in the plane and lying between two given nonintersecting paths, the path with minimum Euclidian length. Applications of the results are given to deterministic productiondistribution models, certain of the stochastic inventoryredistribution models examined by Ignall and Veinott, a deterministic price speculation and storage model, and a zero lead time case of the ClarkScarf series multiechelon model. In addition, applications are given to several maximum likelihood estimation problems in which the parameters satisfy certain linear inequalities. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
It is shown that for any feasible network flow model, there is a flow which simultaneously minimizes every dSchur convex function of the flows emanating from a single distinguished node called the source. The vector of flows emanating from the source in the minimizing flow is unique and is the least dmajorized flow. This flow can be found by solving the problem for the special case where the dSchur convex function is separable and quadratic. Once this flow is found, the solution of the dual problem is reduced to evaluating the conjugate of a function appearing in the dual objective function at the above flow. The computation is extremely simple when the function is separable. These results are extended to situations in which the variables must be integers. An important special case of the problem can be solved geometrically by choosing, from among all paths joining two points in the plane and lying between two given nonintersecting paths, the path with minimum Euclidian length. Applications of the results are given to deterministic productiondistribution models, certain of the stochastic inventoryredistribution models examined by Ignall and Veinott, a deterministic price speculation and storage model, and a zero lead time case of the ClarkScarf series multiechelon model. In addition, applications are given to several maximum likelihood estimation problems in which the parameters satisfy certain linear inequalities. (Author)
On the Number of Solutions to a Diophantine Equation(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Let A sub 1 ..., A sub r, x sub 1 primed ..., x sub r primed and A be known positive integers. Let f(A) be the number of integer solutions (x sub 1 ..., x sub r) satisfying the Diophantine equation the summation from j=1 to r of ((A sub j) x sub j = A) and the conditions O <or = x sub j <or = x sub j primed, j = 1 ..., r. This paper expresses f(A) recursively as a linear function of f(0), f(1) ..., f(A1). (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Let A sub 1 ..., A sub r, x sub 1 primed ..., x sub r primed and A be known positive integers. Let f(A) be the number of integer solutions (x sub 1 ..., x sub r) satisfying the Diophantine equation the summation from j=1 to r of ((A sub j) x sub j = A) and the conditions O <or = x sub j <or = x sub j primed, j = 1 ..., r. This paper expresses f(A) recursively as a linear function of f(0), f(1) ..., f(A1). (Author)
Weak convergence for the superposition and thinning of point processes by
Stanford University(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Weak convergence theorems are obtained for which the limiting distribution is a Poisson process on D(0,1). (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Weak convergence theorems are obtained for which the limiting distribution is a Poisson process on D(0,1). (Author)
Models for the optimal control of Markovian closed queueing systems with adjustable service rates by Emerson Arlin Torbett(
Book
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
The report considers the problem of determining an optimal dynamic control policy for a closed queueing system in which the service facilities may be operated at more than one service rate. The optimality criterion is to minimize the longrun expected average cost per unit time. The author formulates a general control model whose cost structure includes: (1) an operating cost for running each service facility; (2) a switching cost for startingup and shuttingdown the facilities; (3) a holding cost rate for customers waiting or in service; (4) a service facility profit, earned whenever a service completion occurs. After reviewing some results from the theory of semiMarkov decision processes and proving that an optimal stationary deterministic policy exists for Markovian Closed Queueing Systems, analytical results are presented that specify the form of the optimal policy for several models of twostate closed queueing systems and investigate the behavior of the optimal policy as the number of customers in the system is increased. Several interesting future research topics are also identified in the dynamic control area, as well as in the static design area. Of particular interest are optimization problems that have applications to multiprogramming computer systems. (Author)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
The report considers the problem of determining an optimal dynamic control policy for a closed queueing system in which the service facilities may be operated at more than one service rate. The optimality criterion is to minimize the longrun expected average cost per unit time. The author formulates a general control model whose cost structure includes: (1) an operating cost for running each service facility; (2) a switching cost for startingup and shuttingdown the facilities; (3) a holding cost rate for customers waiting or in service; (4) a service facility profit, earned whenever a service completion occurs. After reviewing some results from the theory of semiMarkov decision processes and proving that an optimal stationary deterministic policy exists for Markovian Closed Queueing Systems, analytical results are presented that specify the form of the optimal policy for several models of twostate closed queueing systems and investigate the behavior of the optimal policy as the number of customers in the system is increased. Several interesting future research topics are also identified in the dynamic control area, as well as in the static design area. Of particular interest are optimization problems that have applications to multiprogramming computer systems. (Author)
A Local Time for a Storage Process(
Book
)
1 edition published in 1972 in English and held by 1 WorldCat member library worldwide
A storage system subject to a general release rule and an additive input process is considered. If (X sub t) is the content at time t, then the set X = X sub t; t> or = 0) is a standard Markov process, and the concern is the local time at x = 0 of this process X. Depending on the parameters of the system, namely the release rule and the Levy measure of the input process, there are four cases possible. In terms of the set E = (t : X sub t = 0), these are as follows: E is the union of countably many isolated points; E is the union of countably many disjoint intervals; E is a Cantor set (a perfect set with an empty interior) with positive Lebesgue measure; E is a Cantor set with Lebesgue measure zero. The last is the most interesting case, and the construction of the local time then is the main result. Local times in other cases are also considered along with time inverses and hitting times. (Author)
1 edition published in 1972 in English and held by 1 WorldCat member library worldwide
A storage system subject to a general release rule and an additive input process is considered. If (X sub t) is the content at time t, then the set X = X sub t; t> or = 0) is a standard Markov process, and the concern is the local time at x = 0 of this process X. Depending on the parameters of the system, namely the release rule and the Levy measure of the input process, there are four cases possible. In terms of the set E = (t : X sub t = 0), these are as follows: E is the union of countably many isolated points; E is the union of countably many disjoint intervals; E is a Cantor set (a perfect set with an empty interior) with positive Lebesgue measure; E is a Cantor set with Lebesgue measure zero. The last is the most interesting case, and the construction of the local time then is the main result. Local times in other cases are also considered along with time inverses and hitting times. (Author)
Polyhedral Sets Having a Least Element by
Stanford University(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
For a fixed m x n matrix A, the authors consider the family of polyhedral sets X(sub b) = (x : Ax> or = b), b belongs to R(sup m), and prove a theorem characterizing in terms of A, the circumstances under which every nonempty X sub b has a least element. In the special case where A contains all the rows of an n x n identity matrix, the conditions are equivalent to A sup T being Leontief. Among the corollaries of the theorem, the authors show the linear complementarity problem always has a unique solution which is at the same time a least element of the corresponding polyhedron if and only if its matrix is square, Leontief, and has positive diagonals. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
For a fixed m x n matrix A, the authors consider the family of polyhedral sets X(sub b) = (x : Ax> or = b), b belongs to R(sup m), and prove a theorem characterizing in terms of A, the circumstances under which every nonempty X sub b has a least element. In the special case where A contains all the rows of an n x n identity matrix, the conditions are equivalent to A sup T being Leontief. Among the corollaries of the theorem, the authors show the linear complementarity problem always has a unique solution which is at the same time a least element of the corresponding polyhedron if and only if its matrix is square, Leontief, and has positive diagonals. (Author)
On functions whose stationary points are global minima by Israel Zang(
Book
)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
In this paper a characterization of functions whose stationary points are global minima is studied. By considering the level sets of a real function as a pointtoset mapping, and by examining its semicontinuity properties, we obtain a result that a real function, defined on a subset of Rn and satisfying some mild regularity conditions, belongs to the above family if and only if the pointtoset mapping of its level sets is strictly lower semicontinuous. Mathematical programming applications are also mentioned. (Author)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
In this paper a characterization of functions whose stationary points are global minima is studied. By considering the level sets of a real function as a pointtoset mapping, and by examining its semicontinuity properties, we obtain a result that a real function, defined on a subset of Rn and satisfying some mild regularity conditions, belongs to the above family if and only if the pointtoset mapping of its level sets is strictly lower semicontinuous. Mathematical programming applications are also mentioned. (Author)
Extreme points of leontief substitution systems(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A Leontief matrix is a matrix A having exactly one positive element in each column and for which there is a nonnegative (column) vector x such that Ax is positive. Let X(b) be the set of nonnegative solutions to Ax = b where A is Leontief and b> or = 0. The following results are established. An element of X(b) is an extreme point of X(b) if and only if it is determined by a Leontief basis matrix. If A is integral, the extreme points of X(b) are integral for all nonnegative integral b if and only if the determinant of each Leontief basis matrix equals one. The class of Leontief matrices for which X(b) is bounded for all b> or = 0 is characterized. The infimum of a concave function over X(b) is concave in b on the nonnegative orthant. The above results are shown to extend easily to matrices with at most one positive element in each column. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A Leontief matrix is a matrix A having exactly one positive element in each column and for which there is a nonnegative (column) vector x such that Ax is positive. Let X(b) be the set of nonnegative solutions to Ax = b where A is Leontief and b> or = 0. The following results are established. An element of X(b) is an extreme point of X(b) if and only if it is determined by a Leontief basis matrix. If A is integral, the extreme points of X(b) are integral for all nonnegative integral b if and only if the determinant of each Leontief basis matrix equals one. The class of Leontief matrices for which X(b) is bounded for all b> or = 0 is characterized. The infimum of a concave function over X(b) is concave in b on the nonnegative orthant. The above results are shown to extend easily to matrices with at most one positive element in each column. (Author)
Stable stochastic linear programs and applications by
Stanford University(
Book
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
A class of stochastic linear programs termed stable stochastic linear programs defined in terms of convergence of sequences of stochastic linear programs is introduced. A sufficient regularity condition for such stability is given, slightly stronger than the necessary and sufficient condition that a stochastic linear program (SLP) have optimal value altogether. Applications of this regularity condition to Monte Carlo methods, numerical solution of the distribution problem and twostage programming are given. (Author)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
A class of stochastic linear programs termed stable stochastic linear programs defined in terms of convergence of sequences of stochastic linear programs is introduced. A sufficient regularity condition for such stability is given, slightly stronger than the necessary and sufficient condition that a stochastic linear program (SLP) have optimal value altogether. Applications of this regularity condition to Monte Carlo methods, numerical solution of the distribution problem and twostage programming are given. (Author)
A model for analyzing systems involving sequential crews by Ronald W Boling(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
A model is described which can be used to analyze the behavior of sequential crew systems. Such systems consist of two or more crews following one another in a fixed sequence with each crew completing a particular task on a unit being constructed, repaired or serviced. The model is useful in those cases where crew service times can be approximated by one of the family of Erlang distributions. An analysis of the general behavior of sequential crew systems is included. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
A model is described which can be used to analyze the behavior of sequential crew systems. Such systems consist of two or more crews following one another in a fixed sequence with each crew completing a particular task on a unit being constructed, repaired or serviced. The model is useful in those cases where crew service times can be approximated by one of the family of Erlang distributions. An analysis of the general behavior of sequential crew systems is included. (Author)
Bilinear Programming: Part II. Application of Bilinear Programming(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
In the paper a number of new problems such as constrained bematrix game, multistage Markovian assignment problem, complementary (orthogonal) planning problem, the problem of reducing a sparse matrix into an almosttriangular matrix by row and column permutations, a location problem on a rectangular network, etc., are defined and formulated as the bilinear programming problem (BLP): maximize C(supt) x + d(supt) y + x(supt) Cy subject to x belongs to X, y belongs to Y. where X and Y are m and ndimensional polyhedral convex set, respectively. Further, it is shown that several important classical problems such as 0  1 integer programs, maximization problem of a convex quadratic function subject to linear constrints, twomove game, etc. are reducible to equivalent BLP's. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
In the paper a number of new problems such as constrained bematrix game, multistage Markovian assignment problem, complementary (orthogonal) planning problem, the problem of reducing a sparse matrix into an almosttriangular matrix by row and column permutations, a location problem on a rectangular network, etc., are defined and formulated as the bilinear programming problem (BLP): maximize C(supt) x + d(supt) y + x(supt) Cy subject to x belongs to X, y belongs to Y. where X and Y are m and ndimensional polyhedral convex set, respectively. Further, it is shown that several important classical problems such as 0  1 integer programs, maximization problem of a convex quadratic function subject to linear constrints, twomove game, etc. are reducible to equivalent BLP's. (Author)
The Euler Characteristic of Abstract Polytopes by
Stanford University(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
Abstract polytopes include ordinary convex polytopes as a special case and are defined as systems satisfying certain combinatorial properties of ordinary polytopes. The Euler characteristic is the sum over i with alternating signs of the number of idimensional faces. For ordinary polytopes its value is +1. This relation, however, does not hold in general for abstract polytopes. Since the 3dimensional abstract polytopes correspond 11 to triangulated 2manifolds, the range of their Euler characteristic could be determined by applying known results of manifold theory. The paper investigates the range of the Euler characteristic of abstract polytopes in general. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
Abstract polytopes include ordinary convex polytopes as a special case and are defined as systems satisfying certain combinatorial properties of ordinary polytopes. The Euler characteristic is the sum over i with alternating signs of the number of idimensional faces. For ordinary polytopes its value is +1. This relation, however, does not hold in general for abstract polytopes. Since the 3dimensional abstract polytopes correspond 11 to triangulated 2manifolds, the range of their Euler characteristic could be determined by applying known results of manifold theory. The paper investigates the range of the Euler characteristic of abstract polytopes in general. (Author)
Limit theorems for queues in transportation systems by
M. A Crane(
Book
)
2 editions published in 1971 in English and held by 1 WorldCat member library worldwide
Stochastic queueing models are formulated for three transportation systems. The first consists of a linear network of N+1 terminals served by S vehicles of fixed capacity. Customers arrive stochastically at terminal i, 1 <or = i <or = N, seeking transportation to some terminal j, 0 <or = j <or = i  1, and are served as empty units of vehicle capacity become available at i. The second system consists of a circular network of N terminals in which S vehicles travel in a single direction. Customers arrive stochastically at each terminal seeking transportation to the next terminal in the circle. When a vehicle arrives at a terminal, it remains idle until fully loaded, at which time it transports its passengers to the next terminal. The third system is a generalization of the second in which customers may choose any terminal as a destination, and travel to that terminal need not follow a circular route. A customer at terminal i chooses terminal j with probability pij. (Author)
2 editions published in 1971 in English and held by 1 WorldCat member library worldwide
Stochastic queueing models are formulated for three transportation systems. The first consists of a linear network of N+1 terminals served by S vehicles of fixed capacity. Customers arrive stochastically at terminal i, 1 <or = i <or = N, seeking transportation to some terminal j, 0 <or = j <or = i  1, and are served as empty units of vehicle capacity become available at i. The second system consists of a circular network of N terminals in which S vehicles travel in a single direction. Customers arrive stochastically at each terminal seeking transportation to the next terminal in the circle. When a vehicle arrives at a terminal, it remains idle until fully loaded, at which time it transports its passengers to the next terminal. The third system is a generalization of the second in which customers may choose any terminal as a destination, and travel to that terminal need not follow a circular route. A customer at terminal i chooses terminal j with probability pij. (Author)
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Languages