J. Michael Harrison

Stanford University

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Marco Pavone

Nvidia (United Kingdom)

J. G. Dai

Tongji University

Apoorva Sharma

Indian Institute of Technology Gandhinagar

Ruth Williams

University of California, San Diego

Austin J. Lemoine

The Aerospace Corporation

Assaf Zeevi

Columbia University

Stanley R. Pliska

University of Illinois Chicago

Chelsea Finn

Stanford University

Jeffery G Harrison

Vehicle Technologies Office

Filipe Rodrigues

Technical University of Denmark

Cooperative Institutions

Stanford University

Medway Maritime Hospital

Fort Beaufort Hospital

Umkhuseli Innovation and Research Management

National Oceanic and Atmospheric Administration

Massachusetts Institute of Technology

University of Chicago

University College London

Vaughn College of Aeronautics and Technology

NOAA Climate Prediction Center

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Putting the news in New York and New Orleans: the impact of information frictions on trade

Review of World Economics (2024)

J. Michael Harrison

10.1007/s10290-024-00527-7

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On the Specific Name of the Little Shearwater

Emu - Austral Ornithology (1953)

J. Michael Harrison C. H. B. Grant

Shearwater

10.1071/mu953073

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A Contribution to the Ornithology of Bulgaria

Ibis (1933)

J. Michael Harrison Pawel Pateff

Ornithology

Ibis

10.1111/j.1474-919x.1933.tb03355.x

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Citations (4)

Further Examples

Cambridge University Press eBooks (2013)

J. Michael Harrison

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Content (measure theory)

10.1017/cbo9781139087698.011

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Fluid Equations That Characterize Specific Policies

Cambridge University Press eBooks (2020)

J. G. Dai J. Michael Harrison

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Content (measure theory)

10.1017/9781108772662.008

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Assembly-like queues

Journal of Applied Probability (1973)

J. Michael Harrison

A queueing theoretic model of an assembly operation is introduced. The model, consisting of K ≧ 2 renewal input processes and a single server, is a multiple input generalization of the GI / G /1 queue. The server requires one input item of each type k = 1,…, K for each of his services. It is shown that the model is inherently unstable in the following sense. The associated vector waiting time process W n cannot converge in distribution to a non-defective limit, regardless of how well balanced the input and service processes may be. Limit theorems are developed for appropriately normalized versions of W n under the various possible load conditions. Another waiting time process, equivalent to that in a single-server queue whose input is the minimum of K renewal processes, is also identified. It is shown to converge in distribution to a particular limit under certain load conditions.

Renewal theory

10.2307/3212352

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Citations (179)

Multihop Packet Networks

Cambridge University Press eBooks (2020)

J. G. Dai J. Michael Harrison

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10.1017/9781108772662.013

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On the virtual and actual waiting time distributions of a GI/G/1 queue

Journal of Applied Probability (1976)

J. Michael Harrison Austin J. Lemoine

Consider a stable GI/G/ 1 queue with non-lattice interarrival time distribution. Let G and H be the limiting actual and virtual waiting time distributions respectively. Two separate statements of the relationship between G and H are found in a classical theorem of Takàcs and a more recent (and previously unpublished) theorem of Hooke. A simplified proof of Takàcs's theorem, based on a sample path relationship between the virtual and actual waiting time processes, has recently been advanced. This paper gives a similar proof of Hooke's theorem, based on the same sample path relationship, and demonstrates the utility of the result in analyzing the special case of Poisson input. In particular, by combining the Takàcs and Hooke results one can obtain the Pollaczek–Khintchine formula without any reference to the imbedded Markov chain.

Limiting

10.1017/s0021900200104541

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Citations (11)

Correction: Brownian models of open processing networks: canonical representation of workload

The Annals of Applied Probability (2006)

J. Michael Harrison

Due to a printing error the above mentioned article had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error. A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an "equivalent workload formulation" of a Brownian network model. Denoting by Z(t) the state vector of the original Brownian network, one has a lower dimensional state descriptor W(t)=MZ(t) in the equivalent workload formulation, where M can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing networks, and in that context develops a more extensive interpretation of the equivalent workload formulation, thus extending earlier work by Laws on alternate routing problems. A linear program called the static planning problem is introduced to articulate the notion of "heavy traffic" for a general open network, and the dual of that linear program is used to define a canonical choice of the basis matrix M. To be specific, rows of the canonical M are alternative basic optimal solutions of the dual linear program. If the network data satisfy a natural monotonicity condition, the canonical matrix M is shown to be nonnegative, and another natural condition is identified which ensures that M admits a factorization related to the notion of resource pooling.

Canonical form

Matrix (chemical analysis)

Pooling

10.1214/105051606000000583

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Preface

J. G. Dai J. Michael Harrison

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10.1017/9781108772662.001

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