Monotone matrices and monotone Markov processes

Abstract[Excerpt] Our main purpose in this survey is, therefore, to provide a somewhat unified setting within which the basic features of the theory of income mobility measurement can be outlined. Our aim is to provide a (subjectively) selective introduction to the literature on income mobility, and thereby shed some light on particular aspects of mobility measurement. Consequently, the present study should not be viewed as an exhaustive survey of the related literature. It is rather a very concise account of some key elements of the theory of income mobility measurement.

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“…This observation leads one to confine attention to monotone mobility matrices first introduced by Keilson and Ketser (1977).…”

Section: Monotone Mobility Matricesmentioning

confidence: 99%

The Measurement of Income Mobility: An Introduction to the Literature

Fields¹,

Ok²

1999

Handbook of Income Inequality Measurement

180

144

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“…To this end, consider a state (n 1 , θ; m 1 , m 2 ) with θ = 1. Then, by the Markov reward (or dynamic programming) relation (12) with (11) and (7) substituted, we find…”

Section: Inequalities (28)-(31)mentioning

confidence: 99%

Erlang loss bounds for OT–ICU systems

Dijk

Kortbeek

2009

Queueing Syst

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In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled.There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an M|G|c|c system and an upper bound by an M|G|c-1|c-1 system, hence by simple Erlang loss expressions.The result is based on a product form modification for a special OT-ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.

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“…It is known for a long time that monotonicity [21] and comparability of the one step transition probability matrices of time-homogeneous MCs yield sufficient conditions for their stochastic comparison. This is the fundamental result we use in our algorithms.…”

Section: A Brief Overviewmentioning

confidence: 99%

An Algorithmic Approach to Stochastic Bounds

Fourneau

Pekergin

2002

Performance Evaluation of Complex Systems: Techniques and Tools

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Abstract. We present a new methodology based on the stochastic ordering, algorithmic derivation of simpler Markov chains and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains. This leads to an important reduction on numerical complexity. Stochastic bounds are a promising method to analyze QoS requirements. Indeed it is sufficient to prove that a bound of the real performance satisfies the guarantee.

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Monotone matrices and monotone Markov processes

Cited by 191 publications

References 14 publications

The Measurement of Income Mobility: An Introduction to the Literature

The Measurement of Income Mobility: An Introduction to the Literature

Erlang loss bounds for OT–ICU systems

An Algorithmic Approach to Stochastic Bounds

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