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Journal ArticleDOI

Applied Probability and Queues

01 Nov 1987-Journal of the Operational Research Society (Palgrave Macmillan UK)-Vol. 38, Iss: 11, pp 1095-1096
TL;DR: In this paper, applied probability and queuing in the field of applied probabilistic analysis is discussed. But the authors focus on the application of queueing in the context of road traffic.
Abstract: (1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.
Citations
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Book
01 Jan 1999
TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
Abstract: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

6,884 citations

Journal ArticleDOI
TL;DR: In this paper, a joint process of arbitrage-free asset prices, dividends, and aggregate income is shown to be supported in the equilibrium of an economy with judiciously modeled income heterogeneity.
Abstract: Empirical difficulties encountered by representative-consumer models are resolved in an economy with heterogeneity in the form of uninsurable, persistent, and heteroscedastic labor income shocks. Given the joint process of arbitrage-free asset prices, dividends, and aggregate income, satisfying a certain joint restriction, it is shown that this process is supported in the equilibrium of an economy with judiciously modeled income heterogeneity. The Euler equations of consumption in a representative-agent economy are replaced by a set of Euler equations that depend not only on the per capita consumption growth but also on the cross-sectional variance of the individual consumers' consumption growth.

1,166 citations

Journal ArticleDOI
TL;DR: For simple random walk on aN-vertex graph, the mean time to cover all vertices is at leastcN log(N), wherec>0 is an absolute constant, deduced from a more general result about stationary finite-state reversible Markov chains.
Abstract: For simple random walk on aN-vertex graph, the mean time to cover all vertices is at leastcN log(N), wherec>0 is an absolute constant. This is deduced from a more general result about stationary finite-state reversible Markov chains. Under weak conditions, the covering time for such processes is at leastc times the covering time for the corresponding i.i.d. process.

942 citations


Cites background from "Applied Probability and Queues"

  • ...6 for an introduction, and [34, 263] for more comprehensive treatments....

    [...]

  • ...Almost every introductory textbook on stochastic processes has a chapter or two about Markov chains: among the best are Karlin-Taylor [208, 209], Grimmett-Stirzaker [177] and, slightly more advanced, Asmussen [34]....

    [...]

Journal ArticleDOI
29 Jan 2014-PLOS ONE
TL;DR: The powerlaw Python package provides easy commands for basic fitting and statistical analysis of distributions and seeks to support a variety of user needs by being exhaustive in the options available to the user.
Abstract: Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.

803 citations

Journal ArticleDOI
TL;DR: In this paper, a survey of results about Markov chains on non-countable state spaces is presented, along with necessary and sufficient conditions for geometrical and uniform ergodicity along with quantitative bounds on the rate of convergence to stationarity.
Abstract: This paper surveys various results about Markov chains on gen- eral (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sucient conditions for geomet- ric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift con- ditions. Necessary and sucient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equa- tion or direct regeneration constructions. Finally, optimal scaling and weak convergence results for Metropolis-Hastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.

797 citations

References
More filters
Book
01 Jan 1999
TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
Abstract: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

6,884 citations

Journal ArticleDOI
TL;DR: In this paper, a joint process of arbitrage-free asset prices, dividends, and aggregate income is shown to be supported in the equilibrium of an economy with judiciously modeled income heterogeneity.
Abstract: Empirical difficulties encountered by representative-consumer models are resolved in an economy with heterogeneity in the form of uninsurable, persistent, and heteroscedastic labor income shocks. Given the joint process of arbitrage-free asset prices, dividends, and aggregate income, satisfying a certain joint restriction, it is shown that this process is supported in the equilibrium of an economy with judiciously modeled income heterogeneity. The Euler equations of consumption in a representative-agent economy are replaced by a set of Euler equations that depend not only on the per capita consumption growth but also on the cross-sectional variance of the individual consumers' consumption growth.

1,166 citations

Journal ArticleDOI
29 Jan 2014-PLOS ONE
TL;DR: The powerlaw Python package provides easy commands for basic fitting and statistical analysis of distributions and seeks to support a variety of user needs by being exhaustive in the options available to the user.
Abstract: Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.

803 citations

Journal ArticleDOI
TL;DR: Particular emphasis will be placed on estimation of rare events and on integration of the associated performance function into stochastic optimization programs.

710 citations

Journal ArticleDOI
TL;DR: The model allows stations to have different traffic arrival rates, enabling the question of fairness between competing flows to be addressed, and accurately capture many interesting features of nonsaturated operation.
Abstract: Analysis of the 802.11 CSMA/CA mechanism has received considerable attention recently. Bianchi presented an analytic model under a saturated traffic assumption. Bianchi's model is accurate, but typical network conditions are nonsaturated and heterogeneous. We present an extension of his model to a nonsaturated environment. The model's predictions, validated against simulation, accurately capture many interesting features of nonsaturated operation. For example, the model predicts that peak throughput occurs prior to saturation. Our model allows stations to have different traffic arrival rates, enabling us to address the question of fairness between competing flows. Although we use a specific arrival process, it encompasses a wide range of interesting traffic types including, in particular, VoIP.

660 citations