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Modeling teletraffic arrivals by a Poisson cluster process
8 references·7 citing·30 second hop
Modeling teletraffic arrivals by a Poisson cluster process (2006)Modeling teletraffic arrivals by a Poisso…Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences (2010)Elements of Queueing Theory: …Elements of Queueing Theory (2003)Elements of Queueing TheoryIs Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion? (2002)Is Network Traffic Appriximat…Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models (1998)Heavy Tails and Long Range De…Modelling Extremal Events (1997)Modelling Extremal EventsModelling of extremal events in insurance and finance (1994)Modelling of extremal events …Stopped Random Walks (1988)Stopped Random WalksExtreme Values, Regular Variation and Point Processes (1987)Extreme Values, Regular Varia…Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues (2018)Functional central limit theo…Random walk to innovation: Why productivity follows a power law (2011)Random walk to innovation: Wh…Asymptotics of randomly stopped sums in the presence of heavy tails (2010)Asymptotics of randomly stopp…Tail probabilities for infinite series of regularly varying random vectors (2008)Tail probabilities for infini…Tail behavior of random sums under consistent variation with applications to the compound renewal risk model (2008)Tail behavior of random sums …Tails of random sums of a heavy-tailed number of light-tailed terms (2007)Tails of random sums of a hea…Scaling Limits for Cumulative Input Processes (2007)Scaling Limits for Cumulative…Subexponential distributions and integrated tails (1988)Asymptotics for Weighted Random Sums (2012)Convolution and convolution-root properties of long-tailed distributions (2015)On the tails of waiting-time distributions (1975)Applied Probability and Queues (1987)The Impact of Autocorrelation on Queuing Systems (1993)Heavy tail modeling and teletraffic data: special invited paper (1997)Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options (2004)Continuous Martingales and Brownian Motion (1991)Continuous Martingales and Brownian Motion (1999)Limit Theorems for Stochastic Processes (2003)Infinite-server queues with Hawkes input (2018)On the Distributions of Infinite Server Queues With Batch Arrivals (2018)Shot-noise queueing models (2021)Conditional value-at-risk for general loss distributions (2002)Correlation and Dependence in Risk Management: Properties and Pitfalls (2002)Top Incomes in the Long Run of History (2011)INFORMATION COSTS, PRICING, AND RESOURCE UNEMPLOYMENT (1969)Martingale Methods in Financial Modelling (1997)Simulation modeling for analysis (2010)Asymptotic independence and a network traffic model (2002)SIMULATION METHODS FOR LINEAR FRACTIONAL STABLE MOTION AND FARIMA USING THE FAST FOURIER TRANSFORM (2004)Activity signature functions for high-frequency data analysis (2009)Asymptotic results for multiplexing subexponential on-off processes (1999)The supremum of a negative drift random walk with dependent heavy-tailed steps (2000)Analysis, Design, and Control of Queueing Systems (2002)Extreme Correlation of International Equity Markets (2001)Empirical properties of asset returns: stylized facts and statistical issues (2001)The Asymptotic Efficiency of Simulation Estimators (1992)A stochastic mesh method for pricing high-dimensional American options (2004)
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References

  • 1997Modelling Extremal Events4,397 cited
  • 1994Modelling of extremal events in insurance and finance3,519 cited
  • 1987Extreme Values, Regular Variation and Point Processes3,165 cited
  • 2003Elements of Queueing Theory596 cited
  • 1988Stopped Random Walks384 cited
  • 2010Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences354 cited
  • 2002Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?270 cited
  • 1998Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models176 cited

Cited by

  • 2010Asymptotics of randomly stopped sums in the presence of heavy tails71 cited
  • 2018Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues66 cited
  • 2007Tails of random sums of a heavy-tailed number of light-tailed terms63 cited
  • 2008Tail probabilities for infinite series of regularly varying random vectors56 cited
  • 2008Tail behavior of random sums under consistent variation with applications to the compound renewal risk model44 cited
  • 2011Random walk to innovation: Why productivity follows a power law38 cited
  • 2007

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Scaling Limits for Cumulative Input Processes
27 cited