On a queue with correlated arrivals

Drezner, Zvi

doi:10.1155/s117391269900005x

Cited by 13 publications

(3 citation statements)

References 3 publications

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“…There are many ways to impose a correlation to the arrival process. For instance, the parameters of the process may depend on their past realisation, as in [Dre99], or on some on/off sources, as in [WB99]. Another relevant example of a queue model with correlated arrivals is the so-called Markov Modulated Queueing System (MMQS).…”

Section: Winsten In 1959mentioning

confidence: 99%

Looking Through the Window

Nison¹

2012

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Section: Winsten In 1959mentioning

confidence: 99%

Looking Through the Window

Nison¹

2012

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“…There are many ways to impose a correlation to the arrival process. For instance, the parameters of the process may depend on their past realisation (Drezner 1999), or on some on/off sources (Wittevrongel and Bruneel 1999). Another relevant example of a queue model with correlated arrivals is the socalled Markov Modulated Queueing System.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics for the late arrivals problem

et al. 2018

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We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays ξ i. We describe the model as a bivariate Markov chain, prove its ergodicity and study the joint equilibrium distribution. We write a functional equation for the bivariate generating function, finding the solution on a subset of its domain. This solution allows us to prove that the equilibrium distribution of the chain decays super-exponentially fast in the quarter plane. We exploit the latter result and discuss the numerical computation of the solution through a simple yet effective approximation scheme in a wide region of the parameters. Finally, we compare the features of this queueing model with the standard M/D/1 system, showing that the congestion turns out to be very different when the traffic intensity is close to 1. Keywords Late arrivals • Exponentially delayed arrivals • Pre-scheduled random arrivals • Queues with correlated arrivals • Bivariate generating function Partially supported by PRIN 2012 "Problemi matematici in teoria cinetica ed applicazioni".

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“…There are many ways to impose a correlation to the arrival process. For instance, the parameters of the process may depend on their past realisation, as in [24], or on some on/off sources, as in [67]. Another relevant example of a queue model with correlated arrivals is the so-called Markov Modulated Queueing System.…”

Section: Introductionmentioning

confidence: 99%