A correlated poisson distribution for correlated events

Drezner, Zvi; Farnum, Nicholas R.

doi:10.1080/03610929408831290

Cited by 13 publications

(3 citation statements)

References 8 publications

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“…The correlated Poisson distribution (CPD) (Drezner and Farnum, 1994) defines the probability of observing r events during time period t for a given arrival rate λ and a correlation factor θ. The CPD is the limit of the generalized binomial distribution(GBD) (Drezner and Farnum, 1993) with n trials, initial probability of success p, and correlation factor θ as p → 0 and n → ∞ while np remains constant.…”

Section: The Gbd and Cpd Distributionsmentioning

confidence: 99%

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On a queue with correlated arrivals

Drezner

1999

Journal of Applied Mathematics and Decision Sciences

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In this note we analyze the performance measures of a one server queue when arrivals are not independent. The analysis is based on the correlated Poisson distribution for customers arrival. Service may have any distribution. This type of queue is defined as M C /G/1. The formulas for the performance measures of the queue are derived without any approximation. Surprisingly, these formulas are very simple.

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Section: The Gbd and Cpd Distributionsmentioning

confidence: 99%

“…The mean of the CPD is λ and its variance is λ 1−2θ for θ < 0.5. For θ ≥ 0.5 the variance of the CPD is infinite (Drezner and Farnum, 1994). The probability of r successes in any time period t is (Drezner and Farnum, 1994):…”

Section: The Gbd and Cpd Distributionsmentioning

confidence: 99%

On a queue with correlated arrivals

Drezner

1999

Journal of Applied Mathematics and Decision Sciences

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“…In the continuous-time case, the Poisson process is the simplest Markovian arrival process. This process has been generalized by Cox [6], Consul and Jain [5], and Drezner and Farnum [8]. Different correlation structures have been discussed, but the stationary distributions in the proposed models were restricted to specific classes.…”

Section: Introductionmentioning

confidence: 99%

Tail behavior of the queue size and waiting time in a queue with discrete autoregressive arrivals

Kim¹,

Sohraby²

2006

Advances in Applied Probability

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Autoregressive arrival models are described by a few parameters and provide a simple means to obtain analytical models for matching the first- and second-order statistics of measured data. We consider a discrete-time queueing system where the service time of a customer occupies one slot and the arrival process is governed by a discrete autoregressive process of order 1 (a DAR(1) process) which is characterized by an arbitrary stationary batch size distribution and a correlation coefficient. The tail behaviors of the queue length and the waiting time distributions are examined. In particular, it is shown that, unlike in the classical queueing models with Markovian arrival processes, the correlation in the DAR(1) model results in nongeometric tail behavior of the queue length (and the waiting time) if the stationary distribution of the DAR(1) process has infinite support. A complete characterization of the geometric tail behavior of the queue length (and the waiting time) is presented, showing the impact of the stationary distribution and the correlation coefficient when the stationary distribution of the DAR(1) process has finite support. It is also shown that the stationary distribution of the queue length (and the waiting time) has a tail of regular variation with index -β − 1, by finding an explicit expression for the tail asymptotics when the stationary distribution of the DAR(1) process has a tail of regular variation with index -β.

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Classical Discrete Distributions, Generalizations of

Kemp¹

2004

Encyclopedia of Statistical Sciences

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A correlated poisson distribution for correlated events

Cited by 13 publications

References 8 publications

On a queue with correlated arrivals

On a queue with correlated arrivals

Tail behavior of the queue size and waiting time in a queue with discrete autoregressive arrivals

Classical Discrete Distributions, Generalizations of

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