Bayesian Analysis of a Queueing System with a Long-Tailed Arrival Process

Ramírez, Pepa; Lillo, Rosa E.; Wiper, Michael P.

doi:10.1080/03610910701753861

Cited by 19 publications

(14 citation statements)

References 25 publications

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“…Basawa and Prabhu (1981) considered ML estimators for an G/G/1 queue. Considerable efforts have been devoted to the estimation of parameters in queueing models by Rubin and Robson (1990), Jain (1991), Basawa et al (1996), Rodrigues and Leite (1998), Jain and Rao (2000), Conti (1999), Capitanio and Conti (2004), Yadavalli et al (2006), Wang et al (2006), and Ramirez et al (2008). Recently, Chandrasekhar and Jose (2009) investigated ML and Bayes estimators in a two station tandem queue.…”

Section: Introductionmentioning

confidence: 97%

Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service

Ghorbani-Mandolakani

Rad

Nematollahi

2013

Communications in Statistics - Theory and Methods

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In this article, we consider a two-phase tandem queueing model with a second optional service. In this model, the service is done by two phases. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability , or leaves the system with probability 1 − . Also, there are two heterogeneous servers which work independently, one of them providing the first phase of service and the other a second phase of service. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.

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Section: Introductionmentioning

confidence: 97%

Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service

Ghorbani-Mandolakani

Rad

Nematollahi

2013

Communications in Statistics - Theory and Methods

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“…Bhat and Subba Rao (1987) and Bhat et al (1997) have reviewed this and related aspects. However, the literature on estimation in queuing systems in the post review period has prospered due to contributions from Conti (1999), Rio Insua et al (1998, Armero and Bayarri (1999), Sharma and Kumar (1999), Zheng and Seila (2000), Conesa (1998, 2000), Butler and Huzurbazaar (2000), Huang and Brill (2001), Ausin et al (2004), Mukherjee and Chowdhury (2005), Chu and Ke (2006), Chu and Ke (2007), Ausin et al (2008), Choudhury and Borthakur (2008), Ramirez et al (2008Ramirez et al ( , 2008a, Kiessler and Lund (2009), Jayakrishna Udupa (2009), Xu et al (2011), Srinivas et al (2011), and Chowdhury and Mukherjee (2013.…”

Section: Problem Literature and Planmentioning

confidence: 99%

ML and UMVU estimation in the M/D/1 queuing system

Srinivas

Kale

2016

Communications in Statistics - Theory and Methods

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In the imbedded Markov chain (IMC) analysis of M/G/1 queuing system, X 1 , X 2 , . . . , X n , . . . form a sequence of i.i.d random variables. where X n denotes the number of customer arrivals during the service time of nth customer. In the M/D/1 queue, the distribution of common random variable X is the Poisson distribution with mean ρ, the traffic intensity. This fact is utilized for maximum likelihood (ML) and uniformly minimum variance unbiased (UMVU) estimation of traffic intensity, performance measures, transition probabilities of IMC, and correlation functions of departure process, based on a sample of fixed size n from P(ρ) distribution. Also, consistent asymptotic normality (CAN) property of ML estimators (MLEs) is established. The MLEs and UMVUEs are compared.

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“…The Pareto distribution has often been applied to model the heavy-tail behavior of teletraffic variables [Resnick (1997)] and insurance claims [Philbrick (1985)]. In particular, in Ramirez, Lillo and Wiper (2008) a mixture of k Pareto distributions (k-Par ) is used to model ethernet packets interarrival This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in The Annals of Applied Statistics, 2010, Vol. 4, No.…”

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confidence: 99%

“…An alternative, which we shall apply, is based on a direct approximation of the nonanalytical Laplace transform using a variant of the transform approximation method (TAM ); see Harris and Marchal (1998), Harris, Brill and Fischer (2000) and Shortle et al (2004). The first version of the TAM, known as Uniform TAM or U-TAM , was implemented in Ramírez, Lillo and Wiper (2008), where estimation of the k-Par /M /1 queue was considered. In this paper we propose a variant of the TAM based on both the Uniform and Geometrical TAM s. By combining this variant of the TAM with the Bayesian inference method for the dPlN distribution, we can obtain estimates of queueing properties of interest such as the probability of congestion.…”

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confidence: 99%

Bayesian inference for double Pareto lognormal queues

Ramírez‐Cobo¹,

Lillo²,

Wilson³

et al. 2010

Ann. Appl. Stat.

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In this article we describe a method for carrying out Bayesian estimation for the double Pareto lognormal (dPlN) distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the $\mathit{dPlN}/M/1$ and $M/\mathit{dPlN}/1$ queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the $\mathit{Pareto}/M/1$ system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS336 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Bayesian Analysis of a Queueing System with a Long-Tailed Arrival Process

Cited by 19 publications

References 25 publications

Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service

Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service

ML and UMVU estimation in the M/D/1 queuing system

Bayesian inference for double Pareto lognormal queues

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