Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers

Wang, Tsung-Yin; Ke, Jau‐Chuan; Wang, Kuo-Hsiung; Ho, Shei-Chen

doi:10.1007/s00186-005-0047-z

Cited by 24 publications

(9 citation statements)

References 9 publications

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“…Thiruvaiyaru and Basawa [19] considered an empirical Bayes approach to determine arrival and service rates in M /M /1 queues where arrival and service times are observable. Wang et al [20] proposed an M /M /R/N queue with multi-servers by MLE and also developed the confidence interval formula for the estimated results. Most of these works need complete observation for the parameter inference of queueing models.…”

Section: Related Workmentioning

confidence: 99%

Parameter Estimation of $M_{t}/M/1/K$ Queueing Systems With Utilization Data

Okamura

2019

IEEE Access

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Utilization data are defined as the time series data consisting of time fractions of busy periods in fixed time intervals and are practically used to represent server conditions, such as CPU utilization. In general, it is more challenging to estimate the model parameters from the utilization data since we do not know the exact job arrival time and the service time from the utilization data. In this paper, we consider an approach to estimate the model parameters from the utilization data by assuming a few model assumptions. In particular, we suppose an M t /M /1/K queueing system whose job arrival follows a Non-homogeneous Poisson Process (NHPP) and propose a parameter estimation method for the NHPP approximately from the utilization data based on the maximum likelihood estimation (MLE) via the expectation maximization (EM) algorithm. In numerical experiments, we generate the simulated utilization data of an M t /M /1/K queueing system and investigate the effectiveness of our method. Also, we use the real CPU utilization data to exhibit the performance evaluation. INDEX TERMS Queueing systems, time intervals, utilization data, EM algorithm.

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Section: Related Workmentioning

confidence: 99%

Parameter Estimation of $M_{t}/M/1/K$ Queueing Systems With Utilization Data

Okamura

2019

IEEE Access

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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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“…[14] have evaluated confidence intervals for the mean waiting time of the single server and tandem queues with blocking. Maximum likelihood estimates of multi-server system with heterogeneous servers were obtained by [13]. In [12] have studied the estimation of arrival and service rates for queues based only on queue length data.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis and Statistical Modeling of the Single-Server Non-reliable Retrial Queueing System with a Threshold-Based Recovery

Efrosinin

Sztrik

2015

Communications in Computer and Information Science

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Abstract. In this paper we study a single-server Markovian retrial queueing system with non-reliable server and threshold-based recovery policy. The arrived customer finding a free server either gets service immediately or joins a retrial queue. The customer at the head of the retrial queue is allowed to retry for service. When the server is busy, it is subject to breakdowns. In a failed state the server can be repaired with respect to the threshold policy: the repair starts when the number of customers in the system reaches a fixed threshold level. Using a matrix-analytic approach we perform a stationary analysis of the system. The optimization problem with respect to the average cost criterion is studied. We derive expressions for the Laplace transforms of the waiting time. The problem of estimation and confidence interval construction for the fully observable system is studied as well.

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Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers

Cited by 24 publications

References 9 publications

Parameter Estimation of $M_{t}/M/1/K$ Queueing Systems With Utilization Data

Parameter Estimation of $M_{t}/M/1/K$ Queueing Systems With Utilization Data

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

Performance Analysis and Statistical Modeling of the Single-Server Non-reliable Retrial Queueing System with a Threshold-Based Recovery

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