Measurements and approximations to describe the offered traffic and predict the average workload in a single-server queue

Fendick, Kerry W.; Whitt, Ward

doi:10.1109/5.21078

Cited by 76 publications

(59 citation statements)

References 43 publications

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“…Hence, in this paper the assumption is made that the cargo operations (assessed from the ship aspect) can be defined through the application of the queuing theory. A similar methodology has been used in various scientific papers for modelling and resolving the problems of port operations planning, port capacities estimation and port investments planning which lead to positive advancement in direction of port cargo operations optimization with the goal of minimizing the operational costs [7,8,9]. The theory has also been successfully applied in modelling of port management decision-making process [10].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Ship Cargo Operations by Genetic Algorithm

Hess¹,

Hess²

2012

PROMET

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Section: Introductionmentioning

confidence: 99%

Optimization of Ship Cargo Operations by Genetic Algorithm

Hess¹,

Hess²

2012

PROMET

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“…These derivatives are called the light tra c derivatives and have been previously discussed in 9,8,12]. The light tra c derivatives can be used jointly with the heavy tra c limits for approximating the curve of the delay against the arrival rate.…”

Section: The Light Tra C Derivativesmentioning

confidence: 99%

The MacLaurin series for the GI/G/1 queue

Gong

1992

Journal of Applied Probability

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We derive the MacLaurin series for the moments of the system time and the delay with respect to the parameters in the service time or interarrival time distributions in the GI/G/1 queue. The coe cients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The light tra c derivatives can be obtained from these series. For the M/G/1 queue, we are able to recover the formulas for the moments of the system time and the delay, including the Pollaczek-Khinchin mean-value formula.

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“…For the RQ approximation of the mean steady-state workload, we use the associated index of dispersion for work (IDW) I w ≡ {I w (x): x ≥ 0} introduced by Fendick and Whitt (1989), which is defined by…”

Section: The Mean Steady-state Workload At a G/g/1 Queuementioning

confidence: 99%

Heavy-Traffic Limit of theGI/GI/1 Stationary Departure Process and Its Variance Function

Whitt

You

2018

Stochastic Systems

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Abstract. Heavy-traffic limits are established for the stationary departure process from a GI/GI/1 queue and its variance function. The limit process is a function of the Brownian motion limits of the arrival and service processes plus the stationary reflected Brownian motion (RBM) limit of the queue-length process. An explicit expression is given for the variance function, which depends only on the first two moments of the interarrival times and service times plus the previously determined correlation function of canonical (drift −1, diffusion coefficient 1) RBM. The limit for the variance function here is used to show that the approximation for the index of dispersion for counts of the departure process used in our new robust queueing network analyzer is asymptotically correct in the heavy-traffic limit.

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Measurements and approximations to describe the offered traffic and predict the average workload in a single-server queue

Cited by 76 publications

References 43 publications

Optimization of Ship Cargo Operations by Genetic Algorithm

Optimization of Ship Cargo Operations by Genetic Algorithm

The MacLaurin series for the GI/G/1 queue

Heavy-Traffic Limit of theGI/GI/1 Stationary Departure Process and Its Variance Function

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