Queueing systems with vacations ? A survey

Doshi, Bharat T.

doi:10.1007/bf01149327

Cited by 1,067 publications

(436 citation statements)

References 30 publications

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“…Adding q (1) 1π to both sides, using that 1π − Q 2 is non-singular and π 1π − Q 2 −1 = π we obtain (66).…”

Section: Mean Fluid Levelmentioning

confidence: 99%

“…Making use of the block-partitioned structure of Q (see (1)) and the relation between Q andQ given by (6) we get…”

Section: Important Relationsmentioning

confidence: 99%

“…The state dependent stationary mean fluid level is given by q (1) = q (1) 1π + πRQ + 1 E(σ) π(R − dI) I Ψ Ψ I σ * (−Q) 1π − Q 2 −1 .…”

Section: Mean Fluid Levelmentioning

confidence: 99%

“…Vacation and polling models with discrete (integer) customers have been studied [1,2] and applied on a wide range of application fields of stochastic modeling for long time [3,4]. An interesting property of the vacation models is the stochastic decomposition property [5], which means that the steady-state number of customers in the system can be decomposed to the sum of two independent random variables, the steadystate number of customers in the corresponding queue and the steady-state number of customers presents in the system at arbitrary epoch in the vacation period.…”

Section: Introductionmentioning

confidence: 99%

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Exhaustive fluid vacation model with positive fluid rate during service

Horvth

Telek

2015

Performance Evaluation

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Using an elegant transform domain iterative operator approach exhaustive fluid vacation models with strictly negative fluid rate during service has been analyzed, recently. Unfortunately, the potential presence of positive fluid rate during service (when the fluid input rate is larger than the fluid service rate) inhibits the use of all previously applied methodologies and makes the extension of the analysis approaches of discrete vacation and polling models toward fluid vacation and polling models rather difficult.Based on the level crossing analysis of Markov fluid models the paper introduces an analysis approach which is applicable for the stationary analysis of the fluid level distribution and its moments. In the course of the analysis compact new matrix exponential expressions are obtained for the distribution of fluid level during a busy period starting from a given positive fluid level and by exploiting the relations of upward and downward measures of fluid processes several matrix transformations are applied to avoid Kronecker expansion matrix multiplications. Finally, the obtained fluid level distribution is related with previous results of fluid vacation models.

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“…Adding q (1) 1π to both sides, using that 1π − Q 2 is non-singular and π 1π − Q 2 −1 = π we obtain (66).…”

Section: Mean Fluid Levelmentioning

confidence: 99%

“…Making use of the block-partitioned structure of Q (see (1)) and the relation between Q andQ given by (6) we get…”

Section: Important Relationsmentioning

confidence: 99%

“…The state dependent stationary mean fluid level is given by q (1) = q (1) 1π + πRQ + 1 E(σ) π(R − dI) I Ψ Ψ I σ * (−Q) 1π − Q 2 −1 .…”

Section: Mean Fluid Levelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exhaustive fluid vacation model with positive fluid rate during service

Horvth

Telek

2015

Performance Evaluation

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“…However, it is not imbedded to some known class of vacation queueing models. Vacation models are usually classified (see, e.g., Doshi, 1986;Takagi, 1991;Tian and Zhang, 2006), by the discipline of switching the server off (exhaustive, gated, limited, etc. ) and switching it on (N -, T -, E-strategies, etc.).…”

mentioning

confidence: 99%

Optimization of the service strategy in a queueing system with energy harvesting and customers’ impatience

Dudin

Lee

Dudin

2016

International Journal of Applied Mathematics and Computer Science

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A single-server queueing system with an infinite buffer is considered. The service of a customer is possible only in the presence of at least one unit of energy, and during the service the number of available units decreases by one. New units of energy arrive in the system at random instants of time if the finite buffer for maintenance of energy is not full. Customers are impatient and leave the system without service after a random amount of waiting time. Such a queueing system describes, e.g., the operation of a sensor node which harvests energy necessary for information transmission from the environment. Aiming to minimize the loss of customers due to their impatience (and maximize the throughput of the system), a new strategy of control by providing service is proposed. This strategy suggests that service temporarily stops if the number of customers or units of energy in the system becomes zero. The server is switched off (is in sleep mode) for some time. This time finishes (the server wakes up) if both the number of customers in the buffer and the number of energy units reach some fixed threshold values or when the number of energy units reaches some threshold value and there are customers in the buffer. Arrival flows of customers and energy units are assumed to be described by an independent Markovian arrival process. The service time has a phase-type distribution. The system behavior is described by a multi-dimensional Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for key performance measures are given. Numerical results illustrating the dependence of a customer's loss probability on the thresholds defining the discipline of waking up the server are provided. The importance of the account of correlation in arrival processes is numerically illustrated.

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Priorities inM/G/1 queue with server vacations

Kella

Yechiali

1988

Naval Research Logistics

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Queueing systems with vacations ? A survey

Cited by 1,067 publications

References 30 publications

Exhaustive fluid vacation model with positive fluid rate during service

Exhaustive fluid vacation model with positive fluid rate during service

Optimization of the service strategy in a queueing system with energy harvesting and customers’ impatience

Priorities inM/G/1 queue with server vacations

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