The $$M^{X}/M/c$$ Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

Bouchentouf, Amina Angelika; Guendouzi, Abdelhak

doi:10.1007/s40065-019-0260-x

Cited by 19 publications

(9 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…decreases) along the increasing of χ and α in MWV model. 10. Both E(L wv ) * , P * wv , R * ren , and R * ret increase with the increasing of and β, as intuitively expected.…”

Section: Numerical Analysissupporting

confidence: 72%

See 1 more Smart Citation

Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

Bouchentouf

Houalef

Guendouzi

2022

Acta Universitatis Sapientiae, Mathematica

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.

show abstract

“…decreases) along the increasing of χ and α in MWV model. 10. Both E(L wv ) * , P * wv , R * ren , and R * ret increase with the increasing of and β, as intuitively expected.…”

Section: Numerical Analysissupporting

confidence: 72%

“…Thus, a very limited literature is available for these models. The readers can be referred to Altman and Yechiali [1], Yue et al [27], Altman and Yechiali [2], Yue et al [29], Majid and Manoharan [18], Yahiaoui et al [26], and Bouchentouf and Guendouzi [10].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

Bouchentouf

Houalef

Guendouzi

2022

Acta Universitatis Sapientiae, Mathematica

Self Cite

View full text Add to dashboard Cite

show abstract

“…They computed transient solution, steady state results, the average number of customers in the queue and the system. Very recently, Bouchentouf and Guendouzi [17] analyzed an M X /M/c Bernoulli feedback queueing system with variant of multiple working vacations and reneging which depend on the states of the servers and retention of reneged customers.…”

Section: (I) Vacation Queueing Models With Batch Arrivalmentioning

confidence: 99%

A Review of Vacation Queueing Models in Different Framework

Panta¹,

Ghimire²,

D.Panthi³

et al. 2021

APAM

View full text Add to dashboard Cite

This paper deals with the extensive survey of the vacation queueing systems from its birth in1975 to till date. As the time passes on old-provisions cannot tackle new-problem so new concepts have to be developed. Some of the threshold policies that have been developed from time to time have been reported. Some of the prominent techniques of solution of vacation queueing system have also been cited. The challenges on tackling the problems of vacation queueing systems have been discussed.

show abstract

“…This paper contributes in this sense. In fact, only a few research papers have been done treating this case [9]- [12], [30].…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Bouchentouf

Medjahri

Boualem

et al. 2022

Discrete and Continuous Models

Self Cite

View full text Add to dashboard Cite

In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.

show abstract

The $$M^{X}/M/c$$ Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

Cited by 19 publications

References 21 publications

Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

A Review of Vacation Queueing Models in Different Framework

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Contact Info

Product

Resources

About