Cost optimization analysis for an $$M^{X}/M/c$$ M X / M / c vacation queueing system with waiting servers and impatient customers

Bouchentouf, Amina Angelika; Guendouzi, Abdelhak

doi:10.1007/s40324-018-0180-2

Cited by 19 publications

(4 citation statements)

References 18 publications

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“…The authors in [40] presented the analysis of an M/M/1 model with impatient customers, where the server is allowed to take a maximum number of K consecutive vacations, if there are no customers in the system at the end of a vacation. Bouchentouf and Guendouzi [6] did the cost optimization of an M X /M/c model with waiting server and impatient customers under both single as well as multiple vacation disciplines, by applying the quadratic fit search method (QFSM). Suranga and Liu [31] presented the time-dependent solution of an impatient M/M/1 system with a waiting server and differentiated vacations.…”

Section: Mathematics Subject Classification (2000) 60k25 • 68m20 • 90...mentioning

confidence: 99%

Performance analysis of vacation interruption queue with balking and reneging

Majid

Vijaya

Angelika

et al. 2023

Preprint

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This paper presents a comprehensive study of an infinite buffer M/M/1 queue with variant working vacations subjected to Bernoulli schedule vacation interruption wherein the customers balk with a probability. The server commences a working vacation as soon as the system becomes empty and resumes a regular busy period by interrupting the working vacation with probability 1 − p if the system is non-empty at a service completion instant or continues the vacation with probability p. The customers may renege due to slow service rate during the working vacation. The inter-arrival times, service times (both during regular busy period and working vacation periods), vacation times and reneging times are mutually independent and exponentially distributed. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size for different server states. Various performance measures and the monotonicity on some performance measures with respect to K are discussed, and a cost optimization problem through quadratic fit search method has been considered. The stochastic decomposition structures of the mean queue length and mean waiting time are verified. Mathematics Subject Classification (2000) 60K25 · 68M20 · 90B22

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Section: Mathematics Subject Classification (2000) 60k25 • 68m20 • 90...mentioning

confidence: 99%

Performance analysis of vacation interruption queue with balking and reneging

Majid

Vijaya

Angelika

et al. 2023

Preprint

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“…This situation reflects many real life queueing systems, particularly when dealing with human behaviour. For recent research works on the subject, the reader can refer to Padmavathy et al [19], Ammar [3], Bouchentouf and Guendouzi [9], and Bouchentouf et al [11].…”

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

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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.

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“…[8] examined a queueing model with feedback, reneging and retention of reneged customers, multiple working vacations and Bernoulli schedule vacation interruption. Further, performance and economic analyzes of different queueing models with vacation/working vacation and customer's impatience have been treated by [5,6], [2,3], [4], [19,7], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

Majid¹,

Bouchentouf

Guendouzi

2021

Acta Universitatis Sapientiae, Mathematica

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In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.

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Cost optimization analysis for an $$M^{X}/M/c$$ M X / M / c vacation queueing system with waiting servers and impatient customers

Cited by 19 publications

References 18 publications

Performance analysis of vacation interruption queue with balking and reneging

Performance analysis of vacation interruption queue with balking and reneging

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

Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

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