Optimum alternatives of tandem G/G/K queues with disaster customers and retrial phenomenon: interactive voice response systems

Azadeh, A.; lhoseiny, M. S. Naghavi; Salehi, Vahid

doi:10.1007/s11235-017-0397-x

Cited by 3 publications

(2 citation statements)

References 56 publications

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“…They constructed a cost function and used the OptQuest tool in ARENA software to determine the optimal threshold F to minimize predicted cost per unit time. In [6] Azabeh et.al studied tandem queue with retrial and disaster. They also optimized the proposed G/G/k tandem queue.…”

Section: Introductionmentioning

confidence: 99%

Modelling Dynamic Traffic Loads in Multiserver Queues using G/G/k Queue

Gowrishankar

2024

E3S Web Conf.

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Operations research and marketing management have benefited greatly from the important science of queuing optimisation. We take into account a multiserver single input G/G/k queue for study. This type of queue formation occurs in factories, production facilities, logistics centres, airports, and hospitals where the inter-arrival and service times are frequently not exponentially distributed. Knowing the precise number of service providers needed to avoid congestion at the lowest possible cost would therefore be the main concern. When there are more jobs than servers in a G/G/k queue, the cost incurred by the number of jobs per unit time becomes complex, making it challenging to determine the average cost. As a result, this paper obtains the bound for the ideal number of servers that would reduce the overall cost. Interpolation technique is used to determine the precise number of servers. When there are more servers (k) than job arrivals, the G/G/k queue’s optimal cost per unit time during an execution cycle is obtained. The proposed system is made up of a G/G/k queue that begins operating as soon as the first job enters the system. Due to the general distribution of job arrivals, the time interval between subsequent job arrivals is not always the same. Therefore, the study of an arrival that causes a state transition in the system is taken into account. When there are fewer servers available than job arrivals, an expression is derived to determine the optimal server count. When the number of available servers exceeds the number of jobs in the system, the optimal number of jobs that minimises the average processing cost per unit time for one job is also determined. The simulation results are obtained by simulating this system with MATLAB’s SimEvents toolbox.

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Section: Introductionmentioning

confidence: 99%

Modelling Dynamic Traffic Loads in Multiserver Queues using G/G/k Queue

Gowrishankar

2024

E3S Web Conf.

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“…In general, non-Poisson arrivals make the analysis of queues far more complicated than the case of Poisson arrivals, but they have been considered more recently in the literature (Jain et al 2020 ; Chydzinski 2020 ) due to the fact that non-Poisson arrivals are common in real-world settings. See Kimura ( 1994 ), Kimura ( 1995 ), Whitt ( 1993 ), Medhi ( 2003 ), Azadeh and Salehi ( 2018 ), and Yang et al. ( 2021 ) for analysis of such queues.…”

Section: Introductionmentioning

confidence: 99%

On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study

Gosavi

2022

Oper Res Int J

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We consider the multi-server, single-channel queue, i.e., a G / G / k queue with k identical servers in parallel, under the first-come-first-served discipline in which the inter-arrival process is non-Poisson, the service time has any given distribution, and traffic is of medium intensity. Such queues are common in factories, airports, and hospitals, where the inter-arrival times and service times are typically not exponentially distributed, but rather have double-tapering distributions whose probability density functions taper on both sides, e.g., gamma, triangular etc. For these conditions, a new closed-form approximation based on only the mean and variance of the two inputs, the inter-arrival and service times, is presented. Determining distributions of inputs typically requires additional human effort in terms of histogram-fitting and running a goodness-of-fit test, which is avoided here. The new approximation is tested on a variety of scenarios and its performance is benchmarked against simulation. Further, the new approximation is also implemented on a ventilator case study from the recent COVID-19 pandemic to demonstrate its utility in optimizing server capacity. The approximation provides errors typically in the range 1–15% and 31% in the worst case. In systems where data change rapidly and decisions must be made quickly, this approximation will be particularly useful.

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