Variance reduction in M/M/1 retrial queues using refined descriptive sampling

Idjis, Khelidja; Ourbih-Tari, Megdouda; Baghdali-Ourbih, Latifa

doi:10.1080/03610918.2016.1140778

Cited by 9 publications

(2 citation statements)

References 3 publications

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“…According to this queuing theory, the queue at any single exit of the parking lot can be denoted as a M/M/1/1 queuing system [28]. M/M stands for Poisson arrivals and the negative, exponentially distributed lengths of stay [29]; 1/1 indicates that there is only 1 exit which can only serve 1 vehicle at a time [30]. The average queuing time (including waiting time and service time) of queuing system r is calculated as in [31].…”

Section: Methodsmentioning

confidence: 99%

Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows

Mao

Cao

Gan

et al. 2019

IJERPH

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An optimal evacuation strategy for parking lots can shorten evacuation times and reduce casualties and economic loss. However, the impact of dynamic background traffic flows in a road network on the evacuation plan is rarely taken into account in existing approaches. This research develops an optimal evacuation model with total evacuation time minimization by dividing the evacuation process in a parking lot into two periods. In the first period, a queuing theory is used to estimate the queuing time, and in the second period, a traffic flow equilibrium model and an intersection delay model are employed to simulate vehicles’ route choice. To deal with these models, a modified ant colony algorithm is developed. The results of a numerical example prove that the proposed method has an advantage in improving evacuation efficiency. The results also show that background traffic flows affect not only vehicles’ average queuing time in parking lots but also optimal evacuation route choice. Additionally, a sensitivity analysis indicates that the minimum threshold of headway time that allows vehicles out of a parking lot to merge into the background traffic flows on the roads connecting the exits has a great impact on average queuing time, average travel time, and total evacuation time.

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Section: Methodsmentioning

confidence: 99%

Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows

Mao

Cao

Gan

et al. 2019

IJERPH

View full text Add to dashboard Cite

show abstract

“…[8][9][10] Also, there are studies based on the estimation approaches of various queueing models. [11][12][13][14] In related work, Idjis et al 15 simulated the stationary M/M/1/K retrial queue by employing two sampling methods, i.e., simple random sampling and refined descriptive sample. The techniques were compared in terms of variance reduction percentage and estimated error.…”

Section: Introductionmentioning

confidence: 99%

A comparison of variance reduction techniques in the simulation of a retrial M/M/1/K queue

2022

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Retrial queueing systems play a significant role in the modeling and performance evaluation of various dynamic stochastic systems, such as computer networks, airlines, communication and financial systems. This article presents a comprehensive assessment on the applicability of three popular variance reduction techniques (VRTs) in the performance evaluation of an M/M/1/K retrial queue based on shortest job first served (SJFS) retrial policy. The M/M/1/K retrial queue with SJFS retrial policy is not currently analytically tractable. Therefore, the credibility of such queueing systems is heavily dependent on simulations and accurate output data analysis. We seek to identify the best possible VRT so that a system performance evaluator can focus on optimizing the accuracy of relevant performance metrics under study. A comparative applicability analysis of three VRTs, i.e., antithetic variates, importance sampling, and control variates, on the retrial M/M/1/K queueing model has been presented. Our analysis showed a significant level of reduction in terms of variance and confidence interval size of the final estimates for the control variates technique. Furthermore, it has been found that unlike the other VRTs, the control variates technique shows a consistent trend in variance reductions as the number of retrials increases.

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Maximum Likelihood Estimation of Parameters of a Random Variable Using Monte Carlo Methods

2021

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Variance reduction in M/M/1 retrial queues using refined descriptive sampling

Cited by 9 publications

References 3 publications

Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows

Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows

A comparison of variance reduction techniques in the simulation of a retrial M/M/1/K queue

Maximum Likelihood Estimation of Parameters of a Random Variable Using Monte Carlo Methods

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