A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time

Wang, Kuo Hsiung; Kuo, Ching Chang; Pearn, W. L.

doi:10.1016/j.apm.2007.02.023

Cited by 31 publications

(7 citation statements)

References 19 publications

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“…Case 1. When p = 1 and θ = 1, the proposed model coincides with the model presented by [17]. Case 2.…”

Section: Special Casessupporting

confidence: 66%

Randomized control of arrivals in a finite-buffer GI/M/1 system with starting failures

Yang

2020

RAIRO-Oper. Res.

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This paper proposes a randomized policy for the control of arrivals in a finite-buffer GI/M/1 system with a single server. When the capacity of system is full, no new arrivals are permitted to enter the system. When the number of customers in the system decreases to threshold F , a new arriving customer is allowed to join the system with probability p. The system requires an exponential startup time before allowing customers to enter the system. The startup process may not be successful and is then restarted once again. Using the supplementary variable technique in a recursive process, we obtain the stationary distribution of the system size. Various performance measures of the system are developed. We also create a cost model based on the system performance measures and cost elements. The optimal threshold, optimal capacity and optimal startup rate of the system are determined to minimize the expected cost per unit time. Finally, we provide numerical examples to conduct a sensitivity analysis.Mathematics Subject Classification. 90B22, 60K25.

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“…Case 1. When p = 1 and θ = 1, the proposed model coincides with the model presented by [17]. Case 2.…”

Section: Special Casessupporting

confidence: 66%

Randomized control of arrivals in a finite-buffer GI/M/1 system with starting failures

Yang

2020

RAIRO-Oper. Res.

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“…The F -policy can be employed to resolve the issue of controlling of the arrivals in the queueing system so as to avoid the loss of revenue and inconvenience to the jobs. Based on F -policy, non-Markovian M/G/1/K and G/M/1/K queueing models were investigated by Wang et al [36,35]. The performance analysis of unreliable M/M/2/K queueing model by incorporating both F -policy and N -policy was developed by Jain et al [20].…”

Section: Madhu Jain and Sudeep Singh Sangamentioning

confidence: 99%

Admission control for finite capacity queueing model with general retrial times and state-dependent rates

Jain¹,

Sanga²

2020

Journal of Industrial &Amp; Management Optimization

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The finite state dependent queueing model with F-policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to F-policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value 'F '. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.

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“…For F -policy queues, Wang, Kuo, and Pearn (2008) considered the optimum control of a G/M/1/K system combining F -policy and exponentially startup time before starting to allow clients in the system. The authors applied the supplementary variable technique to develop the steady-state probability distribution of the number of clients in the system.…”

Section: Introductionmentioning

confidence: 99%

Reliability-based measure of a retrial machine repair problem with working breakdowns under the F-policy

Yen

Wang

2020

Computers & Industrial Engineering

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Highlights We consider a F -policy retrial machine repair problem with working breakdowns. One practical illustration of the online-learning cloud system is presented. The differential equations are tabulated and solved by Laplace transform technique. Closed-form expressions for the reliability and the MTTF are explicitly derived. Reliability sensitivity analysis with respect to system parameters are performed. Several management insights for managers to enhance the reliability are provided.

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A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time

Cited by 31 publications

References 19 publications

Randomized control of arrivals in a finite-buffer GI/M/1 system with starting failures

Randomized control of arrivals in a finite-buffer GI/M/1 system with starting failures

Admission control for finite capacity queueing model with general retrial times and state-dependent rates

Reliability-based measure of a retrial machine repair problem with working breakdowns under the F-policy

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