Optimization on (<i>N</i>, <i>p</i>)-policy for an unreliable queue with second optional service and start-up

Yang, Dong; Wang, Kuo Hsiung; Pearn, W. L.

doi:10.1080/10170669.2011.591843

Cited by 7 publications

(5 citation statements)

References 32 publications

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“…Randomized control of N -policy [5,6,14,19,20,[23][24][25] Randomized control of T -policy [12,19,21,26] Randomized control of F -policy [3,4,6,24,29] examined by [13]. For the F -policy M/H 2 /1/K queue with server breakdowns and exponential startup times, [1] formulated an optimization problem to determine the optimal capacity, the optimal threshold, the optimal startup rate, and the optimal repair rate at the minimum expected cost per unit time.…”

Section: Randomized Control Policy Studymentioning

confidence: 99%

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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Section: Randomized Control Policy Studymentioning

confidence: 99%

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

Yang

2020

RAIRO-Oper. Res.

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“…e PGF of ( ) is obtained by (7). Using the property of PGF [13] we obtain the steady-state mean queuing length is as follows:…”

Section: Mean Queuing Length Aer Getting the Probabilitiesmentioning

confidence: 99%

“…In queuing researches, many researchers have studied the queuing system with repairable servers. Most of the works of the repairable queuing system deal with the single-server models [1][2][3][4][5][6][7][8][9]. e works about multiserver repairable systems is not sufficient.…”

Section: Introductionmentioning

confidence: 99%

“…Zhang and Hou [6] analyzed an M/G/1 queue with working vacations and vacation interruptions; they obtained the queue length distribution and steady-state service status probability. Yang et al [7] analyzed an M/G/1 queuing system with second optional service, server breakdowns, and general startup times under ( -policy, they obtained the explicit closed-form expression of the joint optimum threshold values of ( at the minimum cost. Chang et al [8] studied the optimal management problem of a �nite capacity M/H2/1 queuing system, where the unreliable server operatespolicy, a cost model is developed to determine the optimal capacity , the optimal threshold , the optimal setup rate, and the optimal repair rate at a minimum cost.…”

Section: Introductionmentioning

confidence: 99%

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The M/M/NRepairable Queueing System with Variable Breakdown Rates

2013

Discrete Dynamics in Nature and Society

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is paper considers the M/M/ repairable queuing system. e customers' arrival is a Poisson process. e servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. e breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we obtain the steady-state probabilities of the system states, the steady-state availability of the servers, and the mean queueing length of the model.

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“…In such a system, an idle server does not start serving customers unless there are 1 N  customers waiting for service in which N is a fixed value. Extensive literatures exist on the N-policy continuous-time queues with different circumstances, and the readers may refer to Bell (1971), Kimura (1981), Takagi (1993a), Bisdikian (1994), Gakis et al (1995), Wang and Huang (1995), Wang and Ke (2000), Ke and Wang (2002), Ke (2006), Zhang and Xu (2008), Wang and Huang (2009), Choudhury et al (2009), Wang et al (2010), Choudhury et al (2011), Chang and Pearn (2011), and Yang et al (2011), Chen (2012). On the other hand, the N-policy discrete-time queues has just received little attention in the literatures.…”

Section: Introductionmentioning

confidence: 99%

Dynamic control policy for the discrete-time queue

Wang

Chang

2016

IJSOI

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In queueing system, upon the server is idle, one of control policy for determining the timing of server activated is when a fixed number N of customers accumulates for service in the system. However, on some practical situations such as watching video file online, the threshold value N may vary depending on different situations. For such situation, this paper studies a random N-policy Geo/G/1 queue, where N is determined as each new cycle begins. We derive some system characteristics, such as system size, idle period, busy period and sojourn time, by using the probability generating function and supplementary variable technique. We also prove that the system size of a continuous-time random N-policy M/G/1 queue can be approximated by the presented discrete-time model.

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Optimization on (N, p)-policy for an unreliable queue with second optional service and start-up

Cited by 7 publications

References 32 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

The M/M/NRepairable Queueing System with Variable Breakdown Rates

Dynamic control policy for the discrete-time queue

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