在延迟Min (N, D)-策略M/G/1可修排队系统及最优控制策略

Abstract

Abstract:

This paper considers the M/G/1 repairable queueing system with delay Min(N, D)-policy, in which the repair facility subject to breakdowns and then replaced during the repair facility busy period. By using the total probability decomposition technique and employing the Laplace transform tool, some reliability indices of the service station and the repair facility, such as the transient-state and steady-state unavailability, the expected failure number during (0, t] are discussed. Finally, it is determined the optimal control policy (N^*, D^*) such that the long-run expected cost rate is minimum under a given cost structure.

Key words: Repair facility, Delay Min(N, D)-policy, Queueing index, Reliability index, Optimal control policy

CLC Number:

O121

Quyu Pan,Yinghui Tang. Analysis of M/G/1 Repairable Queueing System and Optimal Control Policy with a Replaceable Repair Facility Under Delay Min(N, D)-Policy[J].Acta mathematica scientia,Series A, 2018, 38(5): 1014-1031.

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Figures/Tables 8

References 25

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	D
N	1	2	3	4	5	5.1381	6	7	8	9	10
1	72.7177	72.7177	72.7177	72.7177	72.7177	72.7177	72.7177	72.7177	72.7177	72.7177	72.7177
2	62.9313	62.5521	62.5335	62.5325	62.5325	62.5325	62.5325	62.5325	62.5325	62.5325	62.5325
3	58.9588	57.9496	57.8746	57.8695	57.8692	57.8692	57.8692	57.8692	57.8692	57.8692	57.8692
4	57.7637	56.3324	56.1923	56.1802	56.1793	56.1792	56.1792	56.1792	56.1792	56.1792	56.1792
5	57.7136	56.3969	56.2830	56.2739	56.2733	56.2732	56.2732	56.2732	56.2732	56.2732	56.2732
6	57.9797	57.3362	57.4734	57.5142	57.5207	57.5209	57.5215	57.5216	57.5216	57.5216	57.5216
7	58.2257	58.6056	59.3190	59.5182	59.5541	59.5556	59.5591	59.5597	59.5598	59.5598	59.5598
8	58.3738	59.8524	61.4852	62.0234	62.1400	62.1452	62.1592	62.1618	62.1621	62.1621	62.1621
9	58.4444	60.8845	63.7075	64.8239	65.1145	65.1292	65.1712	65.1801	65.1813	65.1814	65.1814
10	58.4728	61.6369	65.7848	67.7421	68.3483	68.3828	68.4877	68.5132	68.5171	68.5176	68.5177

Analysis of M/G/1 Repairable Queueing System and Optimal Control Policy with a Replaceable Repair Facility Under Delay Min(N, D)-Policy

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