具有p-进入规则和Min(N, D, V)-策略的M/G/1排队系统容量问题研究

Abstract

Abstract:

This paper considers a M/G/1 queueing system with p-entering discipline and Min(N, D, V)-policy, in which the customers who arrive during multiple vacations enter the system with probability p(0 < p ≤ 1). By using the total probability decomposition technique and the Laplace transform, we discuss the transient distribution of queue length at any time t which started from an arbitrary initial state, and obtain the expressions of the Laplace transform of transient queue-length distribution. Moreover, we obtain the recursion expressions of the steady-state queue length distribution. Meanwhile, we discuss the optimal capacity design by combining the steady-state queue length distribution and numerical example. Finally, the explicit expression of the long-run expected cost rate is derived under a given cost structure. And by through numerical calculation, we determine the optimal control policy (N^*, D^*) for minimizing the long-run expected cost per unit time.

Key words: Multiple vacation, p-Entering discipline, Min(N, D, V)-policy, Queue length distribution, Optimal control policy

CLC Number:

O121

Le Luo,Yinghui Tang. System Capacity Optimization Design and Optimal Control Policy (N^*, D^*) for M/G/1 Queue with p-Entering Discipline and Min(N, D, V)-Policy[J].Acta mathematica scientia,Series A, 2019, 39(5): 1228-1246.

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Figures/Tables 3

$p_0$	$p_1$	$p_2$	$p_3$	$p_4$	$p_5$	$p_6$	$p_7$	$p_8$	$p_9$	$p_{10}$	$p_{11}$	$p_{12}$	$p_{13}$	$p_{14}$	$p_{15}$	$p_{16}$	$p_{17}$	$p_{18}$	$p_{19}$	$p_{20}$	$p_{21}$	$p_{22}$	$E[L]$
0.262226	0.234005	0.173473	0.116078	0.073218	0.044167	0.025562	0.014185	0.007539	0.003839	0.001522	0.000609	0.000243	0.000097	0.000039	0.000016	0.000006	0.000002	0.000000	0.000000	0.000000	0.000000	0.000000	1.917604

DN	$1$	$2$	$3$	$4$	$5$	$6$
1	13.144737	9.991536	9.563765	9.521530	9.523348	9.525169
2	13.144737	9.312163	8.666641	8.606744	8.641893	8.668439
3	13.144737	9.098830	8.356363	8.300900	8.391288	8.474396
4	13.144737	9.024516	8.235207	8.184978	8.325796	8.476696
5	13.144737	8.997709	8.185816	8.138259	8.315510	8.527172
6	13.144737	8.987918	8.165466	8.118911	8.319459	8.577624
7	13.144737	8.984325	8.157101	8.110828	8.325154	8.615477
8	13.144737	8.983005	8.153686	8.107553	8.329470	8.640445
9	13.144737	8.982519	8.152304	8.106051	8.332170	8.655647
10	13.144737	8.982304	8.151748	8.105571	8.333699	8.664381
11	13.144737	8.982275	8.151526	8.105234	8.334510	8.669176
12	13.144737	8.982251	8.151438	8.105137	8.334921	8.671714
13	13.144737	8.982242	8.151404	8.105097	8.335123	8.673016
14	13.144737	8.982239	8.151390	8.105082	8.335298	8.673667
15	13.144737	8.982237	8.151385	8.105075	8.335265	8.673985
16	13.144737	8.982237	8.151383	8.105073	8.335285	8.674137
17	13.144737	8.982237	8.151382	8.105072	8.335294	8.674209
17.3	13.144737	8.982237	8.151382	8.105072	8.335296	8.674222
17.4	13.144737	8.982237	8.151382	$\bf{\fbox{ 8.105071}}$	8.335296	8.674226
17.5	13.144737	8.982237	8.151382	8.105071	8.335297	8.674229
18	13.144737	8.982237	8.151382	8.105071	8.335298	8.674243
19	13.144737	8.982237	8.151381	8.105071	8.335300	8.674258
20	13.144737	8.982237	8.151381	8.105071	8.335301	8.674265

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[1]	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.
[2]	Gao Lijun, Tang Yinghui. M/G/1 Repairable Queueing System and Optimal Control Policy with Min(N,D)-Policy [J]. Acta mathematica scientia,Series A, 2017, 37(2): 352-365.

System Capacity Optimization Design and Optimal Control Policy (N^, D^) for M/G/1 Queue with p-Entering Discipline and Min(N, D, V)-Policy

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System Capacity Optimization Design and Optimal Control Policy (N^, D^) for M/G/1 Queue with p-Entering Discipline and Min(N, D, V)-Policy