The stochastic decomposition structure of the waiting time for M/G/1/∞ queue with N-policy and Min(N,V)-policy

TANG Yinghui, LAN Shaojun

Systems Engineering - Theory & Practice ›› 2016, Vol. 36 ›› Issue (1) : 174-183.

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Systems Engineering - Theory & Practice ›› 2016, Vol. 36 ›› Issue (1) : 174-183. DOI: 10.12011/1000-6788(2016)01-0174-10

The stochastic decomposition structure of the waiting time for M/G/1/∞ queue with N-policy and Min(N,V)-policy

  • TANG Yinghui1,2, LAN Shaojun1
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Abstract

In some studies concerning M/G/1/∞ queueing models with N-policy, since the waiting time for a customer arriving during a server off-duty period is no longer independent of the inter-arrival times of customers arriving later, it is difficult to investigate the distribution of equilibrium waiting time, and considerable effort is devoted to study the steady-state queue length and additional queue length of queueing system, while there is relatively little work done on the stationary waiting time and its stochastic decomposition. Due to the fact, in this paper we firstly treat the classical N-policy M/G/1/∞ queueing system. We study the waiting time distribution in equilibrium, and present the stochastic decomposition result of steady-state waiting time as well as the explicit expression for the distribution of additional delay time. Meanwhile, some errors on corresponding results in existed references are pointed out. Further, we consider the M/G/1/∞ queueing systems with multiple server vacations and single server vacation under Min(N,V)-policy. By similar analytical method, we not only obtain the stochastic decomposition result of equilibrium waiting time but also derive the formulas for the mean stationary waiting time and mean additional delay time. Especially, some corresponding results for some special queueing systems can be directly obtained on the basis of the results provided in this paper.

Key words

N-policy and Min(N,V)-policy / M/G/1/∞ queue / steady-state waiting time / additional delay time / stochastic decomposition

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TANG Yinghui , LAN Shaojun. The stochastic decomposition structure of the waiting time for M/G/1/∞ queue with N-policy and Min(N,V)-policy. Systems Engineering - Theory & Practice, 2016, 36(1): 174-183 https://doi.org/10.12011/1000-6788(2016)01-0174-10

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Funding

National Natural Science Foundation of China (71171138, 71571127)
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