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We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
4.
Kun Chen Yong Cheng Yongzhi Chang Enqin Li Qing-Long Xu Can Zhang Xiaoan Wen Hongbin Sun 《Tetrahedron》2018,74(4):483-489
N-Substituted-3(10H)-acridones have been established as visible-light organic photocatalyst. These photosensitizers are efficient for oxidative coupling reaction of N-aryl tetrahydroisoquinolines with various nucleophiles. Notably, N-methyl-3(10H)-acridone (Ia) is stable and can be effectively prepared. It is a water-soluble and atom-economic catalyst, and thus holds promise for green chemical applications. Mechanistic studies confirm a single electron transfer (SET)-induced radical process and a rate-limiting step. Analysis of the photocatalytic reactivity?structure relationship reveals that the acridones are robust and tunable photosensitizers for photoredox catalysis. 相似文献
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Yongzhi Bai Changyu Li Jinghui Zhao Peihe Zheng Yali Li Yongqi Pan Yingping Wang 《Chromatographia》2013,76(11-12):635-642
A high yield method to extract alkaloids from Aconitum coreanum using pulsed electric field (PEF) was developed, and the optimized extraction method compared to the other four extraction methods, consisting of cold maceration extraction, percolation extraction, heat reflux extraction (HRE), and ultrasonic-assisted extraction (UE). The experimental factors of the extraction methods such as electric field intensity, pulse frequency and solid-to-solvent ratio were evaluated. The content of Guanfu base A (GFA) was quantified by liquid chromatography coupled with electrospray ionization tandem mass spectrometry. The results indicated that the highest yield of GFA was 3.94 mg g?1 by PEF with conditions of 20 kV cm?1 electric field intensity, 8 pulse, 1:12 solid-to-solvent ratio, and 90 % ethanol–water solution. Meanwhile, the extraction time of PEF was <1 min, which is much less than the HRE of 10 h and even the newly used technique UE of 40 min. Moreover, the results of PEF extraction method showed obvious advantages, with the highest efficiency (120 L h?1), the shortest extraction time (0.5–1 min), and the lowest energy costs, which could be applied in the industrial production of alkaloids from A. coreanum. Therefore, the application of the PEF extraction method is a promising and constructive method for extraction of GFA. 相似文献
7.
本文介绍了一种快速、简便的测定高含量三醋酸甘油酯的气相色谱法。本法使用10%PEG-20M涂渍在Chromosob W上的色谱柱(2 m×3 mmi.d.),以N_2作载气(40ml/min)氢火焰离子化检测器(FID),柱温180℃,汽化温度200℃,能很好地将三醋酸甘油酯与二醋酸甘油酯分离。并选用十二醇为内标物测定了十批合成样品中的三醋酸甘油酯含量,变异系数<0.4%。 相似文献
8.
We consider an M/M/1 queue with a time dependent arrival rate (t) and service rate (t). For a special form of the traffic intensity, we obtain an exact, explicit expression for the probability p
n
(t) that there are n customers at time t. If the service rate is constant (=), this corresponds to (t)=(t)/=(b–at)–2. We also discuss the heavy traffic diffusion approximation to this model. We evaluate our results numerically. 相似文献
9.
介绍了用自然坐标分析平面运动刚体上各点加速度的方法,并用该方法直是明地讨论了瞬心的加速度和刚体绕瞬心的转动方程。 相似文献
10.
Haiyan Chen Jizhi Dai Yongzhi Liu 《International Journal of Infrared and Millimeter Waves》2004,25(12):1791-1798
IR integrated photonic amplifiers at 1.55m operation will have good foreground in optical phasedarray radars for splitters and signal processing. The saturation gain characteristics of IR integrated photonic waveguide amplifiers (taken Er3+Yb3+ co-doped phosphate glass waveguide amplifiers as an example) are studied theoretically. For the homemade laser glass materials the calculated saturation intensities are 2.22kw /cm2 for signal and 10.15kw/cm2 for pump. The effects of absorption saturation of signal and pump lights on the gain of amplifiers are discussed. 相似文献