STATE-DEPENDENT BENES BUFFER MODEL WITH FAST LOADING AND OUTPUT RATES
成果类型：
Article
署名作者：
Kogan, Y.; Liptser, R.; Shenfild, M.
署名单位：
Technion Israel Institute of Technology; Tel Aviv University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004830
发表日期：
1995
页码：
97-120
关键词：
摘要：
We consider a state-dependent generalization of the exponential Benes model of single-source buffer system in which the source process consists of alternating transmission and idle periods. Martingale methods are applied for analyzing limit nonstationary behavior of the buffer content process, when the buffer is loaded and depleted, with rates proportional to a large parameter N. Depending on traffic conditions, defined by parameters of the model, different types of approximations are established for the buffer content. We show that in heavy traffic the buffer content grows linearly in N, whereas the deviations of the order root N from the deterministic limit are approximated by the Gaussian diffusion process. In moderate traffic the buffer content grows as root N, and the normalized buffer content is approximated by a diffusion process with reflection at zero. In the case of normal traffic, we show that the buffer utilization tends to the ratio of the input-to-output rate. Moreover, we show that the main contribution to the utilization comes from arbitrary small buffer content.