多信道ALOHA和CSMA介质访问协议：马尔可夫描述和大偏差
Multi-channel ALOHA and CSMA medium-access protocols: Markovian description and large deviations
摘要：
本文研究了连续时间内分别采用ALOHA和CSMA协议的多信道通信系统。我们推导出最重要的数量的概率公式：发送尝试的次数和在给定的时间间隔内成功发送消息的次数。我们推导出（1）大时间限制吞吐量的显式公式，（2）引入一个显式和遍历的马尔可夫链进行更深入的概率分析，并使用它来（3）推导出这些量在大时间限制下的罕见事件的指数渐近性，通过大偏差原理。
英文摘要：
We consider a multi-channel communication system under ALOHA and CSMA protocols, resepctively, in continuous time. We derive probabilistic formulas for the most important quantities: the numbers of sending attempts and the number of successfully delivered messages in a given time interval. We derive (1) explicit formulas for the large-time limiting throughput, (2) introduce an explicit and ergodic Markov chain for a deeper probabilistic analysis, and use this to (3) derive exponential asymptotics for rare events for these quantities in the limit of large time, via large-deviation principles.
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