Priority queues with bursty arrivals of incoming tasks.
Priority queues with bursty arrivals of incoming tasks.
复制标题
传入任务突发到达的优先级队列。
DOI：
10.1103/physreve.79.036106
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Kahng
中科院分区：
文献类型：
--
作者：
N. Masuda;J. Kim;B. Kahng
最近增加的大规模数字记录的可访问性使人们能够监控人类活动，例如单个用户连续两次访问门户网站之间的交互时间分布，一个用户连续发送的两个电子邮件，一个人连续两次从图书馆借阅，等等。有趣的是，这些分布表现出一种普遍的行为，D（tau）近似于tau(-delta)，其中tau是事件间时间，而delta近似于1或32。通过基于优先级的队列中任务的等待时间分布，对通用行为进行了建模；等待时间遵循幂律分布P(w)（tau）近似于tau(-alpha), alpha=1或32，取决于排队动态的细节。在这些模型中，假设单位时间间隔内的传入任务数量遵循泊松型分布。然而，对于电子邮件系统，我们测量的单位时间内发送到邮箱的电子邮件数量遵循幂律分布，一般指数为gamma。对于这种情况，我们解析地得到指数，它不一定是1或32，并且根据伽马取非普遍值。我们发展了生成函数的形式来获得指数，它不同于以往研究中使用的连续时间近似。
Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent out by a user, two consecutive library loans made by a single individual, etc. Interestingly, those distributions exhibit a universal behavior, D(tau) approximately tau(-delta) , where tau is the interevent time, and delta approximately 1 or 32 . The universal behaviors have been modeled via the waiting-time distribution of a task in the queue operating based on priority; the waiting time follows a power-law distribution P(w)(tau) approximately tau(-alpha) with either alpha=1 or 32 depending on the detail of queuing dynamics. In these models, the number of incoming tasks in a unit time interval has been assumed to follow a Poisson-type distribution. For an email system, however, the number of emails delivered to a mail box in a unit time we measured follows a power-law distribution with general exponent gamma . For this case, we obtain analytically the exponent alpha , which is not necessarily 1 or 32 and takes nonuniversal values depending on gamma . We develop the generating function formalism to obtain the exponent alpha , which is distinct from the continuous time approximation used in the previous studies.