We consider a status update system consisting of two independent sources and one server in which packets of each source are generated according to the Poisson process and packets are served according to an exponentially distributed service time. We derive the moment generating function (MGF) of the age of information (AoI) for each source in the system by using the stochastic hybrid systems (SHS) under two existing source-aware packet management policies which we term self-preemptive and non-preemptive policies. In the both policies, the system (i.e., the waiting queue and the server) can contain at most two packets, one packet of each source; when the server is busy and a new packet arrives, the possible packet of the same source in the waiting queue is replaced by the fresh packet. The main difference between the policies is that in the self-preemptive policy, the packet under service is replaced upon the arrival of a new packet from the same source, whereas in the non-preemptive policy, this new arriving packet is blocked and cleared. We use the derived MGF to find the first and second moments of the AoI and show the importance of higher moments.

中文翻译：

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具有数据包管理的两源系统中AoI的矩生成功能

我们考虑一种状态更新系统，该系统由两个独立的源和一个服务器组成，其中每个源的数据包都是根据Poisson进程生成的，数据包是按指数分布的服务时间进行服务的。我们通过使用随机混合系统（SHS）在两种现有的源感知包管理策略下推导系统中每个源的信息时代（AoI）的矩生成函数（MGF），我们将其称为抢占式和非抢占式。抢先政策。在这两种策略中，系统（即等待队列和服务器）最多可以包含两个数据包，每个源一个数据包；当服务器繁忙且有新数据包到达时，等待队列中相同源的可能数据包将被新数据包替换。这些策略之间的主要区别在于，在自抢占策略中，正在服务的数据包在来自同一源的新数据包到达时被替换，而在非抢占策略中，此新到达数据包被阻止并清除。我们使用派生的MGF来查找AoI的第一时刻和第二时刻，并显示出更高时刻的重要性。