We consider a multi-source status update system consisting of multiple independent sources, a single server, and a single sink. Each source generates packets according to a Poisson process, and packets are served according to a general service time distribution. The system has a capacity of one packet, i.e., no waiting buffer, and is modeled as a multi-source M/G/1/1 queueing system. We introduce a probabilistically preemptive packet management policy, under which an existing packet from the same source in the system is replaced by an arriving packet with a fixed probability. We derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI (PAoI) for each source under this policy. Numerical results demonstrate the effectiveness of the proposed packet management policy.

翻译：我们研究一个由多个独立信源、单个服务器和单个接收器组成的多源状态更新系统。每个信源根据泊松过程生成数据包，数据包的服务时间服从一般分布。系统容量为一个数据包，即无等待缓冲区，建模为多源M/G/1/1排队系统。我们提出一种概率抢占式数据包管理策略：当同一信源的新数据包到达时，将以固定概率替换系统中该信源的现有数据包。在此策略下，我们推导了各信源信息年龄（AoI）与峰值信息年龄（PAoI）的矩生成函数（MGF）。数值结果验证了所提数据包管理策略的有效性。