An optimal control problem with heterogeneous servers to minimize the average age of information (AoI) is considered. Each server maintains a separate queue, and each packet arriving to the system is randomly routed to one of the servers. Assuming Poisson arrivals and exponentially distributed service times, we first derive an exact expression of the average AoI for two heterogeneous servers. Next, to solve for the optimal average AoI, a close approximation is derived, called the approximate AoI, this is shown to be useful for multi-server systems as well. We show that for the optimal approximate AoI, server utilization (ratio of arrival rate and service rate) for each server should be same as the optimal server utilization with a single server queue. For two identical servers, it is shown that the average AoI is approximately 5/8 times the average AoI of a single server. Furthermore, the average AoI is shown to decrease considerably with the addition of more servers to the system.

中文翻译：

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具有异构服务器的排队系统的信息时代

考虑了异构服务器的最佳控制问题，以最小化信息的平均年龄（AoI）。每个服务器维护一个单独的队列，每个到达系统的数据包都会随机路由到其中一个服务器。假设泊松到达和服务时间呈指数分布，我们首先推导出两个异构服务器的平均 AoI 的精确表达式。接下来，为了求解最佳平均 AoI，导出了一个近似值，称为近似 AoI，这也被证明对多服务器系统很有用。我们表明，对于最佳近似 AoI，每个服务器的服务器利用率（到达率和服务率的比率）应该与具有单个服务器队列的最佳服务器利用率相同。对于两台相同的服务器，结果表明，平均 AoI 大约是单个服务器平均 AoI 的 5/8 倍。此外，随着向系统添加更多服务器，平均 AoI 显着降低。