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.

翻译：考虑不同服务器的最佳控制问题,以尽量减少信息的平均年龄( AoI) 。 每一个服务器都保留一个单独的队列, 到达系统的每包都随机选择到一个服务器。 假设Poisson到达和指数分布的服务时间, 我们首先得出两个不同服务器的平均 AoI 的确切表达方式。 其次, 要解决最佳平均 AoI, 得出一个近似, 称为大致AoI, 这对多服务器系统也有用 。 我们显示, 对于每个服务器的最理想的大约 AoI, 每个服务器的服务器利用率( 到达率和服务率比率)应该与用单一服务器队列的最佳服务器利用率相同。 对于两个相同的服务器, 显示平均 AoI 大约是单个服务器的平均 AoI 的5/8 倍。 此外, 平均 AoI 显示, 随着系统增加服务器, 显示平均 AoI 会大大降低 。