#### Age of Information in Multiple Sensing

##### Alireza Javani, Marwen Zorgui, Zhiying Wang

Having timely and fresh knowledge about the current state of information sources is critical in a variety of applications. In particular, a status update may arrive at the destination much later than its generation time due to processing and communication delays. The freshness of the status update at the destination is captured by the notion of age of information. In this study, we first analyze a network with a single source, $n$ servers, and the monitor (destination). The servers independently sense the source of information and send the status update to the monitor. We then extend our result to multiple independent sources of information in the presence of $n$ servers. We assume that updates arrive at the servers according to Poisson random processes. Each server sends its update to the monitor through a direct link, which is modeled as a queue. The service time to transmit an update is considered to be an exponential random variable. We examine both homogeneous and heterogeneous service and arrival rates for the single-source case, and only homogeneous arrival and service rates for the multiple sources case. We derive a closed-form expression for the average age of information under a last-come-first-serve (LCFS) queue for a single source and arbitrary $n$ homogeneous servers. For $n=2,3$, we derive the explicit average age of information for arbitrary sources and homogeneous servers, and for a single source and heterogeneous servers. For $n=2$ we find the optimal arrival rates given a fixed sum arrival rate and service rates.

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