I. Introduction
The literature in queuing analysis of communication systems is primarily concerned with either minimizing the delay of the individual data packets or with maximizing the throughput achieved in a flow of information. However, for applications where timeliness is critical (e.g., social networks, remote monitoring, machine-type or tactile communication systems), maximizing the freshness of data from a receiver's perspective is a more relevant goal. Minimizing the age of information (AoI), which has been recently proposed as a measure for the freshness of information [1], [2], captures this goal. The AoI in a communication system is defined as the time average of the status age, i.e., of the staleness of the freshest data (status update) currently available. The status age is usually represented by and expressed as \begin{equation*} \Delta(t)=t-u(t), \tag{1} \end{equation*}