Age of Information in a Single-Source Generate-at-Will Dual-Server Status Update System

We study age of information (AoI) in a single-source dual-server continuous-time status update system for the generate-at-will (GAW) scenario, consisting of an information source, two heterogeneous servers, and a monitor (or destination). The technique of stochastic hybrid systems (SHS) has recently been used to obtain the average (or mean) AoI for a work-conserving (WC) zero wait (ZW) system imposed on the Non-parallel Transmission with Monitor Discarding (NT-MD) policy for which out-of-order packets are discarded upon reception by the monitor, for the case of exponentially distributed service times. In this paper, we exactly obtain the distributions (not only the means) of AoI and peak AoI (PAoI) processes for the NT-MD policy, in a more general setting with continuous phase-type distributed service times, by making use of the absorbing Markov chain (AMC) method, which was specifically developed for exact AoI modeling. Additionally, two Parallel Transmission (PT) policies resulting from either monitor discarding (PT-MD), or Source Preemption (PT-SP), are proposed and studied which allows us to comparatively evaluate these policies as a function of certain parameters of the service times. We also propose a non-work-conserving (NWC) NT policy with Freezing and source preemption, called NTF-SP, for which the transmission process is frozen for a certain amount of time upon each transmission, and we comparatively study NTF-SP against its NT-MD counterpart, for exponentially distributed, and also deterministic service times. Numerical results are presented for the validation of the proposed analytical models, and a comparative evaluation of the four transmission policies in terms of mean AoI.