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

TL;DR

The paper tackles AoI in a GAW-2 status update system with two heterogeneous servers, comparing a work-conserving Zero-Wait policy to a non-work-conserving Freeze/Preempt policy. It combines stochastic hybrid systems to obtain mean AoI under ZW and an absorbing Markov chain framework to derive exact AoI and PAoI distributions under both ZW and the F/P policy, using Erlang-$k$ freezing to approximate deterministic delays. Key contributions include closed-form mean PAoI and AoI for ZW and exact AoI/PAoI distributions for both policies, with numerical validation that preemption improves AoI and that appropriately tuned freezing can further reduce AoI. The results offer practical guidance for dual-path status updates, showing how source-side preemption and controlled freezing can enhance information freshness and yield tractable distributional insights. These insights are valuable for IoT and control applications where timely updates across multiple transmission paths are critical, and they establish a framework for extending to more complex server and arrivalConfigurations.

Abstract

We study age of information (AoI) in a single-source dual-server status update system for the generate at will (GAW) scenario, consisting of an information source, dual servers, and a monitor. For this system, the method of stochastic hybrid systems (SHS) was used to obtain the mean AoI for the work-conserving ZW (zero wait) policy with out-of-order packet discarding at the monitor. In this paper, we propose a non-work-conserving F/P (freeze/preempt) policy for which the sampling and transmission process is frozen for an Erlang distributed amount of time upon each transmission, and out-of-order packets are preempted immediately at the source, rather than being discarded at the monitor upon reception. We use the absorbing Markov chain (AMC) method to obtain the exact distributions of AoI and also the peak AoI (PAoI) processes, for both ZW and F/P policies. Numerical results are presented for the validation of the proposed analytical model and a comparative evaluation of ZW and F/P policies.

Figures (7)

• Figure 1: A status update system with one source, two heterogeneous servers, and a monitor. In ZW, sampling/transmission takes place upon a service completion, whereas it is governed by the freeze policy in F/P.
• Figure 2: Sample path of the AoI process $\Delta(t)$. Only generation and reception instances of successful packets are shown.
• Figure 3: (a) CDF of PAoI, $F_{\Phi}(x)$, (b) CDF of AoI, $F_{\Delta}(x)$, depicted as a function of $x$ for Erlang-$k$ distributed freeze time with $k \in \{ 1,10,50 \}$. (S) and (A) refer to results obtained with simulations and the analytical method, respectively.
• Figure 4: Mean PAoI obtained with F/P policy as a function of $\lambda$ when $\mu_2=0.1$ and (a) $\mu_1=0.1$ (b) $\mu_1=0.5$. The mean PAoI for the ZW policy obtained with \ref{['exp:ZWPAoI']} is also depicted as reference.
• Figure 5: Mean AoI obtained with F/P policy as a function of $\lambda$ when $\mu_2=0.1$ and (a) $\mu_1=0.1$ (b) $\mu_1=0.5$. The mean AoI for the ZW policy obtained with \ref{['exp:ZWAoI']} is also depicted as reference.