Minimizing the Age of Two Heterogeneous Sources With Packet Drops Via Cyclic Schedulers

TL;DR

This paper addresses minimizing weighted AoI for two heterogeneous sources sharing a single channel in the presence of packet drops, focusing on age-agnostic cyclic schedulers. It develops a Markov-chain model to compute the exact mean AoI under a fixed cyclic pattern and derives a near-optimal scheduler by showing the optimal placement is a uniform mix of ${\Theta}$ and ${\Theta+1}$ blocks, parameterized by ${a = u_2/u_1}$. An algorithm (with provable guarantees) constructs the placement and cycle parameters to approach the optimum ${\mathbb{E}[\Delta^w_t]}$, demonstrated to outperform baselines such as P-GAW and Eywa across diverse service times and drop probabilities. The framework provides a practical, analyzable approach to timeliness in remote estimation with unreliable channels, offering insight into cycle design and scheduling under realistic errors.

Abstract

In a communication setting where multiple sources share a single channel to provide status updates to a remote monitor, source transmissions need to be scheduled appropriately to maintain timely communication between each of the sources and the monitor. We consider age-agnostic scheduling policies which are advantageous due to their simplicity of implementation. Further, we focus on a special class of age-agnostic policies, called cyclic schedulers, where each source is scheduled based on a fixed cyclic pattern. We use weighted average age of information (AoI) to quantify the timeliness of communication. We develop a Markov chain formulation to compute the exact mean AoI for the case of two-source cyclic schedulers. Based on the obtained age expression, we develop an algorithm that generates near-optimal cyclic schedulers to minimize the weighted average AoI for two heterogeneous sources, in the presence of channel errors.

Figures (6)

• Figure 1: System model.
• Figure 2: Partial state transition diagram for $u_1>2$.
• Figure 3: AoI graph of the schedule $\{S_1,S_2,S_1,S_2,S_2\}$ showing a realization of the area $A_{1,2}$ when $M = 1$.
• Figure 4: Variation of weighted AoI with packet drop probability and mean of $S_1$ for exponential service times ($s_2=3$, $w_1=0.2$, $w_2= 0.8$, $q=0.9$).
• Figure 5: Variation of weighted AoI with packet drop probability of $S_1$ for deterministic service times ($s_1= s_2 =1$, $w_1=0.5$, $w_2= 0.5$, $q=0.9$).

Theorems & Definitions (2)

• Remark 1
• Remark 2