Cyclic Scheduler Design for Minimizing Age of Information in Massive Scale Networks Susceptible to Packet Errors

TL;DR

The paper tackles scalable design of cyclic schedulers to minimize the weighted AoI in massive multi-source networks with packet errors. It develops two analytical frameworks, MC- and MGF-based, to compute AoI for a fixed cyclic pattern and uses this to build scalable schedulers: NOTS for two sources and SAMS for general $N$, with $O(1)$ runtime once the pattern is fixed. Notably, it provides a theoretical lower bound for $N=2$ and proves near-optimality of NOTS, while delivering a practical, convex-optimization–driven SAMS that scales to thousands of sources and outperforms existing age-agnostic baselines in large-scale simulations. The methods offer a viable path for off-line, low-complexity cyclic scheduling in massive IoT networks, with potential extensions to more complex channel models and dynamic arrivals.

Abstract

In multi-source status update systems, sources need to be scheduled appropriately to maintain timely communication between each of the sources and the monitor. A cyclic schedule is an age-agnostic schedule in which the sources are served according to a fixed finite transmission pattern, which upon completion, repeats itself. Such a scheme has a low $O(1)$ runtime complexity, which is desirable in large networks. This paper's focus is on designing transmission patterns so as to be used in massive scale networking scenarios involving a very large number of sources, e.g., up to thousands of IoT sources, with service time requirements and weights being heterogeneous in nature. The goal is to minimize the weighted sum age of information (AoI), called weighted AoI, when transmitting users' packets over a channel susceptible to heterogeneous packet errors. The main tool we use is a stochastic modeling framework using either Markov chains (MC) or moment generating functions (MGF), by which we obtain the weighted AoI for a given transmission pattern, which is not straightforward in the presence of packet drops. Using this framework, we provide a lower bound on the weighted AoI for the particular case of two sources, and also an algorithm to attain this lower bound. Then, by using the same framework, we design a cyclic scheduler for general number of sources with reasonable complexity using convex optimization and well-established packet spreading algorithms, and comparatively evaluate the proposed algorithm and existing age-agnostic scheduling schemes for general number of sources (resp.~two sources) when the lower bound is not available (resp.~when it is available). We present extensive numerical results to validate the effectiveness of the proposed approach.

Figures (9)

• Figure 1: Pull-based status update system (Scenario A) involving a base station (BS) sending polling messages to $N$ users which in turn transmit their status update packets.
• Figure 2: AoI graph of source-$1$ for the pattern $P=[1,2,1,2,3]$ showing a realization of the area $A_{1,2}$ when $M = 1$.
• Figure 3: Partial state transition diagram for $\alpha_n>2$.
• Figure 4: Weighted AoI of a two source system depicted as a function of (a) packet drop probability, (b) mean service time, of source-$1$, for exponential service times ($s_2=3$, $w_1=0.2$, $w_2= 0.8$, $p_2=0.9$).
• Figure 5: Variation of weighted AoI with the packet drop probability of source-$1$ for a scenario with highly variable service times ($s_1= 25$, $s_2 =24$, $c_1=2$, $c_2=15$, $p_2=0.81$, $w_1=0.04$, $w_2=0.96$).

Theorems & Definitions (2)

• Remark 1
• Lemma 1