Age of Information in Multi-source Updating Systems Powered by Energy Harvesting

Abstract

This paper considers a multi-source real-time updating system in which an energy harvesting (EH)powered transmitter node has multiple sources generating status updates about several physical processes.The status updates are then sent to a destination node where the freshness of each status update is measured in terms of Age of Information (AoI). The status updates of each source and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. Unlike most of the existing queueing-theoretic analyses of AoI that focus on characterizing its average when the transmitter has a reliable energy source and is hence not powered by EH (referred henceforth as a non-EH transmitter), our analysis is focused on understanding the distributional properties of AoI in multi-source systems through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the average/MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and source-agnostic/sourceaware preemptive in service strategies. The generality of our results is demonstrated by recovering several existing results as special cases.

Scheduling to Minimize Age of Information with Multiple Sources

“…Similar to the single source case, with multiple sources also, primarily the analysis was restricted for fixed scheduling policies such as FCFS, LCFS, FCFS with preemption etc [9], [10]. Analyzing the distributional properties of AoI when the energy used to transmit updates is sourced from renewable sources called energy harvesting has also been considered in [11], and references therein.…”

“…At any time, only one update from any source can be under service. In a major departure from most of the prior work in the continuous-time model [1], [4]- [7], [9]- [11] that found the distribution of AoI for a fixed scheduling policy, our focus in this work is on finding optimal scheduling policies. Moreover, we also consider a general metric compared to prior work, that is a linear combination of the weighted AoI and the total cost of transmission (service), where a constant cost (which may be different for each source) is counted for each partial/complete transmission (service).…”

“…Remark 7: The rationale for choosing p ℓ 's as the solution of ( 11)-( 13) is that in Lemma 2, we show that the expression (11), with some additional constant terms, is an upper bound on the expected weighted sum cost for the proposed policy E[Γ(π sr )]. Thus the proposed policy is choosing p ℓ 's to minimize an upper bound on its weighted sum cost.…”

“…Remark 9: The probability pℓ (10) that source ℓ is chosen to transmit is a function of both the probability p ℓ (11) with which source ℓ marks a generated packet, and the mean packet inter-generation time µ ℓ at source ℓ. Intuitively, this synchronizes SR-PMS and SR-NSS such that mostly when a source ℓ is chosen to transmit, it has a fresh marked packet to transmit (discussed in Section V-A).…”

“…Next, consider the performance of the stationary randomized policy π sr (Algorithm 1) for the same input. Since γ = 0, c = 0 and N = 1, from the convex optimization problem (11), it is immediate that p = 1 (i.e., π sr marks every generated packet). Also, since the transmission time d i = 0 for every packet, the channel is always free, and every marked packet gets immediately transmitted.…”