1 Minimum Age of Information in Internet of Things with Opportunistic Channel Access

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Minimum Age of Information in Internet of

Things with Opportunistic Channel Access

Lei Wang and Rongfei Fan

Abstract

This paper investigates an Internet of Things (IoT) system in which multiple devices are observing

some object’s physical parameters and then ofﬂoading their observations back to the BS in time with

opportunistic channel access. Speciﬁcally, each device accesses the common channel through contention

with a certain probability ﬁrstly and then the winner evaluates the instant channel condition and decides

to accept the right of channel access or not. We analyze this system through the perspective of Age

of Information (AoI), which describes the freshness of observed information. The target is to minimize

average AoI by optimizing the probability of device participation in contention and the transmission

rate threshold. The problem is hard to solve since the AoI expression in fractional form is complex.

We ﬁrst decompose the original problem into two single-variable optimization sub-problems through

Dinkelbach method and Block Coordinate Descent (BCD) method. And then we transform them to

Monotonic optimization problems by proving the monotonicity of the objective functions, whose global

optimal solution is able to be found through Polyblock algorithm. Numerical results verify the validity

of our proposed method.

Index Terms

Internet of Things, opportunistic channel access, Age of information.

I. INTRODUCTION

In recent years, with the development of the Internet of Things, more and more intelligent

systems, e.g., smart home, connected vehicle, smart industry, etc., have been focused on. In order

L. Wang, is with School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, P. R. China.

(wanglei1995bit@gmail.com)

R. Fan, is with School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing 100081, P. R. China.

(fanrongfei@bit.edu.cn).

arXiv:2210.11119v1 [cs.IT] 20 Oct 2022

to facilitate various intelligent IoT applications, some remote devices are deployed to observe

and monitor the status of environment or equipment, such as temperature, humidity, speed, etc.,

and then upload the information over a wireless network [1].

In many real intelligent systems, such as connected vehicle, smart industry, they are very

sensitive to latency. But some traditional metrics, e.g., delay, throughput, are no longer sufﬁcient

for the time-sensitive characterization of these applications. To capture the information freshness,

a new metric, Age of Information (AoI), has received much attention recently [2]. AoI represents

the elapsed since the generation of an observation which was most recently received by a

destination. Its averaging over time is usually used to analyze and optimize system information

freshness [3].

Early researches of AoI focused more on single device scenarios. However, as IoT ap-

plications become more widespread and networks become more complex, the allocation of

channel resource for a large number of devices deserves to be researched. References [4]–

[8] all investigate multiple access networks with the AoI performance. The work in [4] gives

comparative conclusions on the advantages and disadvantages of TDMA and FDMA respectively

and indicates that multichannel access can provide low average AoI and uniform bounded AoI

simultaneously. The work in [5] investigates the AoI performance in an orthogonal channels

without collisions transmission IoT system with three different scheduling policies, Greedy

policy, Max-Ratio policy, and Lyapunov policy. However, these multiple access protocols cannot

meet the requirements of massive IoT networks due to signaling and control overhead which

increases with network size. Therefore, many researches investigate the AoI performance with

random access. Slotted ALOHA, which is a widely utilized random access protocol because

of its simplicity and low cost in implementation, allow users to share the channel without any

coordination. Speciﬁcally, in slotted ALOHA, sources that wish to send data transmit with a

certain probability in each slot. In [6], the average AoI in the slotted ALOHA protocol is derived,

and it is assumed that once there is only one device transmitting in a time slot, the transmission

must be successful and ﬁnish in one time slot. The research [7] investigate an ALOHA networks

with limited retransmissions. All links experience interference with the same distribution, so the

transmission success probability is constant and the device need to retransmit its updates. More

speciﬁcally, [8] consider that the transmission success probability is depends on the SINR and

a certain threshold, which is changed due to the interference. And all these works make an

assumption that the period of per transmission is constant and not related to the channel state.

Different from these researches, this paper consider a opportunistic channel access, which is

similar to the slotted ALOHA, IoT system, in which channel state is varying with time. Thus, it

need a transmission threshold to determine whether waiting or transmitting in order to limit the

time delay and optimize the AoI. In this framework, what probability that devices will attend

contention with and how to set the transmission rate threshold are of importance for minimization

of the AoI. We present a mathematical framework for analyzing the average AoI in this system

and discuss the impact of the access probability and transmission threshold on the average AoI.

The challenge for the problem is to derive the closed form expression of the average AoI and

give the optimal solution of this complicated formulation, which is overcome through Dinkelbach

method, Block Coordinate Descent (BCD) method, and Monotonic optimization method.

II. SYSTEM MODEL AND PROBLEM FORMULATION

Consider an IoT system with one base station (BS) and NIoT devices, which constitute the set

N,{1,2, ..., N}. These NIoT nodes have the obligation of observing some object’s physical

parameters and then ofﬂoading their observations back to the BS in time. In terms of observation

ofﬂoading, all the NIoT nodes share a common channel with bandwidth B, to access into the

BS.

To be fair with every IoT device and keep observations fresh, the observing and data ofﬂoading

is performed over multiple rounds in the following way, which is also illustrated in Fig. 1. In

each round, there is only one IoT device who can win the right of exclusive use of the common

channel and then perform observation and data ofﬂoading. After ofﬂoading its observation, the

winning IoT device will be inactive in subsequent rounds until all the rest IoT devices have

ofﬂoaded their observations to the BS. Through this operation, in each round there is one IoT

device quits the observation and data ofﬂoading process. We denote there rounds as Round N,

N−1, ..., 1, respectively, and take these Nrounds as one observation cycle. At the end of one

observation cycle, all these NIoT devices are inactive and another observation cycle will be

initialized immediately.

In one of aforementioned round, say Round n, there are nIoT devices having yet to ofﬂoad

their observations to the BS, i.e., nactive IoT devices, three steps of operations can be expected

as follows:

•Step 1: These nIoT devices compete for the right of exclusively accessing the common

channel in an opportunistic way.

•Step 2: The winning IoT device, denoted as n0th IoT device, evaluates the instant channel

condition and then decides to accept the right of channel access or not.

•Step 3: If the n0th IoT device accepts the right of channel access, it will make an instant

observation on the interested object and ofﬂoad it to the BS. If the n0th IoT device does

not accept the channel access right, it will go back to Step 1 and start a new competition

with the rest active IoT devices, which indicates that there may be multiple competitions

of channel accessing right among these nIoT devices in current round.

For the competition in Step 1, divide the time horizon into slots with equal length δ. In every

time slot, these nIoT devices contend for the channel accessing right by broadcasting a pilot

with probability p. Before the emergence of an unique winner, one of the following three possible

cases may happen:

•Case I: There is no IoT device broadcasting a pilot in current time slot, which happens with

probability (1 −p)n. In such a case, these nIoT devices will proceed to contend in next

time slot.

•Case II: There are more than one IoT devices broadcasting a pilot in current time slot. In

such a case, a collision happens and no IoT device wins, these nIoT devices will proceed

to contend in next time slot.

•Case III: There is only one IoT device broadcasting a pilot in current time slot, which

happens with probability pn(p) = np(1 −p)n−1. In such a case, no collision happens and

this unique IoT device wins the competition.

For the channel condition evaluation in Step 2, suppose the channel gain between each IoT

device and the BS experiences independent and identical Rayleigh fading. Moreover, as assumed

in [9], the channel gain over disjoint time slots are also independently and identically distributed.

With these assumptions, denote gn,i as the instant channel gain between the winning IoT device

of ith competition for the right of channel access in Round nand the BS, then the distribution

function of gn,i can be written as f(gn,i) = λe−λgn,i ·1(gn,i ≥0) where 1(·)is the indicator

function. Denote pTas the transmit power of every IoT device and σ2as the power spectrum

density of noise, a transmit rate

Rn,i =Bln 1 + pTgn,i

Bσ2(1)

can be realized between the winning IoT device and the BS. In order to limit time delay of

data ofﬂoading, a threshold of ris imposed on transmit rate, i.e., the winning IoT device will

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1MinimumAgeofInformationinInternetofThingswithOpportunisticChannelAccessLeiWangandRongfeiFanAbstractThispaperinvestigatesanInternetofThings(IoT)systeminwhichmultipledevicesareobservingsomeobject'sphysicalparametersandthenofoadingtheirobservationsbacktotheBSintimewithopportunisticchannelaccess.Speci...

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