1 On the Interplay Between Deadline-Constrained Trafﬁc and the Number of Allowed Retransmissions

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On the Interplay Between Deadline-Constrained

Trafﬁc and the Number of Allowed Retransmissions

in Random Access Networks

Nikolaos Nomikos, Senior Member, IEEE, Themistoklis Charalambous, Senior Member, IEEE,

Yvonne-Anne Pignolet, Nikolaos Pappas, Senior Member, IEEE

Abstract—In this paper, a network comprising wireless devices

equipped with buffers transmitting deadline-constrained data

packets over a slotted-ALOHA random-access channel is studied.

Although communication protocols facilitating retransmissions

increase reliability, packet transmission from the queue experi-

ences delays and thus, packets with time constraints might be

dropped before being successfully transmitted, while at the same

time causing the queue size of the buffer to increase. Towards

understanding the trade-off between reliability and delays that

might lead to packet drops due to the deadline-constrained bursty

trafﬁc with retransmissions, a scenario of a wireless network

utilizing a slotted-ALOHA random-access channel is investigated.

The main focus is to reveal and investigate further the trade-off

between the number of retransmissions and the packet deadline

as a function of the arrival rate. Hence, we are able to determine

numerically the optimal probability of transmissions and number

of retransmissions, given the packet arrival rate and the packet

deadline. The analysis of the system was done by means of

discrete-time Markov chains. Two scenarios are studied: i) the

collision channel model (in which a receiver can decode only

when a single packet is transmitted), and ii) the case for which

receivers have multi-packet reception capabilities. A performance

evaluation for a user with different transmit probability and

number of retransmissions is conducted, demonstrating their

impact on the average drop rate and throughput, while at the

same time showing that there exists a set of values, under which

improved performance can be acquired.

Index Terms—Deadline-constrained trafﬁc, packet deadlines,

queueing, multi-packet reception, discrete-time Markov chains,

delay-sensitive communications, low-latency communications.

I. INTRODUCTION

Future wireless communication networks are envisioned to

play a major role towards enabling autonomous systems in the

context of the Internet of Things (IoT), comprising connected

vehicles, smart devices, or fully automated factories; see,

Preliminary results of this work appeared in [1]. In this paper, we extend

[1] to include the case of multi-packet reception.

N. Nomikos is with the Department of Port Management and Shipping,

National and Kapodistrian University of Athens, 34400 Euboea, Greece (e-

mail: nomikosn@pms.uoa.gr).

T. Charalambous is with the Department of Electrical and Computer

Engineering, School of Engineering, University of Cyprus, Nicosia, Cyprus

(e-mail: charalambous.themistoklis@ucy.ac.cy). He is also with the De-

partment of Electrical Engineering and Automation, School of Electri-

cal Engineering, Aalto University, Espoo, Finland (e-mail: themistok-

lis.charalambous@aalto.ﬁ).

Y.-A. Pignolet is with Dﬁnity Foundation, Zurich, Switzerland (e-mail:

yvonneanne@pignolet.ch).

N. Pappas is with the Department of Computer and Information Science,

Linköping University, Linköping, Sweden (e-mail: nikolaos.pappas@liu.se).

for example, [2]–[5]. The data trafﬁc produced from these

wireless devices, referred to as machine-to-machine (M2M)

communication, will signiﬁcantly differ from the wireless traf-

ﬁc served by currently deployed wireless networks. In greater

detail, wireless devices might transmit packets consisting of

few bytes of information, while being sporadically active.

Moreover, a massive number of devices may demand ubiq-

uitous connectivity, and transmitting packets with extremely

stringent latency and reliability requirements, as it is the case

of mission critical M2M applications, supporting real-time

closed-loop control, one of the essential mechanisms enabling

such emerging applications [6]–[8].

The rapid blooming of applications requiring deadline-

constrained packet transmissions and multimedia broadcasting

over wireless communication networks stimulated research

on deadline-constrained broadcasting, relying on scheduling

[9]–[12] and random access [13]–[17]. The work in [13]

obtained the optimal access probability of secondary nodes in

a cognitive radio network towards maximizing the successful

delivery probability (SDP) under speciﬁc deadline constraints

using simple slotted-ALOHA. The issue of improving the

reliability for the deadline-constrained one-hop broadcasting,

based on the slotted-ALOHA with retransmission was inves-

tigated in [14]. More speciﬁcally, the SDP was derived, as

well as the optimal access probability for SDP maximization.

Regarding retransmissions, their optimal value under speciﬁc

throughput requirements was determined. Queuing analysis of

deadline-constrained broadcasting, but without retransmission

was investigated in [15]. By modeling the system as a discrete-

time Geo/Geo/1 queue with a speciﬁc delivery deadline,

several performance metrics were investigated, including the

loss probability, queue length distribution, mean waiting time,

and SDP. Nevertheless, the analysis of deadline-constrained

broadcasting with retransmissions has not been analyzed yet.

Furthermore, the paper in [16] studied a slotted-ALOHA

network consisting of nodes with energy harvesting capa-

bilities. For this setup, the author proposed an approximate

analytical model for deriving the timely-delivery ratio, since

the interaction of energy and data queues poses signiﬁcant

difﬁculties in obtaining an exact analytical model. Finally,

the author in [17] adopted exploration for multi-channel

ALOHA through preambles before transmitting data packets

in machine-type communication (MTC), showing a maximum

throughput improvement by a factor of 2−e−1≈1.632.

Also, a steady-state analysis with fast retrial was performed,

arXiv:2210.02673v1 [cs.IT] 6 Oct 2022

highlighting that the delay outage probability is signiﬁcantly

reduced for a lightly loaded system.

The ﬁndings of this study can be useful in practical code

domain-based MPR, such as code-division multiple access

(CDMA) and sparse code division multiple access (SCMA)

systems, supporting deadline-constrained applications. At the

same time, this paper can serve as a building block towards

investigating packet scheduling in random access cooperative

networks with deadline constraints. Overall, the contributions

of the paper are as follows.

•First, the successful transmission probability is obtained for

the case where a new packet is generated after the success-

ful transmission of the previous one has been completed

or that packet has been dropped, either due to reaching the

maximum number of allowed retransmissions or expiration.

In this part of the analysis, no data buffering is considered.

•The second part of the analysis investigates stochastic

bursty trafﬁc with buffer-aided devices by means of a

discrete-time Markov chain (DTMC) for single- and multi-

packet reception (MPR). Two cases are distinguished:

(i) ﬁrst, the case where a packet keeps being retransmitted

until expiration or successful transmission. This case

resembles that of [15], however, a different DTMC is

constructed providing directly, the SDP;

(ii) second, the case where the deadline value is larger

than the number of allowed retransmissions. A similar

construction of the DTMC is used and, as a result, the

system performance is analyzed.

•Simulation results are included, validating the theoretical

ﬁndings and demonstrating the effect of different transmit

probabilities and the number of allowed retransmissions

on the drop rate and the average throughput. Finally, the

positive effect of MPR in the network, as expected, is

highlighted.

The remainder of the paper is structured as follows. Sec-

tion II presents the system model adopted in this study and

the necessary preliminaries. Then, Sections III-A and III-B

present the theoretical framework and analysis for the SDP

when a packet is generated after the previous one was either

successfully transmitted or dropped. Furthermore, the impact

of bursty trafﬁc and buffering is also analyzed. In Section IV,

the numerical and simulation results are presented, giving sev-

eral insights about the performance of the considered scenario.

Finally, in Section V we draw conclusions and discuss possible

extensions and future research directions.

II. SYSTEM MODEL AND PRELIMINARIES

In this section, the system model and the necessary pre-

liminaries for the development of our study are presented. For

convenience, Table I includes the notation used throughout the

paper.

A. Network Model

In this work, a network comprising Nnodes, being in

transmission range and sharing the same wireless channel is

considered. While we can consider the case in which each

node iin the network might have its intended destination,

TABLE I

SUMMARY OF NOTATION

Symbol

NNo. of nodes in the network

qTransmission probability

DPacket deadline

nNo. of retransmissions

γSignal-to-Interference-and-Noise Ratio (SINR)

threshold

Ptx Transmit power

Prx Received power

hSmall-scale fading random value (RV)

sReceived power factor

αPath loss exponent

riDistance between node iand the receiver

vRayleigh fading RV parameter

ηNoise power at the receiver

qTransmission probability

pSuccess transmission probability

TSet of transmitting nodes

cNo. of transmitting nodes

λAverage probability of the packet arrival pro-

cess

µSuccess transmission probability of a packet at

the head of the queue

νRatio of qover µ

bNo. of backlogged nodes

pi,c−1

Success transmission probability for node i

when cnodes simultaneously transmit

ps(n, D)

Success transmission probability before packet

expiration or before reaching the allowed no.

of retransmissions

SSuccessful transmission event

XFirst transmission attempt event

UUnsuccessful transmission event

MTransition probability matrix

π(s)

Steady-state of state sbelonging in the set of

states Sfrom which a successful transmission

can take place

π(fD)Steady-state of state fDbelonging in the set of

states FDtransmission is the last

The rest of the states from which the last

unsuccessful transmission of a packet can take

place

in this paper, without loss of generality, we concentrate on

the case where all the nodes transmit towards a common

destination; this also motivates our work on multi-packet

reception. Random access of the wireless medium is assumed

and thus, each node is transmitting with probability qi(for

simplicity of exposition, the same value of qiis assumed

for all nodes, i.e., qi=q∀i). The time is slotted and

each packet transmission requires one slot. Also, instantaneous

and error-free acknowledgements/negative-acknowledgements

(ACK/NACK) are transmitted by the receiver over a separate

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1OntheInterplayBetweenDeadline-ConstrainedTrafcandtheNumberofAllowedRetransmissionsinRandomAccessNetworksNikolaosNomikos,SeniorMember,IEEE,ThemistoklisCharalambous,SeniorMember,IEEE,Yvonne-AnnePignolet,NikolaosPappas,SeniorMember,IEEEAbstractInthispaper,anetworkcomprisingwirelessdevicesequippedwit...

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