Improving LoRa Networks with Distributed Queueing

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Things Journal
IEEE INTERNET OF THINGS JOURNAL, VOL. , NO. 1
Improvement of Multi-Channel LoRa Networks
based on Distributed Joint Queueing
Jun-Hwan Huh, Dion Tanjung, Dong-Hyun Kim, Seunggyu Byeon, and Jong-Deok Kim
Abstract—LoRa has gained popularity in realizing IoT ap-
plications by facilitating long-range communication with low
power consumption. However, LoRa faces scalability issues due
to its unsophisticated random access (RA) protocol, Aloha, which
is vulnerable to collision and not scalable in dense network
scenarios. In contrast, distributed queuing (DQ), a collision-
free contention-based RA protocol, is a promising candidate
for replacing Aloha because of its near-optimal performance
and independence from the traffic load and pattern. However,
DQ is not compatible with LoRa, as it was initially designed
to operate on CableTV that supports the full-duplex (FDX)
bidirectional link. In FDX, the contention feedback overhead
is negligible. Most wireless networks, such as LoRa, support
the half-duplex, for which feedback overhead is considerable.
Furthermore, a reduction in efficiency is aggravated under a
multi-channel environment because of an unbalanced traffic load.
This study proposes a joint distributed queueing protocol to
consider contention for LoRa that minimizes control overhead
and achieves inter-channel load balancing. Our analysis shows
that the proposed protocol reduces the control overhead by up to
70% compared to DQ. The protocol performance demonstrates
near-optimum throughput and access delay, irrespective of the
number of arrivals.
Index Terms—collision tree algorithm, distributed queueing,
LoRa, medium access control
I. INTRODUCTION
Recently, low-power wide-area networks (LPWANs) have
emerged as solutions to specific requirements of Internet of
Things (IoT) applications, which include small data (sev-
eral bytes) transmission, such as for monitoring, telemetry,
and remote control [1]. LPWANs enable energy-constrained
devices to transmit information at a low data rate (few
kilobits per second) across long distances (several kilome-
ters). Commercial LPWANs operate in cellular (NB-IoT, LTE-
M) or unlicensed sub-GHz bands (LoRa, Sigfox). Among
unlicensed-band LPWANs, Long Range (LoRa) has gained
prevalence as the flagship technology [2]. LoRa is a physical
layer standard based on the chirp spread spectrum (CSS) [3];
Manuscript received Mar 26, 2021; revised May 26, 2021; revised Jul 12,
2021; accepted Aug 02, 2021. This research was supported by Basic Science
Research Program through the National Research Foundation of Korea(NRF)
funded by the Ministry of Education (NRF-2020R1I1A306594711). This work
was supported by Institute of Information & communications Technology
Planning & Evaluation(IITP) grant funded by the Korea government(MSIT)
(No. 2020-0-01450, Artificial Intelligence Convergence Research Center [Pu-
san National University]). (Corresponding author: Jong-Deok Kim.)
JH. Huh, D. Tanjung, DH. Kim, and JD. Kim are with the School
of Computer Science and Engineering, Pusan National University, Busan
46241, South Korea (e-mail: ijhhuh10@pusan.ac.kr; tanjung.dn@pusan.ac.kr;
dhkim1106@pusan.ac.kr; kimjd@pusan.ac.kr)
S. Byeon is with the Division of Computer Software Engineering, Silla
University, Busan 46958, South Korea (email: sg0919@silla.ac.kr)
additionally, it supports robust transmission at low data rates
(up to 50 Kbps). LoRaWAN [4], which is the upper layer
standard of LoRa, employs the Aloha random access protocol
for medium access control (MAC). However, Aloha is known
to be highly vulnerable to collisions [5]–[7]. Thus, LoRaWAN
faces scalability issues originating from Aloha [8]–[15].
Devices employing the Aloha protocol attempt to transmit
data, without considering the channel condition, by using a
simple principle: If you have data to send, send the data. This
simple strategy reduces the complexity of network deploy-
ment; however, the packets often collide, and the transmission
is blocked in dense networks. By contrast, distributed queueing
(DQ) [16], a contention-based random access (RA) protocol
that ensures collision-free transmission, is often referred to
as a promising candidate for use in LPWANs [7], [17].
DQ can flexibly cope with unpredictable traffic patterns: it
behaves as an RA-like protocol in a sparse network and as
a scheduling-like protocol when the network becomes dense.
Previous studies demonstrated that DQ shows near-optimal
performance in terms of the throughput and delay, irrespective
of the number of arrivals [16], [18].
However, adapting DQ to LoRaWAN is challenging for two
reasons: the contention overhead and multi-channel access.
First, the contention feedback overhead is high in LoRa
networks. Legacy DQ assumes that the feedback overhead
(downlink) is negligible because the up and downlink are
separated in the target network, Cable TV (CATV). Moreover,
the overhead is comparatively larger due to the small sensor
data in LoRaWAN. Second, an unbalanced inter-channel load
deteriorates DQ performance, as DQ was designed without
considering multi-channel access scenarios. Besides, the Lo-
RaWAN standard adopts random channel selection (RCS) to
access multiple channels. However, RCS leads to the ineffi-
cient use of precious channel resources.
Numerous studies have been conducted to adopt DQ in
wireless networks. Among these, DQ-LoRa [17] and DQ-N
[19] are the latest studies that modified DQ for LoRaWAN.
DQ-LoRa attempts to eliminate empty data slot frames only
if there are no successful collision resolution stations during
the contention phase. DQ-N allows multiple data slot requests
to mitigate unnecessary re-contention. Despite all research
efforts, the contention overhead of DQ is significant in wireless
environments; this issue is serious for LoRa, in which small
sensor data transmission is frequent. Load balancing is also
considered to efficiently utilize multi-channel resources.
To address the issue of scalability in LoRaWAN, in this
paper, we focus on the design and evaluation of distributed
joint queueing (DQ-J). DQ-J is a novel MAC protocol that
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Fig. 1: Example of m-ary contention tree growing process
when the number of arrivals is ten and the number of mini-
slots is three. The numbers in the mini-slots denote the number
of contending stations.
enables robust transmission in large-scale LoRaWAN. In the
existing DQ protocol, overhead is incurred in every transmis-
sion with a fixed number of contention slots. We propose
an enhanced contention resolution scheme that adaptively
controls the number of contention slots based on competition
to reduce overhead. Further, we present a load balancing
method that distributes data traffic into multiple channels
evenly and efficiently. The results demonstrate that the DQ-
J protocol shows a 70% decrease in control overhead and a
23% improvement in throughput compared to the original DQ
when transmitting small data (30 bytes). When the data size
is larger (higher than 40 bytes), DQ-J exhibits near-optimal
(M/D/1 [20]) system performance in a multi-channel LoRa
network, irrespective of the number of arrivals.
Our main contributions are as follows.
• Proposing an enhanced contention resolution scheme that
adaptively controls the number of contention slots based
on the competition situation to achieve low overhead.
• Proposing a load balancing method that evenly distributes
the data traffic into multiple channels.
• Providing numerical and simulation analyses using vari-
ous metrics: contention overhead, throughput, and delay.
In large-scale LoRaWAN, we compare DQ-J with dif-
ferent DQ-based protocols according to the number of
arrivals and size of the payload.
The remainder of the paper is structured as follows. Related
studies are discussed in Section II. Section III introduces
the challenges of employing DQ in a multi-channel LoRa
network. Section IV describes our DQ-J protocol in detail.
The performance analysis of DQ-J is provided in Section V.
Conclusions are drawn in Section VI.
II. RELATED WORKS
A. Distributed Queueing Protocol
The contention tree algorithm (CTA) was first reported
by Capetanakis [21] to improve the random multiple access
protocol. A time-slotted single broadcast channel is shared
by multiple stations (transmitter, terminal, and node) in the
CTA. The m-ary contention tree (nodal degree m) is employed
Fig. 2: Frame structure of DQ.
for collision resolution, and each node of the tree consists of
m consecutive slots, referred to as mini-slots. All contenders
select one of the mini-slots randomly and transmit an ac-
cess request. The coordinator broadcasts the ternary feedback
message by synthesizing the access request from multiple
stations. The ternary feedback includes the states of mini-slots,
i.e., no detection (empty), single station detection (success),
and multiple-station detection (fail). The stations that fail in
contention are reassigned to new descendant nodes, and the
same process is repeated until the collision is resolved. A
simple example of the working of the CTA is shown in Fig.
1.
As an extension of the CTA, Xu and Campbell proposed
DQ, which enables the broadcast channel to be shared by an
infinite number of stations. DQ is widely known to achieve
near-optimal performance (throughput and delay), regardless
of the number of arrivals. In DQ, the collision resolution
and data transmission are managed in parallel by different
distributed queues, namely, the collision resolution queue
(CRQ) and the data transmission queue (DTQ). The frame
structure of DQ is composed of three parts (see Fig. 2): 1) data
slot for collision-free transmission; 2) access request signal
(ARS), consisting of m mini-slots, to join contention; and 3)
feedback packet (FBP) with the feedback contention result of
mini-slots.
The access procedure of DQ is as follows: At first, each
station joins the contention by sending an ARS when there are
data to be transmitted. Consequently, the coordinator broad-
casts FBPs to the contending stations at reserved time slots.
Each FBP contains the ternary states of mini-slots and the
lengths of the CRQ and DTQ. Subsequently, the contending
stations recognize the contention results based on the FBP.
If the contention is successful, the corresponding station will
enter the DTQ and wait for the transmission order. In contrast,
if the contention fails, the station joins the CRQ and waits for
re-contention. An example of the operation of DQ is found in
[7], [16].
The contention resolution interval (CRI) is the primary
metric of DQ. The CRI is defined as the number of time
slots until all initial n collisions are resolved. An early study
[16] assumed that the data slot length is one and the mini-
slot overhead is near zero. This study simplifies the CRI to a
contention resolution round (CRR), and the total number of
CRRs until all stations resolve the collisions is considered. Let
Rn be the expected length of a CRR, then,
Rn =
1 +
Pn−1
k=2
n
k

(m − 1)n−k
Rn(k)
mn−1
1 −
1
mn−1
, (n 2). (1)

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TABLE I
Summary of Existing DQ-based Protocols over Various
Wireless Networks
Protocol Medium
Target
Network
Contention
Overhead
Multi-
Channel
Support
Wired
(full duplex)
Cable TV Negligible No
DQRAP [16]
- -a 1
(base line)
No
DQRAP
/CDMA [22]
CDMA 1 Yes
DQ-N [19] ≤ 1b
DQ-LoRa [17] ≈ 0.9
No
DQ-J
Wireless
(half duplex)
-
-
LPWAN
(LoRa)
≈ 0.25 Yes
a Any available wireless technologies
b Overhead is reduced only during transmission of multiple sets of data
An important result was derived in [16], namely, Rn
= n when m = 3. This means that n collisions can be
resolved in fewer than n rounds if m is larger than three.
Thus, the contention resolution speed is greater than the data
transmission speed. Based on this, the channel throughput of
DQ in the CATV network can be easily obtained. In CATV,
the uplink and downlink are separate, and full-duplex (FDX)
communication is supported, as shown in Fig. 3, such that
stations may obtain immediate feedback from the coordinator.
For n simultaneous arrivals, the channel throughput (ρFD
) of
DQ in the FDX system is as follows.
ρFD
=
α
α + mδ
, (2)
where the lengths of the data slot and mini-slot are α and δ,
respectively.
B. DQ over Wireless Networks
Significant work has been performed on adapting DQ to
various wireless technologies (see Table I): WLAN [23]–[25],
CDMA [22], LTE [7], [26], [27], and LPWAN [17], [19],
[28]. Nevertheless, the contention overhead is a major issue
that remains unaddressed by prior studies; hitherto, contention
overhead mitigation and a multi-channel approach have not
been employed concurrently.
DQ-LoRa [17] was proposed for achieving the scalable
and stable performance of LoRaWAN. The main difference
between DQ and DQ-LoRa is the frame structure. There are
two types of frame sequences: type-I and type-II. Type-I is
the same as the original DQ frame sequence, and type-II is
composed of only ARS and FBP, without a data slot. Type-
II is employed only when there are no resolved collisions.
The authors improved DQ performance by eliminating unused
TABLE II
Evaluation of Rn Value from Numerical Experiments
n
-
Initial Fail Round (Rfail) n/Rn
10 0.5 (5%)
≈ 0.95
100 5 (5.6%)
1000 54 (5.1%)
a Values in parentheses are Rfail/Rn
data slots. A short preamble for ARS, named the random
access preamble (RAP), was likewise considered to reduce
the overhead.
DQ-N [19] was proposed for the crowdsourcing system in
LPWANs. DQ-N allows multiple data slots for stations that
reserve slots through transmission requests (TRs) specially
designed for reserving multiple data slots. Such transmission
mitigates the re-contention overhead if multiple data transmis-
sions are required. However, a TR is significantly longer than
a simple request, as it must include the station id and frame
count of the requesting station, which may result in substantial
control overhead.
DQRAP/CDMA [22] was proposed to efficiently utilize
the logical channels of the code-division multiple access
(CDMA) communication system. The main contribution is a
load-balancing algorithm that effectively distributes the traffic
into a logical channel of the M/M/k system, where k is the
spreading code. The contention load and data load are properly
distributed with the spreading code k based on customized
queueing rules. The research includes a physical receiver
structure proposal, considering the existing CDMA network.
III. CHALLENGES OF DQ IN LPWANS
A. Initial Contention Failure
The typical wireless network is a half-duplex (HDX) sys-
tem, where transmission is possible in only one direction at
a particular time. In HDX systems, such as LoRaWAN, the
throughput of DQ is affected by the FBP overhead (downlink).
Based on (2), the throughput (ρHD
) for a HDX system is
derived as follows, where γ is the length of the FBP slot.
ρHD
=
α
α + mδ + γ
. (3)
During the initial contention phase, DQ contentions succes-
sively fail until the contention tree resolves the first collision.
To observe the impact of initial contention failures, we de-
fined Rn, the total number of rounds until the transmissions
corresponding to all stations are completed. R is calculated as
the sum of n and the number of initially failed rounds (Rfail),
(a) DQ over CATV distribution (FDX) (b) DQ over wireless network (HDX)
Fig. 3: Sequence of DQ access procedure in CATV and wireless network (along with the type of duplex)

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TABLE III
Contention Overhead of DQ in LoRaWAN (with m=3, SF=7)
Payloada
Typeb Data ARS FBP Control Overhead
α mδ γ (mδ + γ) / (α + mδ + γ)
5 30
6 18
45 %
30 70 26 %
100 170 13 %
200 310 8 %
a The payload is given in bytes
b The overhead is calculated as LDAT A, LARS, and LF BP .
such that (Rn n). Table II shows the initial fail count and Rn
for n arrivals under the condition m=3. The result shows that
the number of initially failed rounds accounts for 5% of the
actual competition. In summary, due to the initial contention
failure, the actual throughput (ρHD
· n
Rn
) of DQ is at most 95%
of the expected throughput.
B. Heavy Contention Overhead
The control overhead in DQ is calculated as the sum of the
ARS and FBP slot lengths. Regarding the ARS overhead, DQ-
LoRa [17] employs the random access preamble (RAP), which
requires only two chirp symbols (δ = 2) with no preamble for
a request that can reduce the ARS overhead significantly. The
number of symbols in ARS is calculated as follows.
LARS = mδ = 2m (4)
The FBP must have a 2m bits for ternary feedback and
two bytes for each CRQ and DTQ length [29]. The FBP
is implemented using the implicit header mode in LoRa to
consider overhead [17]. The number of symbols in FBP is
calculated as follows.
LF BP = 18 + 8d
d0.25m + 4e − 5
6
e (5)
The general LoRa packet consists of a preamble and a
payload with the header. The preamble is composed of 12.25
symbols as the default in the LoRa standard. The number of
symbols in the data part is calculated as follows.
LDAT A
= 20.25 + ceil

8PL − 4SF + 28 + 16CRC
4(SF − 2DE)
(CR + 4)

,
(6)
where PL, SF, and CR are the payload size, SF, and coding
rates (1 to 4), respectively. CRC and DE are flags (1: on, 0:
off) of the transmission modes for the cyclic redundancy check
(CRC) and low data optimization.
Table III shows the contention overhead of DQ over Lo-
RaWAN. Each overhead is calculated as described above with
parameters SF = 7, CR = 1 (default for LoRaWAN), and DE=0.
The result indicates that the FBP overhead occupies a large
portion, approximately as much as a 5-byte data slot. The total
control overhead (%) is 45, 26, 13, and 8 when the payloads
(bytes) are 5, 30, 100, and 200, respectively. Consequently,
small data transmission above DQ is very disadvantageous in
LoRaWAN. Moreover, in LoRaWAN, the maximum payload
length is limited by the data rate; the maximum is 59 bytes
(a)
(b)
Fig. 4: Impact of the random channel selection on multi-
channel throughput (ρX̂ and µ); upper/lower bounds represent
the evenly/most-unevenly distributed traffic cases. (a) Impact
of size of payload (K=3) (b) Impact of number of channels
(payload = 30 bytes)
and 250 bytes in the slowest (SF12) and fastest (SF7) modes.
Therefore, small data transmission is mandatory for rapid data
transmission. In summary, the throughput of DQ is limited by
the excessive control overhead, especially FBP, making small
data transmission in LPWAN challenging.
C. Unbalanced Inter-channel Load
In a wireless network, the transmission is performed in
a multi-channel environment. Typically, the MAC protocol
includes a load balancing mechanism that prevents overloading
specific channels and distributes traffic evenly across all chan-
nels, enabling efficient channel resource use. However, DQ
does not have a multi-channel access solution, and LoRaWAN
uses random channel access that is not efficient.
To observe the impact of RCS on multi-channel LoRaWAN,
we set the RCS scenario where N stations randomly select
the number of K channels. The distribution of stations is
defined as X̂ = (x1, x2, · · · , xK) where xK is the number
of stations choosing the Kth channel for communication; the
sum of X̂ equals N. The RCS method results in an unbalanced
inter-channel load that affects the average channel throughput.
Suppose traffic is concentrated in a specific channel, other
channels idle, wasting resources.
In the multi-channel DQ model, the average channel
throughput is determined by the time at which the transfer

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ends in the most crowded channel, which corresponds to
the maximum element of X̂. When X̂ is specified, then the
average channel throughput (ρX̂) can be calculated as follows.
ρX̂ =
N · Frame Time
K · Channel Time
· ρHD
=
N
K · max(X̂)
· ρHD
(7)
To consider overall cases in which channels are selected by
RCS, the probability distribution of X̂ is preceded, which is
expressed as a probability mass function as follows.
P(X̂) =
N
X̂

KN
(8)
Based on Eq. (8), the expected value of ρX̂, µ is given as
µ = E(ρX̂) =
X
X̂
P(X̂) · ρX̂. (9)
The details of the derivation of ρX̂, P(X̂), and µ are
provided in appendix A.
Fig. 4 shows the impact of inter-channel unbalancing on
DQ performance. Observation of the effect of payload size on
the number of fixed channels (K = 3) is shown in Fig. 4 (a).
Each upper bound and lower bound represents the most even,
and most uneven channel distribution cases, respectively, and
the mean value is µ. The result indicates that not only the
deviation of ρX̂ is enormous but also the mean value of (µ) is
approximately 5-10% lower than the upper bound. Fig. 4(b)
represents the impact of K on channel efficiency (µ). The
result reveals that the gap between µ and the upper bound
grows larger when K increases.
IV. DISTRIBUTED JOINT QUEUEING PROTOCOL
A. Multi Parallel Channel Model
In the previous section, we presented several factors that in-
fluence DQ performance degradation. Because the contention
and data frames are paired in the DQ frame, the throughput
is limited by the data length, which is the main factor deter-
mining the control overhead (in Section III-B). Moreover, time
slots for the data may be wasted when the DTQ is empty due to
continuous contention failure (in Section III-A). Furthermore,
numerous channel resources are wasted when channel traffic
is unbalanced (in Section III-C). We propose a multi-parallel
channel model for DQ, namely, the joint channel model, to
address these drawbacks.
This concept involves separating the data slots from the
control slots and managing them in parallel on separate
channels. As shown in Fig. 5, the joint channel model structure
Fig. 5: Structure of joint channel model.
comprises a single joint channel and several data channels. At
the beginning, all contended stations choose the joint channel
for contention. After that, the succeeding stations are evenly
distributed on the data channels. A joint channel may also be
used for data delivery after the contention phase is completed.
For balancing load among the data channels, we propose the
data transmission queueing rules in Section IV-C.
B. Enhanced Contention Resolution Scheme
In the CTA of the original DQ, the three fixed mini-slots
provide a faster collision resolution speed than data trans-
mission. However, in the LoRa link, the excessive contention
overhead poses a challenge in that the sum of ARS and FBP
overhead occupies a large portion of the available data, almost
45%, when transmitting 5 bytes of data. The most fundamental
solution to reduce overhead is to maximize the contention
resolution efficiency (e). The efficiency e can be expressed
as
e =
Number of successful slots
Length of control frame
. (10)
1) Adaptive Contention Mini-slots (ACM): The key to our
approach to adaptively control the mini-slots is to find the
value of m that maximizes e. The problem of optimizing e
has been widely studied in the context of RFID systems for
tag identification. The maximum success probability (36.8%)
was proved in [30], [31] under condition m = n; it is also
well known as the upper-bound performance of the slotted
Aloha protocol. In [31], research was conducted to optimize e
considering additional overhead with a static value. We modify
the equation to consider our target network, LoRaWAN. Eq.
(10) is redefined to consider DQ overhead in LoRaWAN as
e(m) =
S̄
LARS + LF BP
=
n(1 −
1
m
)n−1
1
3
(7m + 61)
, (11)
where S̄ denotes the expected number of success slots. The
detailed derivation of S̄ is provided in Appendix B.
To find the value of m that maximizes e(m), we differentiate
Eq. (11). The detailed optimization process is described in
Appendix C.
Maximize{e(m)} =
de(m)
dm
= 0 (12)
Finally, we obtain mopt that maximizes e from Eq. (12).
mopt(n) =
√
7
√
7n2 + 244n − 244 + 7n
14
(13)
However, in Eq. (13), n is still unknown. Numerous studies
have been conducted to estimate n based on contention results
(S, F, and E) [32], [33]. In [33], the lower bound of n, nLB,
is derived assuming that only two stations collided in failed
slots. nLB can be expressed as follows.
nLB = S + 2F (14)
Similar to the derivation of Eq. (14), in [32], the expected
value of n, n̂, is derived as follows.
n̂ = S + 2.39F (15)

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(a) m-ary tree with ACM (b) joint-tree with ACM
Fig. 6: Simulation result of adaptive CW behavior by contention tree type when n=1000.
The main idea of the ACM is simple; when contention is
intensified (F E = S ≈ 0), m is adjusted to be larger to
resolve contention, and when contention decreases (S F), m
becomes smaller to minimize the control overhead. In ACM,
m is properly adjusted by Eqs. (13) and (15). Accordingly,
the length of each contention frame (ARS, FBP) also changes
and affects the contention overhead. The length of a contention
frame is explained in Section IV-E1, and contention overhead
is evaluated in Section V-A.
We perform a simulation-based analysis to observe ACM
behavior in a massive connection scenario when 1,000 stations
compete to transmit messages. The initial m is set to 10 for
quick contention resolution in the beginning. Fig.6(a) shows
the length of adaptive m (primary y-axis) and the size of con-
tending stations (secondary y-axis) at each contention round
(x-axis). The following steps detail the operation of ACM. In
Round 0 (Tree Level 0), initial contentions are blocked, and
all colliding stations are distributed to a maximum of ten (i.e.,
initial m) leaf nodes. Further, m grows exponentially when
using the ACM algorithm. In Rounds 1–10 (Tree Level 1),
the contention is still intensified, such that m continues to
increase to around 100. During this period, a massive number
of leaf nodes are created due to a large value of m. After
Round 10 (Tree Level 2), m decreases to efficiently resolve
a small number of contending stations distributed over many
leaf nodes.
Summarizing the operation of ACM, the window size is
well-adjusted, reflecting the contention history. However, the
enormous m causes a new overhead and a massive number of
leaf nodes. The number of leaf nodes indicates the contention
round number. We proposed a novel contention tree structure
fit to ACM, namely, a joint contention tree, to fill this gap.
2) Joint Contention Tree Structure: The proposed joint
contention tree structure is designed to enable bulk collision
resolution in line with the ACM algorithm. The main idea is to
suppress the spread of collisions across multiple leaf nodes in
each contention round and then resolve as many collisions as
possible per round. In a joint tree (see Fig. 7), all newly created
leaf nodes are merged in every tree level. Consequently,
all colliding stations participate in every round until they
successfully resolve contention. The number of contenders
decreases by S; therefore, the number of contenders in the next
contention round can be expressed as n = n̂ − S = 2.39F.
Previously, we observed the behavior of ACM in the joint
collision tree using the same simulation-based analysis. As
shown in Fig. 6 (b), there are two significant differences
between the m-ary and joint trees. The first one is the number
of contentions. In the joint tree, the total number of contention
rounds was 16, down 97% from 483 in the m-ary tree. The
other difference is the adaptive control timing and speed. The
ACM algorithm is more smoothly operated in a joint tree; m
exponentially increases in the initial contention phase (before
round 6) and decreases smoothly to approximately mopt (after
round 6). However, the total number of contention rounds is
not equal to the control overhead in the adaptive mini-slots
approach because ARS and FBP overhead is affected by the
size of m. A comparison in terms of the overhead is provided
in the performance evaluation (see Section V).
C. Data Transmission Queueing Rules
In the proposed DQ-J, each station performs contention
resolution and data transmission procedures in parallel. The
rule used for CRQ is unnecessary because every colliding
station will join the contention until the collision is resolved.
Then, each station only maintains multiple DTQs for the multi-
channel transmission. There are three types of queueing rules:
Fig. 7: Structure of joint contention tree

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Fig. 8: Example of DQ-J protocol. The 10 stations transmit over three channels, and the initial m is set to 10.
the data transmission rule (DTR), DTQ selection rule (DSR),
and DTQ reallocation rule (DRR). These rules address the
answers to the following questions: (1) who can transmit and
when, (2) what is the channel to send, and (3) who will
transmit via the joint channel after the contention resolution
period (CRP)?
(a) Data transmission rule (DTR): Essentially, FCFS (first
come, first served) rules are used for DTQs. Each station
that enters the DTQs transmits data sequentially at the
time slots of the data.
(b) DTQ selection rule (DSR): During the contention phase
(F 6= 0), the station that successfully resolves collision
enters the shortest DTQs of data channels. The FBP
contains the contention results and the length of the
DTQ for each channel. Considering that multiple stations
resolve the collision simultaneously, the shortest data
channel’s DTQ is selected and entered in the order of
mini-slots.
(c) DTQ reallocation rule (DRR): After the contention
phase, some of the remaining stations in the DTQs
move to the joint channel’s DTQ. The remaining stations
determine the endpoint of contention by checking when
F = 0 in FBP. After that, the stations re-enter the DTQ
of the joint channel until the overall DTQ lengths are the
same, using the last-in, first-out policy.
D. Multi-Channel Access Procedure
The example shown in Fig. 8 illustrates the operation of
DQ-J with K = 3, N = 10, and initial m = 10. The contention
resolves and data transmission process works parallel in mul-
tiple channels, a single joint channel, and two data channels.
In every round, the next mini-slot size (m) is precalculated
based on FBP. In the CRI, the succeeding station selects multi-
DTQ by DSR, and after all collisions are resolved, the DTQs
are re-allocated by DRR. In the beginning, all stations (n0 to
n9) join the contention by receiving a sync beacon frame. In
round 1, all stations contend: the 2-slot collides and the 3-slot
remains empty. Thus, mopt is calculated as 9 by ACM. In
round 2, only n2, n4, n5, n7, and n8 have contended: the 1-
slot collides while the 5-slot remains in an empty state. Thus,
mopt is decreased to 5. In parallel, pre-succeeding stations n1
and n9 are transmitted in data channels by DTR. In round 3,
only n2 and n5 have contended, and both succeed. No station
can be transmitted due to n1, and n9 still sends data. In the
additional round, the remaining stations waiting in the DTQ
detect the end of CRP and perform DTQ reallocation using
rule #2. The transmission works parallel to the overall channel.
E. Frame Structure over LoRaWAN
In DQ-J, the frame structure is composed of a control and
a data frame. Unlike the original DQ, in DQ-J, the length of
ARS and FBP is adaptively changed in every round by ACM.
FBP includes the length of multiple DTQs to support various
channels, and CRQ information is not included. The duration
of the contention and data frames are calculated by multiplying
the length of a frame with the duration of a single symbol,
tsymbol.
tsymbol =
2SF
BW
(16)
1) Contention Frame: Both ARS and FBP in the contention
frame are affected by the length of the adaptive m. In ARS,
two LoRa can implement each mini-slot. Thus, the ARS
duration (Tmδ) can be represented as
Tmδ = TARS = LARS × tsymbol = 2m × tsymbol, (17)
where tsymbol is a single symbol time in LoRaWAN.
In FBP, each frame must have a 2m bits for ternary feedback
and 2K bytes for multi-DTQ of K channels. The duration of
the FBP slot (Tγ) can be represented as
Tγ = TF BP = LF BP (m, k) × tsymbol
= (18 + 8d
d0.25m + 2Ke − 5
6
e) × tsymbol.
(18)

Things Journal
Finally, the contention frame overhead, TOH
, can be repre-
sented as the sum of the ARS and FBP durations. Then,
TOH
(m, K) = Tmδ + Tγ. (19)
2) Data Frame: Let Tα be the duration of the data slot,
where PL is the size of the payload (bytes). Then,
Tα = TDAT A = LDAT A(PL) × tsymbol. (20)
V. PERFORMANCE EVALUATION
In this section, we evaluate the performance of DQ-J with
the following metrics:
(a) Contention Overhead: The total contention resolution
time and number of rounds until all stations resolve
collisions.
(b) Channel Throughput: The average occupied time of data
slots during the data transmission period (DTP) of all
channels.
(c) Access Delay: The average time it takes for each station
to complete transmission.
In the following section, we compare the simulation results
of the proposed DQ-J, original DQ [16], and DQ-LoRa [17].
A. Contention Overhead
In this section, we evaluate the performance of collision res-
olution to measure the contention overhead in dense network
scenarios. Two metrics are set to measure the contention over-
head: the contention resolution period (CRP) and contention
resolution round (CRR), representing the time occupation of
the contention frame and the number of contention frames,
respectively.
Our collision resolution scheme in DQ-J operates based on
ACM. According to ACM, the mini-slot length is changeable
at every contention round. Therefore, the expected mini-slot
results are calculated before the control overhead calculation.
We derive the expected number of S, F, and E. The details
of the derivation are provided in Appendix B.
We take S̄, F̄, and Ē as the expected values of S, F, and
E. Then,
Ē = m · Pr(Xi = empty) = m(1 −
1
m
)n
,
S̄ = m · Pr(Xi = success) = n(1 −
1
m
)n−1
,
F̄ = m − E − S
= m − m(1 −
1
m
)n
− n(1 −
1
m
)n−1
.
(21)
In DQ-J, the collided stations participate in contention
until the collision is resolved by the joint tree mechanism.
Therefore, the CRP can be expressed by a recursive equation
as follows.
PCR
(n, m)=
(
TOH
(m, K), n = 1
TOH
(m, K)+PCR
(n−S̄, mopt(n̂ − S̄)), n ≥ 2
(22)
TABLE IV
Comparison of Control Overhead of Various DQ Protocols
by Mini-slot and Contention Tree Types
Protocol
-
Mini-slot
Type
Tree
Type
Initial
m
CRR CRP
DQ DQ-LoRa fixed
m-ary
3 906 ≈ 22.1s
DQ-Jam adaptive
10 483 ≈ 13.5s
DQ-Jaj joint 10 16 ≈ 6.8s
(a)
(b)
Fig. 9: (a) Contention resolution ratio by time of various CRAs
when n = 1000. (b) CRP comparison of various CTAs with
number of arrivals, n.
The other metric, CRR, can be easily derived by replacing
the overhead with a counter in (22). Then,
R(n, m) =
(
1, n = 1
1 + R(n − S̄, mopt(n̂ − S̄)), n ≥ 2.
(23)
We measure the contention overhead of various DQ pro-
tocols. Table IV lists the different DQ protocols divided by
the mini-slot type and contention tree types. DQ and DQ-
LoRa operate based on the same CTA from [21], such that
the contention overhead is the same. DQ-Jam and DQ-Jaj both
operate based on adaptive mini-slots, but only DQ-Jaj operates
on the joint contention tree. In the table IV, the CRR and CRP
results are derived by simulation in a dense network scenario

Things Journal
where 1,000 stations attempt transmission simultaneously.
First, to observe the impact of ACM, we compare DQ
and DQ-Jam. The CRR length of DQ-Jam is almost shorter
than 47% of DQ and DQ-LoRa. The CRP is also reduced
by almost 40%. It can be observed from Fig.9 (a) that the
DQ-Jam is resolving contention earlier and faster at the initial
contention period compared to DQ and DQ-LoRa. However,
the contention resolution speed decreases after the elbow point
(EP) due to the large number of leaf nodes created.
Second, to observe the impact of the joint tree, we compare
DQ-Jaj with other protocols. In particular, DQ-Jaj resolved all
contentions in merely 16 rounds. Thus, the CRR of DQ-Jaj
was reduced by more than 97% compared to DQ and DQ-Jam.
The EP does not appear because the joint tree disturbs the tree
growing horizontally. Moreover, the initial contention failure
was lower than those of DQ and DQ-LoRa. However, the CRP
of DQ-Jaj was not reduced as significantly as in CRR because
of the large mini-slot size.
Fig. 9 (b) shows the impact of the number of arrivals
on CRP. The adaptive window algorithm reduces the CRP
by approximately 40% compared with DQ-Jam and DQ. An
additional 30% reduction of CRP is achieved via a joint tree,
compared with DQ-Jaj and DQ-Jam. The analysis shows that
the proposed DQ-J reduces the overhead by 70% compared to
DQ and DQ-LoRa, regardless of the number of arrivals.
B. Channel Throughput
Average system throughput for multiple K channels is
expressed as
ρmulti =
nTα
K · PDT
. (24)
PDT
represents the data transmission period (DTP), the
duration by which every contending station completes the
data transmission. In the joint channel model, all channels
are used only for data transmission after CRP, and we define
this time as the data dedicated transmission period (DDTP),
PDDT
. Therefore, DTP can be expressed as the sum of CRP
and DDTP:
PDT
= PCR
+ PDDT
. (25)
By calculating (25), we have (22) and PDDT
remains. In
the joint channel model, PDDT
can be calculated as
PDDT
=
NDDT
Tα
K
, (26)
where NDDT
is the expected number of transmissions during
PDDT
. We obtain NDDT
from
NDDT
= n − NCR
, (27)
where NCR
is the expected number of transmissions during
PCR
, and it is calculated as
NCR
=





0 , K = 1
(K − 1)PCR
Tα
, K ≥ 2.
(28)
The impact of the payload size and the number of arrivals
on the multi-channel system throughput is shown in Fig. 10.
(a) any n
(b) Payload: 30 bytes
Fig. 10: Throughput comparison between DQ-J and other
protocols according to (a) payload and (b) n. DQ-J operates
in a multi-channel environment with k=3. All other protocols
operate on a single channel and the number of stations is set
to n/k for fair comparison.
The comparison between DQ-J and others with respect to
payload size is shown in Fig. 10 (a). The result shows that
the throughput of DQ and DQ-LoRa dramatically decreases
when the payload is smaller. DQ-LoRa is highly affected by
the payload size, as it is designed by omitting empty data
slots. In DQ-J, throughput is improved by 23% and 18% when
transmitting small data (30 bytes). Further, the throughput is
near 90% when the data size is 40 bytes, and it is nearly
optimal when the data size increases.
Fig. 10 (b) shows the impact of arrival numbers in various
DQ protocols. The payload size is set to small (30 bytes)
to match the conditions of a representative transmission in
LoRaWAN. The results show a flat trend over various DQ-
based protocols with any n. This is a meaningful result
and indicates that DQ is scalable in a large-scale network.
We conclude that the proposed ACM algorithm and joint
contention tree also maintain the advantage of DQ.

Things Journal
C. Access Delay
The total access delay of DQ-J is calculated as the sum of
the departure time of data. In a multi-channel environment, the
type of departure is divided based on the endpoint of the CRP.
The total delay for stations that have completed transmission
before and after the CRP is denoted as dCRI
and dDDT I
,
respectively. The data dedicated transmission interval (DDTI)
represents the time from the end of the CRP to DTP.
The average access delay in DTP, DDT
, is represented as
DDT
=
dCR
+ dDDT I
n
= NDDT
PCR
+
Tα
2

n+
(NCR
)2
K − 1
+
(NDDT
)2
K

,
(29)
where
dCR
= (K − 1)Tα
NCR
K−1
X
N=1
N, (30)
and
dDDT I
= NDDT
PCR
+ KTα
NDDT
K
X
N=1
N. (31)
The impact of the payload size and number of arrivals on
the multi-channel system delay is shown in Fig.11. Here, the
M/D/1 system represents the ideal protocol, and each station
waits in the queue and performs sequential transmission. Fig.
11(a) shows the impact of payload size on average delay. The
results show that the delay of the original DQ increases more
quickly and to a greater extent than that of other protocols
when the payload is increased, while that of DQ-J increases
slowly and is close to that of M/D/1. When the payload
is 30 bytes, the average delay of DQ-J is about 25% and
13% lower than that of DQ and DQ-LoRa, respectively. These
results indicate that DQ-J provides a significant improvement
of performance in terms of delay, even if the payload is small.
Fig. 11(b) compares the access delays of various DQ
protocols according to n. Because the original DQ and DQ-
LoRa theoretically resolve more than one collision per round,
the average access delay has a stable form; it linearly increases
as n increases. The graph of DQ-LoRa moves down the y-
axis more than the original DQ because there is a short
initial contention failure. In contrast, the slope of the DQ-
J graph is gentle and similar to that of M/D/1. This slight
difference is attributed to the amount of time spent on collision
resolution during the CRP and is nearly unaffected by the total
n. Consequently, it is possible to verify that competition and
data transmission were efficiently performed in joint and data
channels.
VI. CONCLUSION
This study presents a DQ-J protocol that improves the
scalability of LoRa communications in multi-channel environ-
ments. DQ-J settles the excessive contention overhead via the
(a) n = 1000
(b) Payload: 30 bytes
Fig. 11: Delay comparison between DQ-J and other protocols
according to (a) payload and (b) n. All other protocols operate
on a single channel and the number of stations is set to n/k
for fair comparison.
collaboration of the adaptive mini-slots algorithm and joint
contention tree structure. Furthermore, DQ-J proposes a load-
balancing mechanism that exploits multi-channel resources to
address the unbalanced channel load on RCS. Our protocol
demonstrates a 70% lower contention overhead than that of
the original DQ. The throughput is observed to be higher than
90% when the data size is sufficiently large, regardless of
arrival numbers. Further, the delay performance is close to that
of M/D/1 (the optimal system). Thus, we verify that DQ-J
allows a massive number of LoRa stations to transmit small
sensor data with near-optimal performance within a dense
network.
Furthermore, we proposed a collision resolution scheme that
collaborates with the ACM algorithm and joint contention tree
to mitigate the control overhead. ACM is a type of optimiza-
tion algorithm that determines the number of contention slots

Things Journal
based on limited feedback information from each slot state.
For advanced approaches, a more accurate and lightweight
method of approximating the number of contenders is needed;
this could reduce the control overhead in the initial contention
phase. We plan to develop PHY layer techniques to detect the
number of stations in contention slots in future works.
APPENDIX A
Derivation of ρ and µ.
The cases concerning the problem “ways for N stations
to randomly select K channels” can be interpreted as the
combinatorial problem of “ways to put N objects into K
bins.” The well-known solution to this problem uses the multi-
nomial theorem. In multinomial expansion, the coefficient of
each term indicates the number of ways in the bin selection
problem.
To aid intuitive understanding, we provide an example with
a simple scenario in which N = 2 and K = 3. The example
expression is (c1 + c2 + cK=3)N=2
, where cK represents the
Kth channel. Each term indicates the number of ways to select
the channel. For example, 2c1
2
c2
0
c0
3 means that the number
of ways for all stations to choose the 1st channel is two.
The following multinomial expansion represents the general
case (regarding N and K).
(c1 +· · ·+cK)
N
=
X
x1+x2+···+xK =N

N
x1, x2,. . ., xK
K
Y
t=0
ct
xt
(A.1)
For simplicity, we set (x1, x2, . . . , xK) as the distribution X̂
which is derived from multinomial theorem where xK is the
number of stations choosing the Kth channel; the sum of X̂
equals N. (A.1) can be written concisely using multi-indices:
(c1 + · · · + cK)
N
=
X
|X̂|=N

N
X̂

cX̂
, (A.2)
where cX̂
= c1
x1
c2
x2
· · · cK
xK
.
In Eq. (A.2), the coefficient of each term represents the
number of cases that X̂ appear. The total number of cases
is easily calculated by using the multinomial theorem as
KN
. Based on this, the probability distribution of X̂ can be
expressed as a probability mass function as follows.
P(X̂) =
N
X̂

KN
(A.3)
For a given X̂, the average channel throughput, ρX̂, is given
as follows.
ρX̂ =
N · Frame Time
K · Channel Time
· ρHD
=
N
K · max(X̂)
· ρHD
(A.4)
Finally, the expected value of ρX̂ is given as follows based
on Eqs. (A.3) and (A.4).
µ = E(ρX̂) =
X
X̂
P(X̂) · ρX̂ (A.5)
APPENDIX B
Derivation of S̄, F̄ and Ē.
The random variable Xi denoting the probability that
k stations select the ith slot is a binomial distribution as
follows. We write Xi ∼ B n, 1
m

where n is the number of
stations and m is the number of mini-slots.
Pr(Xi = k) =

n
k

1
m
k
m − 1
m
n−k
(B.1)
Then, the probability that the ith slot is empty or success
is given as
Pr(Xi = empty) = Pr(Xi = 0) =

m − 1
m
n
(B.2)
and
Pr(Xi =success)=Pr(Xi = 1)=n

1
m

m − 1
m
n−1
.
(B.3)
Finally, the expected values of S, E, and F are respectively
given as
Ē = m · Pr(Xi = empty) = m(1 −
1
m
)n
, (B.4)
S̄ = m · Pr(Xi = success) = n(1 −
1
m
)n−1
, (B.5)
and
F̄ = m − E − S
= m − m(1 −
1
m
)n
− n(1 −
1
m
)n−1
.
(B.6)
APPENDIX C
Proof of Eq. (13).
The optimization method for m with additional overhead
was presented in [31], and we modified it to fit our ACM
algorithm, considering DQ overhead in LoRaWAN. The con-
tention resolution efficiency, e, can be expressed as
e =
The number of success slot
Length of Control Frame
. (C.1)
In Eq (C.1), there are two variables that affect e. First,
the number of successful slots can be substituted by the
expected number of successful slots, S̄, which is pre-calculated
in Appendix B. Second, the length of the control frame is
calculated as the sum of LARS and LF BP , calculated in Eqs.
(4) and (5). For simplicity, we remove the step function in
LF BP by taking the median value of each step. LF BP is
rewritten as
L0
F BP =
1
3
(m + 61). (C.2)

Things Journal
The length of the control frame can be expressed as follows.
LControl = LARS + L0
F BP =
1
3
(7m + 61) (C.3)
Based on Eq. (C.3), e can be rewritten to consider DQ and
LoRaWAN as follows.
e(m) =
S̄
LControl
=
n(1 −
1
m
)n−1
1
3
(7m + 61)
(C.4)
To find m that maximizes e, we differentiate Eq. (C.4).
Maximize{e(m)}=
d(e(m))
dm
=
d
3n
7m + 61
· (1 −
1
m
)n−1
!
dm
=
3n
7m + 61
m − 1
m
!n−2(
− 7
7m + 61
m − 1
m
!
+
n − 1
m2
)
= 0.
(C.5)
To obtain 0 on the right-hand side of Eq. (C.5), we calculate
the following.
(
− 7
7m + 61

m − 1
m

+
n − 1
m2
)
=
− 7m(m − 1) + (n − 1)(7m + 61)
m2(7m + 61)
=
− 7m2
+ 7nm + 61(n − 1)
m2(7m + 61)
= 0.
(C.6)
By using the quadratic formula in (C.6), finally, we can
obtain the optimal mini-slot size, considering DQ overhead in
LoRaWAN, as follows.
mopt =
√
7
√
7n2 + 244n − 244 + 7n
14
. (C.7)
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[32] B. Zhen, M. Kobayashi, and M. Shimizu, “Framed aloha for multiple rfid
objects identification,” IEICE Transactions on Communications, vol. 88,
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[33] H. Vogt, “Efficient object identification with passive rfid tags,” in
International Conference on Pervasive Computing. Springer, 2002,
pp. 98–113.
Jun-Hwan Huh received the B.S. and M.Sc. de-
grees in computer engineering from Pusan National
University, Busan, Korea, in 2015 and 2020, respec-
tively. Currently, He is pursuing the Ph.D. degree
with the School of Computer Science and Engineer-
ing, Pusan National University. His research interests
include low-power wide-area networks, cloud radio
access networks, distributed MIMO, and the Internet
of Things.
Dion Tanjung received the B.S. degree in informat-
ics engineering from Universitas Telkom, Indonesia,
in 2015 and the M.S. degree in computer science
from Pusan National University, Korea, in 2020.
Currently, he is a Ph.D. student at Pusan National
University, Busan, Korea. His current research in-
terest includes LPWAN and IoT.
Dong-Hyun Kim received the B.S. and M.S. de-
grees in information and communication engineering
from DongEui University, Busan, Korea, in 1998 and
2004, respectively, and his Ph.D. in electrical and
computer engineering from Pusan National Univer-
sity, Busan, Korea, in 2013. His current research
interests include RFID/USN, quality of services,
multimedia transmission, and mobility support in
wireless networks.
Seunggyu Byeon received the B.E, the M.E, and the
Ph.D. degrees in computer engineering from Pusan
National University, Busan, Republic of Korea, in
2011, 2015, and 2020, respectively. He has been with
Silla University as an assistant professor in the divi-
sion of computer software engineering, Busan, Re-
public of Korea. His research interests are primarily
related to automatic machine learning and federated
learning for Internet of Things environments.
Jong-Deok Kim received the B.S., the M.S., and the
Ph.D. degrees in computer science and engineering
from Seoul National University, Seoul, Korea, in
1994, 1996, and 2003 respectively. Since 2004, he
has been with Pusan National University as a pro-
fessor in the School of Computer Science and Engi-
neering, Busan, Korea. His current research interests
are primarily related to intelligence networking and
computing technologies for the Internet of Things.

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