QoS Constrained Semi-Persistent Scheduling of Machine Type Communications in Cellular Networks

Abstract

The dramatic growth of machine-to-machine (M2M) communication in cellular networks brings the challenge of satisfying the Quality of Service (QoS) requirements of a large number of M2M devices with limited radio resources. In this paper, we propose an optimization framework for the semi-persistent scheduling of M2M transmissions based on the exploitation of their periodicity with the goal of reducing the overhead of the signaling required for connection initiation and scheduling. The goal of the optimization problem is to minimize the number of frequency bands used by M2M devices to allow fair resource allocation of newly joining M2M and human-to-human communications. The constraints of the problem are delay and periodicity requirements of M2M devices. We first prove that the optimization problem is NP-hard, then propose a polynomial-time heuristic algorithm employing a fixed priority assignment according to the QoS characteristics of devices. We show that this heuristic algorithm provides an asymptotic approximation ratio of 2.33 to the optimal solution for the case where the delay tolerances of devices are equal to their periods. Through extensive simulations, we demonstrate that the proposed algorithm performs better than the existing algorithms in terms of frequency band usage and schedulability.

Full text

1
QoS Constrained Semi-Persistent Scheduling of
Machine Type Communications in Cellular
Networks
Goksu Karadag, Recep Gul, Yalcin Sadi and Sinem Coleri Ergen
Abstract—The dramatic growth of machine-to-machine
(M2M) communication in cellular networks brings the
challenge of satisfying the Quality of Service (QoS) re-
quirements of a large number of M2M devices with limited
radio resources. In this paper, we propose an optimization
framework for the semi-persistent scheduling of M2M
transmissions based on the exploitation of their periodicity
with the goal of reducing the overhead of the signaling
required for connection initiation and scheduling. The goal
of the optimization problem is to minimize the number
of frequency bands used by M2M devices to allow fair
resource allocation of newly joining M2M and human-to-
human communications. The constraints of the problem
are delay and periodicity requirements of M2M devices.
We first prove that the optimization problem is NP-
hard, then propose a polynomial-time heuristic algorithm
employing a fixed priority assignment according to the
QoS characteristics of devices. We show that this heuristic
algorithm provides an asymptotic approximation ratio of
2.33 to the optimal solution for the case where the delay
tolerances of devices are equal to their periods. Through
extensive simulations, we demonstrate that the proposed
algorithm performs better than the existing algorithms in
terms of frequency band usage and schedulability.
Index Terms—scheduling, machine type communica-
tions, cellular networks, QoS constraints
I. INTRODUCTION
M2M communication is defined as the conveyance of
sensing and actuation data among machines to perform
sensing, processing, decision making and acting on deci-
sions without any human supervision in the communica-
tion cycle. Total automation of devices without including
human effort in mobile communication together with the
advancement in inexpensive sensors and devices have
led to a variety of applications in smart grid, smart
Goksu Karadag and Sinem Coleri Ergen are with the depart-
ment of Electrical and Electronics Engineering, Koc University,
Istanbul, Turkey, e-mail: {gkaradag16,sergen}@ku.edu.tr.
Recep Gul is with the department of Information Technology
and Electrical Engineering, ETH Zurich, Zurich, Switzerland, e-
mail: guelr@nari.ee.ethz.ch. Yalcin Sadi is with the the
department of Electrical and Electronics Engineering, Kadir Has Uni-
versity, Istanbul, Turkey, e-mail: yalcin.sadi@khas.edu.tr.
Sinem Coleri Ergen acknowledges the financial support by the Turkish
Academy of Sciences (TUBA) within the Young Scientist Award
Program (GEBIP) and METU-Prof. Dr. Mustafa Parlar Foundation
Research Encouragement Award.
city, smart home, vehicular telematics, health services
and industrial environment [1], [2]. These applications
mostly require seamless coverage over a large area to
facilitate the communication of M2M devices and M2M
servers in different network domains. Therefore, cellular
network will be widely used in collecting M2M data.
M2M devices are expected to be connected to the cel-
lular network either directly or through M2M gateways
that collect data from M2M devices using short-range
technologies. By 2019, more than 40% of all connected
devices are projected to be M2M devices [3]. Almost
all existing M2M applications are based on GPRS due
to the advantages of low device cost, high geographic
coverage, international interoperability and immediate
business entry [4]. However, the limited capacity of
GPRS cannot support large number of M2M devices
expected to be deployed in the near future. Dedicated
M2M cellular architectures, such as SigFox and LORA
[5], are built to provide high coverage with very low cost
connectivity and long battery lifetime. However, they
can only support very low throughput, on the order of
a few bytes per minute. Thus, exploiting existing LTE
infrastructure and providing a native support in 5G for
fast growing M2M services is of paramount importance.
The conventional connection-oriented data communi-
cation in LTE requires a user equipment (UE) in idle
mode to make a connection before sending data to
the base station (BS). The UE first initiates random
access procedure by transmitting a randomly selected
preamble, out of all preambles with equal probability, to
the BS. The BS responds with a random access response,
including the identity of the detected preamble and an
initial uplink resource grant for the transmission of a
connection setup request message. Upon reception of
random access response, the UE sends connection setup
request message by using the initial uplink resource
grant. The BS then responds with the connection setup
response message to the UE. If UE succeeds in the
random access procedure, it switches to the connected
mode, sends a scheduling request and buffer status report
to the BS and receives an uplink grant from the BS
for sending the data at the higher layers. Following the

2
transmission of the data, the UE is disconnected from
the BS.
The usage of M2M communications in LTE networks
optimized for human-to-human (H2H) communications
results in efficiency and congestion problems [6]. First,
M2M devices generate small amount of data, in contrast
to H2H communication with high data rates. The size
of the signaling packets used in the random access
procedure and at higher layers is much larger than that
of the payload to be sent by M2M devices, resulting
in low efficiency. Second, the number of M2M devices
within a cell can be significantly large and high number
of M2M devices may be activated simultaneously by an
external event. The large number of M2M devices trying
to access eNodeB within a short period of time results
in severe congestion. Third, the uplink-to-downlink ratio
for M2M devices is much larger than that of H2H com-
munications. The large size of signaling packets required
to request the transmission of small size data packets
again decreases the efficiency of the network. Fourth,
M2M devices usually require high energy efficiency due
to battery dependent operation and wide range of quality-
of-service (QoS) performance in terms of delay and
reliability. The lack of consideration of these constraints
in LTE results in suboptimal performance. Finally, M2M
devices generate data at mostly predetermined times, in
mostly periodic manner, at predetermined locations with
low or no mobility as opposed to highly mobile and
unpredictable H2H devices, such as smart phones. These
features have been exploited only in a limited manner in
the literature.
Up to now, several M2M communication studies have
focused on increasing the success rate and decreasing
the delay of M2M devices due to the high number
of accessing devices. These works mostly analyze and
optimize the candidate 3GPP solutions for controlling
RAN overload [7], including access class barring (ACB),
random access resource separation, M2M specific back-
off, slotted access methods. ACB methods aim to min-
imize the congestion for the higher priority devices by
the optimization and transmission of the ACB related
parameters, including a probability factor and barring
timer for different classes, by eNodeB in case of network
load [7], [8], [9], [10]. Devices start random access
procedure with a probability factor corresponding to their
classes, and perform random backoff, while consider-
ing the barring timer value, otherwise. Random access
resource separation methods either split the available
preambles or allocate different random access slots to
M2M and H2H devices, mostly to minimize the effect
of high number of M2M devices on H2H devices [7],
[8]. M2M specific backoff schemes reduce the overload
by assigning different backoff timers to M2M and H2H
devices, with the goal of spreading access attempts of
devices in time in order to reduce congestion [8], [11].
Slotted access method is based on the assignment of
dedicated random access slots to M2M devices based
on their identity and RA cycle parameter broadcast by
eNodeB [7]. However, the usage of large RA cycles in
the case of overload may lead to large delays. Apart
from 3GPP solutions, novel mechanisms have also been
proposed to solve overload control problem introduced
by massive M2M accesses, e.g. [12], [13], [14], [15].
[12] proposes novel preamble collision resolution rather
than collision avoidance for massive number of M2M
devices. If the preamble of an M2M device has collided,
the collision resolution ensures the random access reat-
tempts from a reserved set of preambles. The rate of
collision is used in the optimization of the number of
preambles in each reserved set. [13], [14] embed the
transmission of the small M2M data into the random
access process by attaching data to connection setup
request message in the third stage to minimize delay.
[15] proposes a self-optimization framework to achieve
maximum M2M throughput based on the adaptation
of the resource block composition and access barring
parameter according to the amount of available resource
blocks and M2M traffic load. All of these methods aim
to improve the delay, throughput and success rate of
M2M transmissions, however fail to provide any QoS
guarantees as they employ a random access procedure.
Moreover, none of these schemes exploit the periodicity
of M2M communications to reduce the random access
overhead.
Another set of prior studies focus on the dynamic
scheduling of M2M communications at each Trans-
mission Time Interval (TTI) based on the assumption
that BS knows their channel conditions, data backlog
states and delay tolerance. [16], [15], [17], [18], [19]
propose an uplink scheduling algorithm, considering
both channel condition and maximum delay tolerance.
[20] proposes a delay dependent scheduling based on
giving higher priority to the M2M devices exceeding
their delay threshold until they are served. None of these
works, however, consider the delay and signaling over-
head of random access and periodic update of channel
conditions and UE buffer status over some dedicated
control channel in the evaluation of the performance of
these scheduling algorithms [21]. Dynamic scheduling of
small packets are expected to cause substantial control
signaling overhead. Furthermore, these studies do not
exploit periodicity of MTC devices.
Semi-persistent scheduling has been proposed for
Voice over Internet Protocol (VoIP) in the past [22], [23],
[24], [25], recently being extended for M2M commu-
nications [26], [27] exploiting the predetermined peri-
odic nature of M2M communications. Semi-persistent
scheduling is based on the allocation of a sequence

3
of TTI-resource unit chunks and fixed modulation to
a UE for a certain amount of time. Unlike persistent
scheduling that also preallocates resources for retrans-
missions, which may cause mismatch between allocated
and actually needed resources, semi-persistent schedul-
ing adopts dynamic scheduling for retransmissions on
unused resource units. This fixed allocation both guar-
antees meeting QoS requirements and decreases control
signaling overhead in downlink control channel and
uplink random access. [23], [25] demonstrates the higher
performance of semi-persistent scheduling of VoIP com-
pared to dynamic scheduling. [22] examines the feasi-
bility of semi-persistent scheduling with initial random
access to determine the VoIP capacity as a function of
the maximum number of VoIP terminals that can be
allowed provided that their random access delay does
not exceed a predefined delay constraint. The extension
of semi-persistent scheduling for M2M communications
requires considering their differentiating features from
VoIP, including less dynamic nature and wider range of
QoS requirements. M2M devices generate traffic mostly
with the same period over a longer duration at a fixed
location, in contrast to VoIP calls arriving randomly with
short durations. Besides, the packet generation periods
varies in the range between 1ms and several minutes
for M2M communications compared to 10 −40 ms
for multimedia applications, requiring novel scheduling
algorithms.
Semi-persistent scheduling algorithms developed for
M2M communications aim to meet the QoS constraints
of M2M devices over a wide range [26], [27], [28]. The
basic idea is to group M2M devices based on their QoS
characteristics, including packet arrival rate, maximum
tolerable jitter and acceptable probability of jitter vio-
lation. The scheduling algorithm in [27] considers the
case with zero acceptable jitter violation probability. The
algorithm assigns an allocated access grant time interval
(AGTI) to the clusters according to their priority, at the
beginning of their packet generation period. Each AGTI
comprises L allocation units. Each M2M device in each
cluster is assigned one allocation unit to transmit at most
one packet in the corresponding AGTI. If AGTIs for
different clusters overlap, the AGTI of the cluster with
lower priority is delayed. This scheduling is extended
with the additional opportunistic scheduling of the clus-
ters with nonzero acceptable jitter violation probability
in [26] and scheduling of Poisson modeled event-driven
traffic in [28]. Since these studies allocate the entire
AGTI to a cluster, the M2M devices in the lower priority
clusters may suffer from high delay and may not even
meet their jitter constraints in the presence of massive
M2M deployment. Moreover, these algorithms do not
consider the adverse effect of AGTI based scheduling
on H2H communications.
Radio resource allocation schemes should address the
effective partition of resources between M2M and H2H
communications so that QoS requirements of both can
be satisfied. Such co-existence has only been considered
for dynamic scheduling algorithms in a limited context.
Most scheduling algorithms give strict priority to H2H
over M2M without providing any QoS guarantee for
M2M devices [18], [29]. A solution for this problem
is to give high priority to voice, video, M2M services
of real-time communication over normal priority traffic
such as buffered video, data services and M2M non-real
time data services [30], [31], or allocate both H2H and
M2M using utility based scheduling [32]. All of these
works adopt dynamic scheduling without considering the
associated signaling overhead. The extension to semi-
persistent scheduling is an open problem. Moreover,
these studies do not provide any QoS guarantees exploit-
ing the periodic nature of M2M transmissions.
In this paper, we propose a novel semi-persistent
scheduling algorithm to guarantee satisfying the delay
requirements of periodic real-time M2M communication
with minimum usage of the frequency spectrum. The
proposed framework aims to achieve fair allocation of
radio resources between M2M and H2H communication
by making efficient use of the scarce spectrum and
exploiting the unique characteristics of M2M commu-
nication while satisfying their QoS requirements. Fre-
quency spectrum minimization is introduced for the first
time in the literature with the goal of minimizing the
effect of real-time M2M devices on newly arriving or
non-real time M2M and H2H applications. The original
contributions of the paper are as follows:
•We provide a semi-persistent scheduling framework
based on the persistent scheduling of the periodic
M2M communication to meet their maximum tol-
erable jitter constraints, inclusion of newly arriving
periodic real-time M2M communication via a call
admission control algorithm and dynamic schedul-
ing of event-triggered M2M and H2H considering
the priorities among them.
•We formulate the radio resource allocation with the
objective of minimizing the number of frequency
bands used by the real-time periodic M2M devices
while meeting their stringent timing requirements as
a binary integer programming problem. We prove
that the optimization problem is NP-hard. Fre-
quency band minimization problem is introduced
for the first time in the literature.
•We propose an efficient fathoming based smart enu-
meration search algorithm, called Efficient Depth-
First Search Algorithm (EDFS), to obtain the opti-
mal solution. The algorithm is based on the depth-
first search method for branch and bound technique.
Although this decreases the runtime compared to

4
binary integer programming formulation, it still
requires an exponential runtime in the number of
M2M devices.
•We propose a polynomial time heuristic algorithm,
called Minimum Frequency First-Fit Allocation
(MFFFA) Algorithm, for the radio resource allo-
cation problem of M2M devices. The main feature
of the proposed algorithm is to employ a priority
assignment based on the transmission period of
devices and allocate as many devices as possible to
a frequency band as long as the delay requirement
of each device is satisfied. We provide the worst
case performance of the proposed algorithm with
respect to optimal solution under certain conditions.
•We propose a call admission mechanism to ef-
fectively manage the admission of new devices.
We formulate an optimization problem with the
goal of serving maximum number of devices while
satisfying the QoS requirements of both existing
and newly arriving devices. We prove that the re-
sulting problem is again NP-hard. We then propose
a polynomial time heuristic algorithm, called First
Fit Occupied Bands (FFOB) Algorithm, based on
the principle that the frequency band should be used
efficiently to serve as many devices as possible.
•The superior performance of the proposed algo-
rithms compared to previously proposed efficient
random access methods and persistent schedul-
ing algorithms has been demonstrated for different
number of devices and varying delay requirement
values via extensive simulations.
The rest of the paper is organized as follows. Section
II describes the system model and assumptions. Section
III describes the semi-persistent scheduling framework.
Section IV provides the formulation of the optimization
problem and the proof of its NP-hardness. Section V
describes the proposed efficient smart enumeration based
exponential time search algorithm. Section VI presents
the proposed polynomial time heuristic radio resource
allocation algorithm and the analysis of its worst case
performance under certain conditions. Section VII gives
the call admission control scheme. Section VIII provides
the performance evaluation of the proposed resource
allocation algorithm. Finally, Section IX concludes the
paper.
II. SYSTEM MODEL AND ASSUMPTIONS
The system model and assumptions are detailed as
follows.
1) We consider a cellular network with a base station
serving a large number of M2M devices with
diverse traffic characteristics and H2H devices, as
shown in Fig. 1-a. Most M2M devices are time-
triggered, generating data periodically, with period
Fig. 1: a) System architecture, b) Time-frequency re-
source allocation
pifor node i[33]. Example applications include
smart grid, e-health [34], intelligent transportation
[35], [36] and industrial supply systems [33].
There may be further event-triggered M2M devices
and H2H devices generating data at random times.
2) Each device is allocated time-frequency resource
elements called Resource Blocks (RBs), as shown
in Fig. 1-b. In LTE, a resource block is a time-
frequency unit with 0.5 ms time duration and 180
kHz bandwidth. The length of minimum schedul-
ing unit [37] is an integer multiple of resource
block length, thus providing a time granularity for
scheduling. RB-based granularity is expected to be
preserved in 5G cellular networks, even though
the size of an RB may change [38]. For periodic
data generating devices, multiple RBs may be
allocated in a period but these RBs do not have
to be allocated consecutively.
3) We define Unit Frequency Band (UFB) as the
frequency band of 1 RB width, as shown in Fig.
1-b. Each device is assigned to one UFB; i.e. once
a device is allocated to a UFB, all packets of that
device will be transmitted on that particular UFB.
This partitioned scheduling is preferred as it pro-
vides lower scheduling overhead without allowing
the packets of the same device to migrate to the
different bands [39].
4) The QoS (Quality of Service) requirement of M2M
devices is represented by maximum allowable de-
lay that we call delay tolerance, denoted by difor
node i. Satisfying delay requirements is critical
especially in safety critical operations such as
navigational data communications [40], health care
applications [41], and real-time control systems
[42].
5) Time-triggered M2M devices are assigned pri-
orities in the decreasing order of their periods,
denoted by pifor node i; i.e. a lower period implies
a higher priority. Devices with lower periods have
lower delay tolerances (since a packet must be

5
Fig. 2: Scheduling Framework
transmitted before the next packet is generated),
thus giving priority to low period devices ensures
that their strict delay requirements are satisfied.
In the case of equality of periods, devices with
lower delay tolerances are prioritized. If delay
tolerances are also equal, then devices with higher
transmission times are prioritized. If transmission
times are also equal, they are randomly assigned
priorities.
6) Time-triggered M2M devices are given priority
within a certain number of UFBs, denoted by
kmax.kmax may be determined according to traffic
density, number of devices or channel condition.
Once time-triggered M2M devices are allocated
within kmax bands, event-triggered M2M and H2H
devices can be scheduled if resources are available.
The scheduling outside these kmax bands where
time-triggered M2M devices are not allocated is
out of scope of this paper.
III. SCHEDULING FRAMEWORK
The base station uses semi-persistent scheduling to
allocate resources to time-triggered M2M devices, and
dynamic scheduling to include event-triggered M2M and
H2H devices in the schedule. Semi-persistent schedule is
regenerated with period P, much larger than the update
period of dynamic scheduling, denoted by transmission
time interval (TTI). Semi-persistent scheduling is en-
abled by the fact that the data generation times of time-
triggered M2M devices are pre-known given their data
generation period. Since the signaling required to initiate
connection and request resources for the transmission
of data is eliminated, both signalling and scheduling
overhead is reduced. There may still be time-triggered
M2M devices joining and leaving the network between
the regeneration times of the semi-persistent schedule.
For those arriving the network, call admission algorithm
is executed, considering both existing and newly arriving
devices. The time-triggered M2M devices leaving the
network are excluded from the schedule.
The proposed scheduling framework is shown in Fig.
2. Semi-persistent schedule is updated regularly with
period Pwhile allowing the inclusion of newly arriving
and exclusion of leaving time-triggered M2M devices
in the semi-persistent schedule and scheduling of event-
triggered M2M and H2H every TTI. The period P
may be determined according to the traffic density of
time-triggered M2M devices and kmax. With low traffic
density and low bandwidth usage, the schedule can
be updated over longer intervals; i.e. Pcan be larger,
since the resources are not so scarce, hence, do not
require frequent optimization. On the other hand, if
traffic density for time-triggered M2M devices is high
and a large number of UFBs are allowed to be used,
then the schedule can be updated over shorter intervals.
In the construction of the semi-persistent schedule, the
goal is to use minimum number of UFBs for the alloca-
tion while satisfying the period and delay requirements
of the time-triggered M2M devices. If the regenerated
schedule cannot allocate these devices within maximum
number of available bands kmax, then the lowest priority
devices are dropped such that the remaining devices
can be allocated within kmax bands. In between the
regeneration times of the semi-persistent schedule, the
newly arriving time-triggered M2M devices are allocated
using call admission control algorithm. Call admission
control algorithm assumes the pre-allocation of previ-
ously assigned devices and aims to minimize the total
number of UFBs used following the allocation of new
devices. Call admission control algorithm guarantees the
usage of at most kmax UFBs by not admitting the lowest
priority devices if needed. Following the allocation of
all time-triggered M2M devices, at any TTI, if there
are still idle bands within kmax, then event-triggered
M2M and H2H devices can be scheduled. In order to
schedule these devices, the base station may use any
previously proposed dynamic scheduling algorithm for
cellular networks such as [43].
IV. DESCRIPTION OF THE OPTIMIZATION
PROBLEM
In this section, we first provide the motivation for the
objective of the minimization of the number of UFBs
occupied by time-triggered M2M devices, then formulate

6
the QoS constraints of periodic M2M devices, give the
formulation of the resulting optimization problem, and
finally prove its NP-hardness.
A. Objective Function
The objective function of the minimization of the
number of UFBs is motivated by the spectrum scarcity,
separation of resources allocated to machines and hu-
mans, and presence of newly joining time-triggered ma-
chines, event-driven devices and human-to-human com-
munication with various QoS requirements as follows:
•Massive number of M2M devices consume scarce
radio resources that are already strained by H2H
communications [44]. Sustaining acceptable QoS
with these scarce resources requires efficient utiliza-
tion of the available spectrum resources [45]. This
can be achieved by minimizing number of UFBs
allocated to M2M devices.
•Frequency bands reserved for M2M and H2H de-
vices need to be separated for fair allocation of
resources and exploitation of pre-determined traffic
generation characteristics of time-triggered M2M
devices. Many M2M applications have strict timing
requirements; such as medical applications, assisted
living, industrial control and navigational data com-
munications [46], [47], [40]. If H2H and M2M
bands are not separated and H2H communications
are given priority, then these delay sensitive M2M
applications suffer excessive delays and resource
starvation due to H2H devices. Similarly, many
H2H applications such as online gaming, internet
browsing, video streaming, and VoIP have strict
latency requirements [48], [23]. If M2M communi-
cations are given priority, these delay-sensitive H2H
applications may experience performance degrada-
tion due to massive number of M2M devices allo-
cated to the same bands. Moreover, the exploitation
of the packet generation characteristics of time-
triggered devices through semi-persistent schedul-
ing requires a separation from the devices with
random packet generation characteristics. The num-
ber of frequency bands allocated to time-triggered
M2M devices must be minimized in order to serve
more M2M devices and provide more resources for
H2H communications.
•The generated semi-persistent schedule should al-
low the scheduling of new devices generating pack-
ets at random times within their strict delay con-
straints. Due to strict delay requirements, there must
be sufficient radio resources immediately available
for such devices. This requires an efficient usage
of radio resources by time-triggered M2M devices
so that some idle resources are available for such
delay sensitive devices.
Previous semi-persistent scheduling algorithms devel-
oped for M2M communications fail to provide any such
objective function, allocating the entire AGTI to a clus-
ter, resulting in adverse effect on the delay performance
of lower priority clusters of M2M devices and H2H
communications [26], [27], [28]. On the other hand, the
objective function of previous random access or dynamic
scheduling based M2M communication studies include
maximization of success rate [7], [8], [9], [10], [11],
[12], minimization of delay [7], [8], [16], [15], [17], [18],
[19], [30], [31], [32] and maximization of throughput
[15]. These studies, however, fail to combine these
objectives with QoS constraints due to random access
procedure, or do not consider the delay and signaling
overhead of the associated random access and periodic
update of channel conditions in dynamic scheduling.
B. QoS Constraints
The QoS constraints of time-triggered M2M devices
must ensure that delay tolerances are never violated, i.e.
worst case delay is less than the corresponding delay
tolerance. For any device, the worst case delay occurs
when the device wants to transmit a packet at the same
time with all higher priority devices. In that case, the
device has to wait for all higher priority devices to
transmit their data. The mathematical expression for the
worst case delay serves as a computationally simple
sufficient condition for satisfying delay tolerances.
Let N,δ∗
iand τibe the number of time-triggered
devices on the same band, delay bound and transmission
time of device i, respectively. Assume that devices are
ordered according to their priorities; i.e. if device iis
prior to device l, then i<l. The QoS constraint is
formulated based on the extension of the delay bound
formulation in [26] for variable transmission times as
follows:
δ∗
i=τi+
i−1
X
l=1
dpi
pl
eτl≤di,(1)
for i∈[1, N ].
C. Formulation of Optimization Problem
The optimization problem for minimizing the number
of UFBs used by the time-triggered M2M devices while
satisfying their period and delay tolerance constraints is
formulated as follows:
minimize kmax
X
k=1
yk(2a)
subject to
kmax
X
k=1
xik = 1, i ∈[1, N ](2b)

7
N
X
i=1
xik ≤Nyk, k ∈[1, kmax](2c)
τi+
i−1
X
l=1
dpi
pl
eτlxlk ≤di+(1−xik)Ti, i ∈[1, N ], k ∈[1, kmax]
(2d)
variables
yk∈ {0,1}, xik ∈ {0,1}, i ∈[1, N], k ∈[1, kmax ](2e)
where Ti=τi+PN
l=1dpi
pleτl−diensuring that the
inequality in Eqn. (2d) is always satisfied when xik = 0.
The variables of the problem are yk, k ∈[1, kmax ],
binary variable taking value 1if there exists a device
allocated to UFB k, and 0otherwise; xik, i ∈[1, N ], k ∈
[1, kmax], binary variable taking value 1if device iis
allocated to UFB k, and 0 otherwise. The objective is
to minimize the number of UFBs used. Eqn. (2b) states
that each device is scheduled to one UFB. Equation (2c)
represents that a UFB is used if there exists at least
one device allocated to that band. Eqn. (2d) provides
delay bound constraint. This optimization problem is an
Integer Programming problem.
D. NP-Hardness of Optimization Problem
Theorem 1: The optimization problem (2) is NP-Hard.
Proof: We reduce the NP-hard 3-partition problem to
our scheduling problem. Consider a set of 3Apositive
integers, S={a1, a2, .., a3A}, where B
4< ai<B
2and
B∈Z+for all i∈[1,3A]and P3A
i=1 ai=AB. The
3-partition problem aims at answering the question of
whether the set Scan be divided into Adisjoint sets
S1, .., SAsuch that for each m∈[1, A],Pai∈Smai=
Bis satisfied. Note that each disjoint set has exactly
3 elements since otherwise, B
4< ai<B
2, i ∈[1,3A]
and Pai∈Smai=B,m∈[1, A]constraints yield a
contradiction.
Let us define a problem instance where the delay
tolerance and the period are equal to B, i.e. di=pi=B,
and transmission time τi=ai, where B
4< ai<B
2
and B∈Z+for all i∈[1,3A],P3A
i=1 ai=AB,
kmax =A. The necessary and sufficient condition for
the schedulability of these devices is that the node set
is divided into Adisjoint sets S1, .., SAsuch that the
sum of their transmission times is not larger than the
period; i.e. Pai∈Smai≤Bfor m∈[1, A]. Using
the contradiction argument of the 3-partition problem,
exactly 3 devices need to be scheduled at each band.
Since the sum of all transmission times is satisfied with
equality, i.e. P3A
i=1 ai=AB, the sum of the transmission
times of the devices assigned to a specific band should
also be equal to B, i.e. Pai∈Smai=B. Then, this
problem has a solution if and only if given instance of 3-
Partition Problem has a solution. Since this construction
is carried out in polynomial time, the problem of whether
a set of devices Swith integer transmission times is
schedulable on kmax bands is NP-hard. Obviously, if
the problem of finding minimum number of bands that
can schedule the set Scan be solved in polynomial time,
then the problem whether the set Scan be scheduled on
kbands can be solved in polynomial time as well, for
any k∈Z+. Thus, the problem of finding minimum
number of bands to schedule set Sis also NP-hard. 
V. EFFICIENT DEPTH -F IR ST SEARCH ALGORITHM
A straightforward search algorithm is based on the
enumeration of all possible assignments of the M2M
devices to the frequency bands such that each device is
allocated to only one frequency band and the devices
are allocated to RBs in the order of their priorities,
and checking whether delay tolerances of the devices
are satisfied. The optimal solution is then the minimum
of the number of the frequency bands used by the
feasible assignments. The complexity of this search is
O(NkN
max). The delay tolerance of each of the Nnodes
needs to be checked for kN
max possible band allocations.
We will propose an efficient pruning based search
algorithm based on the construction of a tree and devel-
opment of pruning conditions to fathom the branches of
the tree, by exploiting the problem structure to decrease
the complexity of the brute-force search. In the search
algorithm, we use a tree structure for the assignment of
the M2M devices to the frequency bands with each node
represented by zr= (i1, i2, ..., iN), where the devices
are enumerated in the order of decreasing priority. The
root of the tree is (0,0, ..., 0), representing that none of
the devices are allocated to any band yet. In the j−th
level of the tree, each of the nodes in the previous level is
branched into kmax nodes, representing the allocation of
the j−th node to the corresponding frequency band. The
leaves of the tree represent the assignment of the nodes
to the frequency bands, without including any zero entry.
The proposed algorithm is based on the construction of
this tree from the root by using depth-first search (DFS)
and pruning of the nodes during the construction without
checking their descendants in the case the following
conditions are met:
1) The allocation of the device on the particular band
that the node represents violates the delay bound
for the device.
2) The allocation of the device on the particular band
that the node represents results in a worse solution
than the best feasible solution already obtained.
For both conditions, note that descendant nodes do not
change the allocation of devices represented by the
parent node. Therefore, if the delay bound is violated
for a device on a particular band, the violation cannot be
reverted on descendant nodes. Similarly, if the allocation

8
of the device requires more bands than the best solution
obtained so far, then the search through descendant nodes
will not decrease the number of required bands. The DFS
enables to quickly obtain a feasible solution that can be
used as an upper bound for subsequent search, thereby
eliminating solutions that are far from optimal.
Algorithm 1 Efficient Depth-First Search Algorithm
(EDFS)
1: initialize variables: bestF easible=N,F={all nodes},
CN = zeros(N,1), optimalAllocation=zeros(N,1);
2: while F6=∅do
3: if RCN =∅and C N is not at level Nthen
4: F←F\CN ;
5: CN ←Parent of C N ;
6: else if CN satisfies any pruning condition then
7: F←F\(R∗
CN ∪C N);
8: CN ←Parent of C N ;
9: else if CN is not at level Nthen
10: CN ←Child in RC N with minimum band value;
11: else if max (CN )≤bestF easibl e and delay bound
is not violated then
12: bestF easible=max(CN);
13: optimalAllocation =C N ;
14: CN ←Parent of C N ;
15: F←F\(RCN ∪C N);
16: CN ←Parent of C N ;
17: end if
18: end while
The Efficient Depth-First Search Algorithm (EDFS),
given in Algorithm 1, is described next. The algorithm
starts the search from the root node by initializing the
current node, denoted by Current Node (CN), to a zero
vector. The best feasible solution and the band allocation
vector corresponding to optimal solution, denoted by
bestF easible and optimalAllocation, are initialized to
Nand zero vector, respectively (Line 1). Note that there
may be multiple optimalAllocation vectors satisfying
the optimal band number. Our algorithm stores only
one of the optimalAllocation vectors corresponding to
optimal band number. Fis the set of unexplored nodes
and initialized to all nodes. RCN refers to unexplored
children of node CN .R∗
CN contains all unexplored
descendants of node CN . If the current node does not
have any unexplored children and is not at the level
N; i.e. it is not one of the leaves of the search tree,
then the current node is marked explored, returning
to parent node (Lines 3-5). If the current node has
children to be explored but satisfies at least one of
the the pruning conditions, then the node and all its
descendants are marked explored, returning to parent
node (Line 6-8). If the current node has children to
be explored and does not satisfy pruning conditions,
then the algorithm proceeds with the unexplored child
node with minimum band value (Lines 9-10). If the
current node is at the level Nand provides a better
feasible solution than bestF easible,bestF easible is
updated while storing CN in the optimalAllocation
vector (Lines 11-13). Since from each parent node, we
move to the unexplored child node with the minimum
band value, all other unexplored nodes of the same
parent will provide a worse solution. Thus, the current
node is updated with the parent node, while marking
the parent and all unexplored children explored, and
moving the next parent node again (Lines 14-16). The
algorithm terminates when all nodes are explored (Line
2). The output of the algorithm is optimalAllocation.
If optimalAllocation is a zero vector, then no feasible
solution exists.
VI. MINIMUM FREQUENCY FIRST-FIT
ALLOCATION ALGORITHM
Although the EDFS algorithm described in Section V
decreases the complexity of the straightforward search
algorithm with a smart pruning mechanism, the com-
plexity of the algorithm is still exponential, which may
not be manageable with the increasing number of H2H
and M2M devices in LTE/5G stations [27]. The proposed
polynomial time heuristic algorithm is closely related to
the EDFS algorithm with two features decreasing the
runtime complexity. First, instead of exploring all the
nodes in the tree, the heuristic algorithm explores only
one branch of the tree starting from the root node and
moving to the feasible child node with the minimum
band number at each step. Second, the devices with the
same traffic and QoS characteristics are grouped into
clusters with the goal of assigning the nodes in bulks
instead of one-by-one.
A. Algorithm Description
Algorithm 2 Minimum Frequency First-Fit Allocation
(MFFFA) Algorithm
1: Input:dc
i,pc
i,τc
i,Nifor i∈[1, M ]
2: Output:K,U F Bk, for k∈[1, K]
3: k= 1;
4: while Pi∈[1,M]Ni6= 0 do
5: UFBk=zeros(1, M );
6: for i= 1 : Mdo
7: crossDelay = 0;
8: for j= 1 : i−1do
9: crossDelay =crossDelay +UFBk
jdpc
i
pc
jeτc
j;
10: end for
11: remDelay =dc
i−crossDelay;
12: if remDelay > 0then
13: UFBk
i= min(Ni,bremDelay
τc
ic);
14: end if
15: Ni=Ni−UFBk
i;
16: end for
17: k+ +;
18: end while
19: K=k;

9
We propose the Minimum Frequency First-Fit Allo-
cation (MFFFA) Algorithm, given in Algorithm 2, as
described next. MTC devices are clustered into Mclus-
ters based on packet arrival period, maximum allowable
delay and transmission time, denoted by pc
i,dc
iand τc
i
for cluster i, respectively. Nidenotes the number of
unallocated devices from cluster i.crossDelay is the
extra delay the device experiences due to devices in
higher priority clusters. UFBkis an M−dimensional
vector, with the i−th entry, denoted by UFBk
i, storing
the number of devices from cluster iin band k.UFBk
is initialized to a zero vector (Line 5). The algorithm
allocates the devices starting from the highest-priority
cluster (Line 6). First, crossDelay on each cluster i
from higher priority clusters is calculated (Lines 7−10).
Then, the difference between the delay tolerance and
experienced delay due to higher priority clusters, denoted
by remDelay, is computed to determine the number
of devices from cluster ithat can be allocated in band
k. If the calculated number is larger than the number
of remaining devices from cluster i, then all remaining
devices in cluster iare allocated to that particular band.
Otherwise, the number of remaining devices from this
cluster will be updated for the allocation to the following
bands (Lines 11 −15). The algorithm stops when there
are no remaining unallocated devices from the clusters
(Line 4).
B. Algorithm Illustration Through An Example
In Fig. 3, we describe the workings of our algorithm
through an example. Let the number of clusters be 3. The
cluster parameters are given by dc
1= 2, pc
1= 2, τ c
1=
1, N1= 3, dc
2= 3, pc
2= 3, τ c
2= 1, N2= 2, dc
3=
3, pc
3= 6, τ c
3= 1, N3= 4. The first, second and third
clusters are denoted by A, B and C, respectively. We
start allocating devices from cluster A. Since there is
no higher priority cluster, there is no delay imposed
by other clusters on A, setting crossDelay to 0. The
remDelay is d1−crossDelay = 2 −0 = 2. We
can allocate remDelay/τ1= 2/1 = 2 devices from
cluster A on the first UFB, updating UFB1
1= 2.
Now, we try cluster B on the first UFB. The delay
imposed on cluster B from cluster A on the first band
is, UFB1
1∗ dp2
p1e ∗ τ1= 2 ∗ d3/2e ∗ 1 = 4. However,
4> d2= 3, i.e. the delay imposed on cluster B is larger
than its tolerance. Thus, we cannot allocate any device
from cluster B on the first UFB. Similarly, the delay
imposed by cluster A on cluster C is 2∗ d6/2e ∗ 1=6
and 6> d3= 3. Thus, no device from cluster C can
be allocated on the first band. We move to the second
UFB. We still have the third device from cluster A.
We allocate this device on the second UFB. Now, we
proceed to cluster B, the second highest priority cluster.
The cross delay is d3/2e ∗ 1 = 2. The remaining delay
Fig. 3: Algorithm Description: An example
is d2−crossdelay = 3 −2=1. We can allocate
remdelay/τ2= 1/1 = 1 device from cluster B on the
second band. For cluster C, the devices on the second
UFB would impose d6/2e+d6/3e= 5 > d3delay, thus
cluster C cannot be allocated on the second UFB. With
this procedure, we allocate the remaining devices on the
third and the fourth UFB.
C. Worst Case Performance Analysis
In this section, we find the approximation bound of
the MFFFA algorithm under certain conditions. For this
purpose, we will need Lemma 1 and Lemma 2.
Consider a set of M2M devices S={a1, .., aN},
where each device ajhas implicit deadline, period pj
and transmission time τjRB, with τjbeing an inte-
ger, for j∈[1, N]. For each device aj, define a set
S0
j={bj1, .., bjτj}, where each device bji, i ∈[1, τj],
has 1RB transmission time and period pj. Define S0as
∪N
j=1S0
j.
Lemma 1: Set Sis schedulable on a single band if
and only if set S0is schedulable on a single band.
Proof: Assume set S is schedulable. Then, τjRBs are
allocated within each period pjof device aj. Allocate
each bji, i ∈[1, τj]at the time instant when the i−th
RB of device ajis allocated. Since this holds for an
arbitrary j, the set S0is also schedulable.
Assume set S0is schedulable. Then, all devices in
subset S0
jare scheduled within time interval (t, t +pj).
There are τjdevices with 1RB transmission time in
subset Sj. Allocate the i−th RB of device ajat the
time instant when device bjiis allocated, for i= 1, .., τj.
With this allocation scheme, all τjRB’s of device ajare
allocated in time interval (t, t +pj). Since this holds for
an arbitrary j, the set Sis schedulable. 
Lemma 2: Let τj= 1 for j∈[1, N ]. For any
scheduling policy, the preemptive allocation yields the
same schedule as the non-preemptive allocation.
Proof: Assume that a packet from the device aistarts
transmission at time t=t0RB, where t0∈Z+. This

10
implies that all higher priority devices that generated a
packet up to time t0RB have completed their transmis-
sion. Since the devices generate data at integer multiples
of 1 RB, there can be no preemption in (t0, t0+ 1) RB
interval. Since transmission times are equal to 1 RB, the
packet from device aicompletes its transmission at time
t=t0+ 1 RB without any preemption. 
1) Worst Case Performance With Implicit Deadlines:
We first find the approximation bound of the MFFFA
algorithm under the following conditions: Devices gen-
erate data at integer multiples of 1RB and devices
have implicit deadlines; i.e. their delay tolerances are
equal to their periods. In order to find the approximation
bound, we will use the approximation bound provided
for Rate-Monotonic-First-Fit (RM-FF) algorithm in [49].
RM-FF algorithm greedily allocates devices onto bands
starting from the highest priority device. However, RM-
FF allows preemption whereas MFFFA does not. Also,
MFFFA orders devices in increasing period, lower pe-
riod implying higher priority, whereas RM-FF allocates
devices with respect to any given priority order.
Theorem 2: Let K0denote the minimum number of
U F B bands required to schedule the set Sand Kbe the
minimum number of U F B bands required to schedule
the set Sby MFFFA algorithm. Then, the following
relation holds:
K≤[2 + (3 −23
2)
24
3−2]K0+ 1 ≈2.33K0+ 1 (3)
Proof: The schedulability of the set Sis equivalent to
that of S0containing devices of 1RB transmission time
due to Lemma 1. Moreover, the preemptive schedule of
the set S0is equivalent to its non-preemptive schedule
due to Lemma 2. Thus, MFFFA is an instance of the
RM-FF algorithm, where the given priority order coin-
cides with the order of increasing period. Therefore, the
performance bound of the RM-FF algorithm in Eqn. (3)
given in [49] can be used for MFFFA. 
2) Worst Case Performance With Simply Periodic Set
of Devices: Next, we find the approximation bound of
the MFFFA algorithm under the following conditions:
The transmission time of devices is 1RB and devices
are simply periodic; i.e. for any two devices aiand aj
with periods pi< pj,pjis an integer multiple of pi.
Devices have implicit deadlines and generate data at
integer multiples of 1 RB.
Theorem 3: Let K0denote the minimum number of
U F B bands required to schedule the set Sand Kbe the
minimum number of U F B bands required to schedule
the set Sby MFFFA algorithm. Then, the following
relation holds:
K≤1.5K0(4)
Proof: The proof is based on the demonstration of
the equivalence between our scheduling problem and
bin-packing problem, and using the bound derived for
the First-Fit Decreasing (FFD) algorithm proposed for
bin-packing problem. First, we show that our schedul-
ing problem is equivalent to bin-packing problem. Bin
packing problem can be described as follows: We have
objects with different sizes and bins with identical capac-
ities. We need to pack these objects into bins such that
the number of bins used is minimized. Let us consider a
bin-packing problem. The size of an object corresponds
to the utilization of a device, i.e. ratio of the transmission
time of a device to its period. Each UFB is associated
with a bin. Accordingly, the sum of the utilizations of the
devices assigned to each UFB gives the total size of the
objects in a bin. To complete the equivalence, we will
use the following result in [50]: For a preemptive, simply
periodic system with implicit deadlines, the rate mono-
tonic (RM) algorithm, an algorithm that allocates devices
based on the priority order in which lower period implies
higher priority, is schedulable on a uniform processor
if and only if the total utilization of devices is equal
to or less than 1. Therefore, if we use RM algorithm
at each UFB, total utilization of devices allocated to a
UFB cannot exceed 1, resulting in bin capacity of 1.
The objective of minimizing the number of UFBs is then
equivalent to the objective of minimizing the number of
bins in bin-packing problem.
Based on this equivalence, we will use the bound of
the FFD algorithm proposed for bin-packing problem
in [51]. FFD first sorts items in non-increasing order
of their sizes and places them in the lowest indexed
bin as they appear, i.e. First-Fit principle. On the other
hand, MFFFA first orders devices in increasing period,
i.e. non-decreasing utilization, and allocates them with
nonpreemptive RM algorithm on individual UFBs based
on First-Fit principle. Further note that since we use
devices generating data at integer multiples of RBs with
1RB transmission time, preemptive RM schedule is
equivalent to nonpreemptive RM schedule due to Lemma
2. Thus, MFFFA is equivalent to First Fit Decreasing
algorithm proposed for bin packing problem, for which
the approximation bound is proven to be 1.5. 
VII. CALL ADMISSION CONTROL
Call admission control algorithm aims to manage the
admission and resource allocation of newly joining time-
triggered M2M devices between the regeneration times
of the semi-persistent schedule. Given the allocation
of the existing time-triggered M2M devices, the newly
arriving time-triggered M2M devices are scheduled with
the goal of using minimum number of UFBs while pro-
viding their QoS guarantees. The usage of at most kmax
UFBs is guaranteed by not admitting lowest priority
devices as needed.

11
A. Call Admission Optimization Problem
Call admission optimization problem aims to mini-
mize the number of bands used throughout the semi-
persistent period Pwhile satisfying the QoS require-
ments of both existing and newly arriving devices. The
devices arriving earlier are given higher priority since
they are scheduled before those arriving later in time.
If two devices arrive at the same TTI, then the priority
ordering is the same as the one described in Section
II. Once the devices are allocated resources within the
schedule, the resource allocation is not updated until the
next regeneration time of semi-persistent schedule. The
optimal allocation at each TTI requires the knowledge
of the requirements of the devices arriving both before
and after that TTI within two regeneration times of
the semi-persistent schedule, since the objective is to
minimize the number of UFBs and allocation cannot be
changed until the next schedule regeneration. Thus, the
optimization problem is offline. Although the resource
allocation algorithms must be online since we do not
assume the availability of any information on newly
arriving devices, this optimization problem is useful in
providing a theoretical lower bound on the UFB usage.
The call admission optimization problem is exactly the
same as the optimization problem described in Section
IV, with the exception of a modified priority ordering.
This problem is NP-hard. In order to prove this, take a
specific instance of the problem where the number of
TTIs between two regeneration times of the schedule is
equal to 1. In that specific instance, the call admission
optimization problem is equivalent to the optimization
problem provided in Section IV, which is proved to be
NP-hard in Section IV-C. Therefore, solving the call
admission optimization problem requires an exponential
runtime in the number of newly arriving devices. The op-
timization problem further requires an offline algorithm,
which is not possible to implement in practice. Thus,
we propose an online fast and efficient call admission
heuristic algorithm for the solution of this problem.
B. Call Admission Algorithm
The proposed heuristic call admission algorithm is
shown in Fig. 4. First Fit Occupied Bands (FFOB)
Algorithm is first executed to allocate newly arriving
devices to the UFBs some parts of which are already
occupied by existing devices. If there are still unallocated
devices after running the FFOB algorithm, the base
station allocates remaining devices to new bands by
using MFFFA algorithm. If call admission mechanism
requires more bands than kmax, then the lowest priority
device is dropped. This continues until the allocation
requires at most kmax UFB bands.
FFOB algorithm is similar to MFFFA except its ex-
ecution on the UFBs some parts of which are already
assigned to the previously arrived devices. Similar to
Fig. 4: Call admission control mechanism
MFFFA, devices are ordered according to their priorities,
and then are allocated to the lowest number UFB on
which they can be allocated. Unlike MFFFA that aims
to allocate all devices, FFOB leaves the allocation of the
devices that cannot be allocated within already occupied
bands to the MFFFA algorithm for their allocation on
new bands as shown in Fig. 3. Let the delay tolerance,
period, transmission time and number of newly arriving
devices, denoted by dc
i,pc
i,τc
i,Ni, respectively, for
i∈[1, M ], be given. Let UFBkbe an M−dimensional
vector, with the i−th entry, denoted by UFBk
i, storing
the number of devices from cluster iin band k. The input
of the FFOB algorithm is UFBk
icontaining the number
of devices from cluster i∈Mthat are already allocated
on band k. The output of the algorithm is the number of
unallocated devices after running the algorithm, Ni, and
updated UFBk
i. Starting from the highest priority cluster,
cross delay, the delay experienced due to devices already
allocated to band k, is calculated (Lines 5-8). Note that
unlike MFFFA, devices experience an additional delay
from all devices that are already assigned. Then, the
remaining delay is computed to determine the number
of devices that can be additionally allocated from the
corresponding cluster with exactly the same procedure
applied in MFFFA (Lines 11-12).
VIII. PERFORMANCE EVALUATION
The goal of the simulations is to compare the per-
formance of the proposed scheduling and call admis-
sion algorithms to that of previously proposed algo-
rithms, including clustering-based scheduling algorithm
[26], basic LTE without ACB, and LTE system with
dynamic optimal ACB [6], and optimal solution in
terms of schedulability and usage of frequency band.
In clustering-based scheduling algorithm, denoted by
MAM, devices are grouped into clusters according to
their periods and delay tolerances. Clusters are assigned

12
Algorithm 3 First Fit Occupied Bands Algorithm
1: Input:dc
i,pc
i,τc
i,K,Nifor i∈[1, M ],UF B k, for
k∈[1, K]
2: Output:Nifor i∈[1, M ],UF B k, for k∈[1, K]
3: for i= 1 : Mdo
4: for k= 1 : Kdo
5: crossDelay = 0;
6: for j= 1 : Mdo
7: crossDelay =cr ossDelay +UFBk
j∗ d pc
i
pc
je ∗ τc
j;
8: end for
9: remDelay =dc
i−crossDelay;
10: if remDelay > 0then
11: UFBk
i=UFBk
i+ min(Ni,bremDelay
τic);
12: Ni=Ni−min(Ni,bremDelay
τic);
13: end if
14: end for
15: end for
priorities according to their periods such that clusters
with lower periods have higher priorities. The transmis-
sion times of all devices are assumed to be equal to 1RB.
The clusters are assigned to TTIs such that devices in
the same cluster are allocated resources at the same TTI
using different UFBs and no device from other clusters
can be assigned to this TTI. Since MAM assumes the
availability of unlimited number of frequency bands,
we additionally include a mechanism for the case in
which the allocation of a cluster exceeds the frequency
band limit: If the allocation of a cluster requires more
UFBs than the maximum number of UFBs in a TTI,
the cluster is subdivided into new clusters, each new
cluster fitting within the maximum number of frequency
bands. The call admission procedure proposed for MAM
allocates the newly coming device to the existing TTIs
if the device belongs to an existing cluster and there
are available resource blocks in the corresponding TTI,
and creates a new cluster for the device otherwise. The
basic LTE refers to random access method that does not
use any access class barring method, and is denoted by
basic LTE. In the event of collision at the random access,
colliding devices wait for a backoff time. Packet losses
occur under the following conditions: If the number
of retransmissions for a packet exceeds the maximum
number of retransmissions or if a device produces the
next packet before successfully transmitting a packet.
For the LTE system with dynamic optimal ACB, denoted
by DACB, the base stations dynamically set the ACB
parameter to its optimal value obtained in [6]. With
respect to physical layer, in order to get the best possible
result out of random access based solutions we will make
the following assumptions as in [52]: the channel is ideal,
there is no signal loss due to radio propagation problems,
and once a preamble is successfully transmitted, the
device accesses the channel. LTE parameters are adopted
from [53]: backoff time = 20 ms, maximum number of
retransmissions = 10, number of preambles = 54, random
access opportunity period = 5ms. Finally, the optimal
solution is denoted by OPT.
Simulation results are obtained based on 1000 random
network topologies, in which devices are uniformly dis-
tributed within a circle of radius rwith the base station
at the center. Simulation of the medium access protocols
is performed in an event-based simulator developed in
MATLAB, called M2MSCHEDULE, and simulation of
the optimal algorithm is performed in GAMS, a high-
level modeling platform for expressing and solving lin-
ear, nonlinear and mixed integer optimization problems.
Both simulators are publicly available in [54]. We as-
sume that the transmission time of all M2M devices is
equal to 1RB for comparison to the MAM algorithm.
Each TTI comprises of 100 RBs. The packet generation
period of the clusters is chosen from [10,2000] ms, based
on practically used values in [26], and delay tolerance
of clusters is uniformly chosen in the range from 10 ms
to the randomly chosen packet generation period unless
otherwise stated and denoted by uniform deadline case.
A. Schedulability Performance
Fig. 5 shows the schedulability percentage of differ-
ent access mechanisms for different number of M2M
devices. The schedulability percentage is defined as
the percentage of the total number of packets that are
successfully sent (i.e. packets that are not lost) out of
the total number of packets generated. The number of
clusters is fixed to 12. The schedulability performance
of the MFFFA algorithm outperforms both variations
of random access mechanisms and previous schedule
based algorithm due to the proposed efficient resource
allocation mechanism. MFFFA succeeds in allocating all
devices within the frequency band limit with a slight
drop below 100% for around 5000 devices, where the
frequency band limit is reached. The schedulability of
the MAM algorithm deteriorates drastically with increas-
ing number of devices. Available frequency bands fail to
suffice for increasing number of devices, causing clusters
that reach the frequency band limit to be subdivided into
new clusters. This increase in the number of clusters
results in increased delay and decreased schedulability
percentage. On the other hand, the schedulability per-
formance of random access based methods deteriorates
as the number of devices increases with the increasing
number of collisions in the network. As expected, the de-
terioration in performance is smaller in DACB than basic
LTE due the dynamic optimization of ACB parameter.
Fig. 6 shows the schedulability percentage of different
scheduling algorithms for different number of M2M
clusters. The number of devices is fixed to 2000. As
random access based methods do not depend on cluster-
ing, they are not included. The smart resource allocation
mechanism of the MFFFA algorithm achieves much

13
0 2000 4000 6000 8000 10000
Number of devices
0
20
40
60
80
100
Schedulability percentage
MFFFA
MAM
basic LTE
DACB
Fig. 5: Schedulability percentage of MFFFA, MAM,
basic LTE and DACB algorithms for different number
of M2M devices, where kmax = 100.
2 4 6 8 10 12 14 16
Number of clusters
0
20
40
60
80
100
Schedulability percentage
MFFFA
MAM
Fig. 6: Schedulability percentage of MFFFA and MAM
algorithms for different number of M2M clusters, where
kmax = 100.
better schedulability performance than MAM algorithm
for different number of clusters. MAM algorithm fails
to allocate all devices within the frequency band limit
for any given cluster number. Each cluster occupies
a single TTI in MAM, resulting in increasing delay
and decreasing schedulability percentage with increasing
number of clusters.
B. Frequency Band Usage Performance
Fig. 7a and Fig. 7b show the number of frequency
bands used by different scheduling algorithms for dif-
ferent number of clusters for the uniform deadline and
implicit deadline cases, respectively. The number of de-
vices belonging to each cluster is uniformly chosen from
[10,50]. For both cases, the average number of frequency
bands used by MAM approaches to its maximum very
quickly as the number of devices increases. The number
of frequency bands used by MAM depends only on the
number of devices in the cluster since each device in
the cluster uses one frequency band. As the number of
clusters increases, the probability that a cluster has a
higher number of devices also increases. MFFFA, on the
other hand, significantly outperforms MAM for different
number of clusters. Furthermore, MFFFA performs very
close to the OPT. Since the implicit deadline case is less
restrictive than the uniform deadline case, MFFFA and
OPT are able to allocate the same number of devices
using fewer bands whereas the performance of MAM
remains the same.
Fig. 8a and Fig. 8b show the number of frequency
bands used by different scheduling algorithms for dif-
ferent number of devices for the uniform deadline and
implicit deadline cases, respectively. The number of
clusters is 12. Different number of devices are uniformly
distributed among clusters. As stated before, the number
of frequency bands used by the MAM depends only
on the maximum number of devices within the clusters.
Thus, for both cases, as the number of devices increases,
the number of frequency bands used by the MAM
increases. MFFFA, on the other hand, again performs
much better than MAM. The effect of implicit deadlines
is similar to Fig. 7.
C. Performance Evaluation of Proposed Call Admission
Control Mechanism
Fig. 9 shows the number of frequency bands used
by various call admission control mechanisms, i.e., the
proposed call admission control mechanism (FFOB),
call admission mechanism proposed for MAM [26] and
offline optimal solution. The algorithm starts with 12
clusters and 50 devices randomly distributed among
these clusters. The simulation duration is 20 s. The
arrival of devices for each cluster at any TTI is modeled
as a Poisson process with mean λ= 0.001. Semi-
persistent schedule update period is set to 10 s. The
proposed call admission mechanism is very efficient in
the frequency band usage. The number of frequency
bands occupied in MAM increases much more rapidly
than that of the proposed algorithm FFOB as new devices
arrive to the network. Since MAM algorithm does not
use the scarce frequency resources efficiently, high traffic
load leads to resource starvation. Further note that call
admission algorithm needs to be restarted periodically so
that the base station can allocate devices in an efficient
manner. In other words, at the schedule update points
only, we drop the condition that early arriving devices
have the priority for FFOB. Thus, all the devices that are
present at those points are treated with respect to their
periods. This explains why the optimal solution, which
also updates its schedule at schedule update points,
improves at the schedule update point (at 10 s).
IX. CONCLUSION
We study the problem of M2M packet scheduling
with QoS guarantees in cellular networks, particularly
considering the radio resource starvation problem in
5G technology with dramatically growing numbers of
M2M applications and devices. Accordingly, we propose
a novel optimization framework with the objective of

14
0 2 4 6 8 10 12
Number of clusters
0
10
20
30
40
50
Number of bands
MAM
MFFFA
OPT
(a) Uniform deadline case
0 2 4 6 8 10 12
Number of clusters
0
10
20
30
40
50
Number of bands
MAM
MFFFA
OPT
(b) Implicit deadline case
Fig. 7: Number of frequency bands used by MFFFA, MAM and OPT for different number of clusters.
50 100 150 200 250 300 350
Number of devices
0
10
20
30
40
Number of bands
MFFFA
MAM
OPT
(a) Uniform deadline case
50 100 150 200 250 300 350
Number of devices
0
10
20
30
40
Number of bands
MFFFA
MAM
OPT
(b) Implicit deadline case
Fig. 8: Number of frequency bands used by MFFFA, MAM and OPT for different number of devices.
0 0.5 1 1.5 2
Time (ms) 104
0
5
10
15
20
25
30
35
Number of bands
FFOB
OPT
MAM
Fig. 9: Number of frequency bands used by FFOB,
MAM and OPT in call admission control as time pro-
gresses.
minimizing the number of frequency bands occupied
by a given set of M2M devices, while guaranteeing
their delay and periodicity constraints. The optimization
problem is proven to be NP-hard upon which we provide
an efficient heuristic scheduling algorithm. We estab-
lish performance guarantees for the proposed heuristic
algorithm by constructing an approximation bound to
the optimal. We further provide a call admission control
scheme to dynamically manage the arrivals of new de-
vices to the network. Extensive simulations demonstrate
that the proposed algorithm performs much better than
the existing algorithms with very close performance to
that of the optimal solution in minimizing the frequency
band usage and maximizing schedulability. Furthermore,
the proposed call admission control mechanism demon-
strates the robustness of the proposed framework in a
dynamic environment with changing traffic load and
characteristics.
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