Hybrid Random Access and Data Transmission Protocol for ...

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 1, JANUARY 2015 33

Hybrid Random Access and Data TransmissionProtocol for Machine-to-Machine Communications

in Cellular NetworksDimas Tribudi Wiriaatmadja, Student Member, IEEE, and Kae Won Choi, Member, IEEE

Abstract—To address random access channel (RACH) conges-tion and high signaling overhead problems of machine-to-machine(M2M) communication in cellular networks, we propose a newdesign of a random access procedure that is exclusively engineeredfor the M2M communication. Our design has two prominentfeatures. One is a fast signaling process that allows M2M userequipment to transmit data right after preamble transmission ona physical RACH to reduce the signaling overhead. The other is aself-optimization feature that allows the cellular system to produceoptimal M2M throughput by adaptively changing resource block(RB) composition and an access barring parameter according tothe amount of available RBs and the M2M traffic load. We derive aclosed-form analytic formula for the M2M traffic throughput andpropose a joint adaptive resource allocation and access barringscheme based on the analytic results. By simulation, we show thatthe proposed scheme exhibits a near-optimal performance in termsof the capacity.

Index Terms—Machine-to-machine communication, M2Mscheduling, random access, overload control, access barring,Long-Term Evolution (LTE).

I. INTRODUCTION

IN recent years, the use of cellular networks such as a Long-Term Evolution (LTE) technology [1], [2] for machine-to-

machine (M2M) communications has attracted great attentionfrom both the research community and the industry [3], [4].The ubiquitousness of cellular networks is a major driving forcewhich motivates M2M application developers to adopt cellularnetworks for their numerous remote monitoring and controllingapplications. To cellular operators, this growth of new M2Mapplications has opened up a new market opportunity in thecellular industry. However, there are two critical problems thatneed to be addressed for efficient cellular M2M communi-cations. One is high signaling overhead [5] and the other iscongestion vulnerability [6], [7].

Manuscript received January 5, 2014; revised April 6, 2014 and May 25,2014; accepted May 26, 2014. Date of publication June 2, 2014; date of currentversion January 7, 2015. This work was supported in part by the Basic ScienceResearch Program through the National Research Foundation of Korea (NRF)funded by the Ministry of Education, Science and Technology (2011-0013966)and in part by the National Research Foundation of Korea (NRF) grant fundedby the Korean government (MSIP) (2014R1A5A1011478). The associate ed-itor coordinating the review of this paper and approving it for publicationwas D. Niyato.

The authors are with the Department of Computer Science and Engineeringand the Convergence Institute of Biomedical Engineering and Biomaterials,Seoul National University of Science and Technology, Seoul 139-743, Korea(e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TWC.2014.2328491

The traditional cellular network, which is originally engi-neered for human-to-human (H2H) communications, has beenconsidered not suitable to handle the unique characteristics ofM2M applications [8]. The M2M applications, such as smartmetering, e-health, and intelligent transportation, are character-ized by small-sized data intermittently transmitted by a massivenumber of M2M devices. The connection-oriented commu-nication in the conventional cellular systems (e.g., LTE) caninduce excessive signaling overhead in the case of transmittingsmall-sized data for M2M communications [5]. Moreover, thesituation in which a huge number of M2M devices attempt toaccess cellular networks at the same time can lead to severecongestion especially in a physical random access channel(PRACH) [6], [7].

In this paper, we first propose a novel design of a hybridrandom access and data transmission protocol optimized forM2M communications to reduce excessive signaling overhead.If an M2M user equipment (UE) employs the conventionalconnection-oriented data communication, the M2M UE firstsends a connection setup request to a base station (BS) by usinga random access procedure, performs a complicated signalingprocess for sending only a small amount of data, and then isdisconnected from the BS. To remove this inefficiency, we pro-pose to simplify the data communication procedure by allowingM2M UEs to send data right after preamble transmission on thePRACH without explicitly establishing a connection.

In the proposed hybrid random access and data transmissionprotocol, there are two potential bottlenecks. One is causedby collisions in the PRACH, and the other is due to limitedradio resources in the uplink data channel. An excessive numberof M2M UEs participating in a random access procedure canlead to severe congestion in the PRACH [6]. If more than oneM2M UEs choose the same preamble in a PRACH, the BSschedules the same resource blocks (RBs) in the uplink datachannel for these M2M UEs. This situation in turn results ina collision in the uplink data transmission since the BS cannotdecode the data transmission from more than one UEs via thesame RBs. Besides collisions in the PRACH, limited radioresources for the uplink data channel for the M2M traffic isanother performance-limiting factor. Since M2M UEs share theuplink RBs with H2H UEs, only a part of RBs are availableto M2M UEs. Therefore, even if an M2M UE successfullysends a preamble in the PRACH without any collision, itmay happen that the BS cannot allocate any uplink RB tothat M2M UE for data transmission due to the shortage ofavailable RBs.

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34 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 1, JANUARY 2015

To resolve the above-mentioned bottleneck problems, wepropose a joint adaptive resource allocation and access barringscheme. The adaptive resource allocation scheme decides thenumbers of RBs for the PRACH and the uplink data channelsin an optimal way. To relieve congestion in the PRACH, wecan increase the number of RBs allocated for the PRACH.However, we have to decrease the number of RBs for uplinkdata channels at a cost of an increased number of RBs for thePRACH, which possibly results in making uplink data channelsa bottleneck of M2M data transmission. Therefore, it is ofgreat importance to optimally allocate RBs to the PRACH andthe uplink data channel. In line with the adaptive resourceallocation scheme, we also adopt an access barring scheme tocontrol the M2M traffic load [7]. In the access barring scheme,an access barring parameter determines the probability that theaccess to the PRACH is allowed. Each M2M UE participatesin the random access procedure with the probability given bythe access barring parameter. Therefore, the BS can control theM2M traffic load by adjusting the access barring parameter.

In this paper, we derive a closed-form analytic expressionfor the throughput of M2M traffic according to the numberof RBs allocated to the PRACH as well as the M2M trafficload. Based on the throughput analysis, we also obtain a closed-form optimal solutions for the number of RBs for the PRACHand the access barring parameter. The proposed joint adaptiveresource allocation and access barring scheme finds the optimalresource allocation and access barring parameter from theseclosed-form optimal solutions. By simulation, we show thatthe analysis agrees with the simulation results. The simulationresults also show that the proposed scheme exhibits a near-optimal performance in terms of the capacity.

The contribution of this paper is summarized as follows.

• We propose a hybrid random access and data transmissionprotocol tailored for M2M communications to minimizethe signaling overhead.

• We derive a closed-form formula for the M2M trafficthroughput as functions of the number of RBs allocatedfor the PRACH and the M2M traffic load.

• We propose a joint adaptive resource allocation and accessbarring scheme, based on the analytic results on the M2Mthroughput.

The rest of the paper is organized as follow. In Section II,we explain preliminaries on the random access procedure inthe LTE system and the related works. Section III introducesthe system model and the proposed hybrid random access anddata transmission protocol. In Section IV, we analyze the M2Mthroughput of the proposed protocol and derive the optimalparameters maximizing the throughput. Section V explains thejoint adaptive resource allocation and access barring scheme,based on the analytic results. In Section VI, we present numer-ical results and the paper is concluded in Section VII.

II. PRELIMINARIES AND RELATED WORKS

A. Random Access Procedure in LTE System

In this subsection, we provide a brief introduction to therandom access procedure that is used for initial access in the

Fig. 1. Power delay profile on a PRACH.

LTE system [1], [9]. When a user equipment (UE) intends toestablish a connection to a base station (BS), the UE initiatesa random access procedure by sending a preamble to the BSvia a physical random access channel (PRACH). A PRACH isa time–frequency radio resource, which is multiplexed togetherwith a physical uplink shared channel (PUSCH) and a physicaluplink control channel (PUCCH).

On a PRACH, a UE can transmit a preamble, which isa Zadoff–Chu sequence. The Zadoff–Chu sequence satisfiesa constant amplitude zero autocorrelation (CAZAC) property[10]. The CAZAC property allows multiple orthogonal se-quences to be generated from the same Zadoff–Chu sequenceby cyclically shifting the Zadoff–Chu sequence. In a PRACHin the LTE system, a UE can choose and send a preamble out of64 orthogonal preambles, which are made from the Zadoff–Chusequence. Upon receiving preambles via a PRACH, the BScalculates a power delay profile to detect which preamblesare sent.

In Fig. 1, we present an example power delay profile calcu-lated by the BS. In this example, four UEs send preambles to theBS in a PRACH. UE 1 sends preamble 4, UE 2 sends preamble26, UE 3 sends preamble 1, and UE 4 sends preamble 4. Notethat multiple peaks are observed for each transmitted preambledue to delay spread. To find out a certain preamble is sent or notbased on a power delay profile, the BS estimates the total energyduring the interval corresponding to the preamble, and decidesthat the preamble is sent if and only if the estimated energyis higher than a threshold. In this example, the BS detects thatpreambles 1, 4, and 26 are sent. However, the BS does not knowhow many UEs have sent each preamble so that at this point thecollision is still undetected.

The random access procedure is completed by the followingfour steps [1], [9].

• Preamble transmission (step 1): A UE randomly selects apreamble out of all available preambles with equal proba-bility and transmits a preamble to the BS via a PRACH.

• Random access response (step 2): Upon detecting pream-bles, the BS sends a random access response (RAR) foreach detected preamble via a physical downlink sharedchannel (PDSCH). An RAR conveys the identity of thedetected preamble and an initial uplink resource grant forthe transmission of a connection setup request messagein step 3.

• Connection setup request message (step 3): When a UEreceives an RAR corresponding to the selected preamble,the UE can send the connection setup request message byusing the initial uplink resource grant in the received RAR.

• Connection setup response message (step 4): If the BS suc-ceeds in receiving the connection setup request message


WIRIAATMADJA AND CHOI: RANDOM ACCESS AND DATA TRANSMISSION PROTOCOL FOR M2M COMMUNICATIONS 35

in step 3, the BS sends the connection setup response mes-sage to the UE. The random access procedure is completedif the UE receives the connection setup response message.

If two or more UEs select the same preamble in step 1 (i.e., acollision happens), these UEs send the connection setup requestmessages in step 3 through the same uplink RBs. In this case,the BS cannot decode the messages and the random accessprocedure fails due to the collision. The failed UEs shouldrestart the random access procedure from step 1.

The current LTE system is basically connection-oriented.When a UE in the idle mode has data to send to the BS, theUE first initiates the above random access procedure to makea connection. After the UE succeeds in the random accessprocedure, the UE moves to the connected mode and go throughadditional higher layer signaling procedures before it can senddata. For transmitting data, the UE sends a scheduling requestand a buffer status report to the BS via a dedicated uplinkcontrol channel (i.e., PUCCH) and receives an uplink grant viaa dedicated downlink control channel (i.e., physical downlinkcontrol channel (PDCCH)). We can see that this connection-oriented data transmission procedure is too expansive for M2Mapplications with small-sized data transmission, since this pro-cedure involves a large signaling overhead [5].

B. Related Works

In this subsection, we introduce previous works on cellularM2M communication. The foremost problem in accommo-dating M2M traffic into cellular networks is identified as aradio access network (RAN) overload problem [6]. The ThirdGeneration Partnership Project (3GPP) has suggested a varietyof solutions to the RAN overload problem, for example, ex-tended access barring (EAB), separate PRACH for machine-type communication (MTC), MTC specific backoff scheme,and pull based scheme [11].

The RAN overload control for M2M communication bearsresemblance to the traffic load control in the traditional slottedALOHA system, studied by a large body of literature (e.g.,[12]–[14]). Inspired by these works, several works on theRAN overload control for M2M communication have beenpublished (e.g., [15]–[18]). In [15], the transient behavior offinite-user multichannel slotted ALOHA systems is approxi-mately analyzed for the application to M2M communication.The authors of [16] propose a prioritized random access schemeto solve the RAN overload problem while providing quality-of-service (QoS) to different M2M classes. The cooperative accessclass barring scheme among different BSs is proposed in [17].In [18], the authors propose a fast adaptive slotted ALOHAscheme that accelerates the tracking process of network status.

The RAN overload problem can also be tackled by moreefficiently using the radio resources for the random accessprocedure as proposed in [19]–[21]. In [19], the authors proposea novel random access scheme based on fixed timing alignmentinformation at a large number of fixed-location M2M devices toreduce a collision probability. In [20], the amount of availablecontention resources is increased by expanding the contentionspace to the code domain, enabling the support of an increasednumber of M2M users. In the scheme proposed in [21], M2M

UEs form coalitions and perform relay transmission with anobjective to reduce network congestion.

Some group-based schemes are proposed to efficiently con-trol a massive number of M2M users (e.g., [3] and [22]). Thegroup-based feature proposed in [3] supports a large numberof M2M users with small data transmission and enormouslydiverse QoS requirements. In [22], the authors analyze signal-to-interference-ratio distributions and derive efficient resourceallocation schemes for spatial multi-group random access inmulticell systems.

The uplink scheduling of M2M users has been studied by[5], [23], and [24]. The challenges in M2M scheduling arepresented and some initial solutions are provided in [5]. In[23], the authors propose uplink scheduling algorithms, whichtake into account both the channel condition and the maximumdelay tolerance. In [24], the authors study the problem of poweroptimal uplink resource allocation both for time-division mul-tiple access (TDMA) and frequency-division multiple access(FDMA).

This paper proposes to reduce a signaling overhead forM2M communication by means of a hybrid random accessand data transmission protocol, which has not been studied byany previous work.1 The proposed protocol performs a jointadaptive resource allocation and access barring scheme forachieving uplink scheduling and RAN overload control at thesame time. Compared to the proposed protocol, the existingworks in cellular M2M communication have the followingshortcomings. The existing RAN overload control schemestarget to mitigate overload only in the random access procedure,but they do not consider overload in the uplink data channel.The existing M2M scheduling algorithms are not practical sincethey do not consider the random access procedure, which isnecessary for handling intermittent M2M data traffic, and sincethey make an impractical assumption that the BS knows thechannel conditions and the data backlog states of a massivenumber of M2M users.

III. SYSTEM MODEL AND PROPOSED PROTOCOL

A. System Model

We consider a single cell centered by a BS in a cellularwireless network. M2M UEs and H2H UEs coexist in this celland share radio resources. We assume that the number of M2MUEs is far greater than that of H2H UEs.

We consider the uplink of an orthogonal frequency divisionmultiple access (OFDMA) system (e.g., the LTE system). Inthe OFDMA system, one resource element (RE) is the smallestradio resource unit which consists of one OFDM subcarrierduring one OFDM symbol interval. A resource block (RB) isdefined as an aggregation of a certain number of REs. The BSallocates radio resources in the unit of an RB.

Fig. 2 illustrates the time–frequency domain model of uplinkradio resources for the proposed protocol. Time is dividedinto cycles, each of which is indexed by t. The M2M-relatedoperation is performed every cycle. Within a cycle, a PRACH

1The conference version of this paper has been published in [25].



Fig. 2. Time–frequency domain model of uplink radio resources for theproposed protocol.

for M2M communications is followed by data channels forM2M communications. Let us define a data channel as anaggregation of RBs for transmitting one data packet from oneM2M UE. The composition of a PRACH and data channelsis adaptively changed by the BS over cycles. Let Nt and Ht

denote the numbers of RBs allocated to a PRACH and datachannels in cycle t, respectively.

In a PRACH in cycle t, Bt preambles are constructed fromNt RBs by using an equation

Bt = ηNt, (1)

where η is defined as the number of preambles that can be con-structed from one RB. The number of preambles per RB, η, isdependent upon a cell radius as well as the requirements on thedetection performance and the timing estimation accuracy [1].

We assume that one M2M UE sends at most one fixed-sizepacket within a cycle.2 The modulation and coding scheme(MCS) level for data transmission is fixed to a sufficientlylow level so that a packet can reliably be decoded by the BSwithout adaptive modulation and coding (AMC). Therefore, anM2M UE uses only one data channel, which consists of a fixednumber of RBs, within a cycle. Let δ denote the number of RBsconstituting one data channel. Then, Dt data channels can beconstructed from Ht RBs in cycle t as

Dt =

⌊Ht

δ

⌋. (2)

In the proposed protocol, radio resources for M2M and H2Hcommunications are separately managed. Before the start ofcycle t, the radio resource manager calculates the amount ofradio resources for M2M and H2H communications. Let Qt

denote the number of RBs reserved for M2M communicationsin cycle t. An RB for M2M communications can be usedeither for constructing a PRACH or a data channel. Then, thefollowing condition should be satisfied.

Nt +Ht ≤ Qt. (3)

The radio resource manager can determine Qt based on theinformation on the traffic loads of H2H and M2M communica-

2With minor modification, the proposed protocol can also support multiplevariable-size packets transmitted by an M2M UE within a cycle. However, wedo not deal with that case in this paper for simplifying the model.

TABLE ITABLE OF KEY MATHEMATICAL SYMBOLS

tions. For example, in the LTE system, the radio resource man-ager can be aware of the traffic load of H2H communicationsfrom the buffer status report, which carries the information onhow much data is in uplink buffers of H2H UEs. On the otherhand, the traffic load of M2M communications can be estimatedby using the load estimation algorithm that will be explainedin Section V-A. Based on the information on the traffic loads,the radio resource manager decides Qt in such a way that thesystem-wide performance target is optimized. Note that thedetailed operation of the radio resource manager is out of scopeof this paper. From the point of view of the proposed protocol,Qt is a given parameter decided by the radio resource managerevery cycle.

From (2) and (3), when Qt and Nt are given, the number ofavailable data channels in cycle t is d(Nt, Qt), where

d(n, q) =

⌊q − n

δ

⌋. (4)

Then, the condition Dt ≤ d(Nt, Qt) should be satisfied incycle t.

The list of key mathematical symbols used in this paper issummarized in Table I.



B. Hybrid Random Access and Data Transmission Protocolfor M2M Communication

In this section, we introduce the proposed hybrid random ac-cess and data transmission protocol. In our proposed protocol,we have six steps executed in sequence in each cycle, which arei) PRACH scheduling, ii) access barring, iii) preamble transmis-sion, iv) data channel scheduling, v) uplink data transmission,and vi) acknowledgement. From now on, we explain the abovesteps one by one.

• PRACH scheduling (step 1): Before each cycle t begins,the BS estimates the number of active M2M UEs in cyclet, based on the observations obtained until cycle (t− 1).Here, an active M2M UE in cycle t is defined as an M2MUE which has a data packet to send in cycle t. From this es-timation, the BS decides the number of RBs for a PRACH(i.e., Nt) and the access barring parameter, denoted byRt. Then, the BS broadcasts the configuration of RBs fora PRACH as well as the access barring parameter via adownlink control channel.

• Access barring (step 2): At the start of each cycle, forthe access barring, an active M2M UE randomly choosesx out of the uniform distribution between zero and one.Then, the M2M UE compares x with the access barringparameter Rt, and participates in random access in cyclet only when x ≤ Rt. Therefore, the probability that anM2M UE participates in random access in cycle t is Rt.

• Preamble transmission (step 3): After the access barring,each participating M2M UE randomly chooses one pream-ble out of Bt available preambles with equal probability.Then, the participating M2M UE transmits the chosenpreamble to the BS via the PRACH.

• Data channel scheduling (step 4): On the PRACH, theBS detects all the preambles transmitted by M2M UEs.For each detected preamble, the BS schedules one uplinkdata channel which consists of δ RBs. Let V detect

t denotethe number of detected preambles in cycle t. Recall thatonly d(Nt, Qt) data channels can be scheduled in cycle t.Therefore, if V detect

t ≤ d(Nt, Qt), the BS schedules re-spective data channels for all detected preambles. On theother hand, if V detect

t > d(Nt, Qt), the BS randomly se-lects d(Nt, Qt) preambles out of V detect

t detected pream-bles and schedules data channels only for the selectedpreambles. The scheduling results are reported to theM2M UEs via a downlink control channel in the formof a random access response (RAR) message. An RARmessage contains scheduling information that associatesa preamble index to the corresponding scheduled datachannel.

• Uplink data transmission (step 5): Each M2M UE looksfor the RAR message that contains the preamble indexmatching the preamble sent by itself. Upon receiving thematching RAR message, an M2M UE transmits a datapacket to the BS on the data channel indicated by the RARmessage. If more than one M2M UEs receive the sameRAR message since they choose the same preamble, theytransmit data packets in the same data channel. In this case,

the BS cannot decode any data packets on the same datachannel due to interference.

• Acknowledgement (step 6): The BS tries to decode datapackets on all scheduled data channels. If a data packet issuccessfully received, the BS sends an acknowledgementmessage for the received data packet via a downlinkcontrol channel. In the acknowledgement message, theidentifier of the corresponding M2M UE is specified. AnM2M UE, which receives an acknowledgement message,reports to an upper layer that the data packet is suc-cessfully transmitted. If an M2M UE does not receiveany acknowledgement message until the end of the cycle,the M2M UE assumes that data transmission fails andreattempts to transmit the data packet in the next cycle.

C. Probabilistic Transition of System Variables in ProposedM2M Protocol

In this subsection, we investigate how the system variables(e.g., the number of active M2M UEs) probabilistically evolveover cycles. Let Ut denote the number of active M2M UEs atthe start of cycle t. The active M2M UEs participate in randomaccess with probability Rt. Therefore, if Pt denote the numberof participating M2M UEs in cycle t, the probability that Pt =p given Ut = u is

Pr[Pt = p|Ut = u] =

(u

p

)(Rt)

p(1−Rt)(u−p). (5)

To send a preamble, a participating M2M UE chooses onepreamble out of Bt preambles. Let Mt,b denote the numberof M2M UEs that select preamble b in cycle t, and let Mt =(Mt,1, . . . ,Mt,Bt

). Then, we have Pt =∑Bt

b=1 Mt,b. The prob-ability that Mt = m given Pt = p is a multinomial distributionsuch that

Pr[Mt = m|Pt = p] =p!

m1! · · ·mBt!

(1

Bt

)p

. (6)

The BS detects preamble b if preamble b is transmittedby at least one M2M UE (i.e., if Mt,b ≥ 1). The number ofdetected preambles in cycle t, which is denoted by V detect

t ,is equal to the number of preambles b such that Mt,b ≥ 1 forb = 1, . . . , Bt.3 Note that the BS does not know how manyM2M UEs select a detected preamble. The BS can schedule adata channel to a detected preamble. Let us define a scheduledpreamble as a preamble to which a data channel is scheduled.Let St,b denote a scheduling indicator that is one if preambleb is a scheduled preamble; and zero, otherwise. We also defineSt = (St,1, . . . , St,Bt

).If there are a sufficient number of available data channels

(i.e., V detectt ≤ d(Nt, Qt)), the BS schedules data channels to

3In this paper, we assume that the probability of miss detection and falsealarm errors in preamble detection is very small. Therefore, we can safelyignore detection errors in analyzing the system.



all detected preambles, that is, St,b = 1 for all b such thatMt,b ≥ 1. Otherwise, if V detect

t > d(Nt, Qt), the BS schedulesdata channels only to d(Nt, Qt) preambles randomly selectedout of V detect

t detected preambles. Therefore, the number ofscheduled preambles in cycle t, denoted by V sched

t , is given by

V schedt = min

{d(Nt, Qt), V

detectt

}. (7)

The probability that St = s given that Mt = m andd(Nt, Qt) = x is

Pr [St = s|Mt = m, d(Nt, Qt) = x] =

(vdetect

vsched

)−1

, (8)

where sb = 0 for all b such that mb = 0, vsched is the numberof b’s such that sb = 1, vdetect is the number of b’s such thatmb = 1, and vsched = min{x, vdetect}.

According to Mt,b and St,b, we can categorize each preambleb into the following four cases.

• Idle preamble (Mt,b = 0, St,b = 0): Preamble b is notchosen by any M2M UE.

• Unscheduled preamble (Mt,b ≥ 1, St,b = 0): Preamble bis chosen by at least one M2M UE, but no data channel isscheduled to preamble b.

• Collision preamble (Mt,b > 1, St,b = 1): A data channelis scheduled to preamble b, but preamble b is in collisionsince it is selected by more than one M2M UEs.

• Success preamble (Mt,b = 1, St,b = 1): Preamble b isselected by only one M2M UE, and a data channel isscheduled to preamble b. The M2M UE selecting preambleb successfully transmits a data packet.

Let V idlet , V unsched

t , V collt , and V succ

t denote the number ofidle, unscheduled, collision, and success preambles in cycle t,respectively. Note that the BS is able to know which case apreamble belongs to after the cycle.

The number of M2M UEs that successfully transmit datapackets in cycle t is equal to the number of success preambles,i.e., V succ

t . An M2M UE, which fails to transmit a data packetin cycle t, reattempts in cycle (t+ 1). Therefore, the number ofthe reattempting M2M UEs in cycle (t+ 1) is (Ut − V succ

t ).Other than these reattempting M2M UEs, new active M2M

UEs arrive at the system for transmitting a data packet. Let At

denote the number of new active M2M UEs that arrive duringcycle t. We define λ as the arrival rate of M2M UEs, whichis the expected number of M2M UEs arriving during a cycle.We assume that At follows a Poisson distribution with mean λ.Therefore, we have

Pr[At = i] =(λ)i exp(−λ)

i!. (9)

By adding up the number of the reattempting UEs and thenew active UEs, we can calculate the number of the active UEsin cycle (t+ 1) as

Ut+1 = Ut − V succt +At. (10)

IV. THROUGHPUT ANALYSIS AND PARAMETER

OPTIMIZATION FOR PROPOSED SCHEME

DURING A SINGLE CYCLE

A. Throughput Analysis

In this subsection, we analyze the throughput of the proposedscheme within a cycle given the number of participating M2MUEs and the number of RBs for the PRACH. The throughputwithin a cycle is defined as the expected number of M2M UEsthat successfully transmit data packets in a cycle, which is equalto the expected number of success preambles. Therefore, thethroughput is given as E[V succ

t ]. We conduct this analysis underthe condition that the numbers of RBs for M2M communica-tions and the PRACH (i.e., Qt and Nt, respectively) are given asQt = q and Nt = n. Then, the number of available preamblesis Bt = ηn and the number of available data channels is d(n, q).

To simplify the analysis, we use the Poisson assumption,which is widely used to analyze a slotted ALOHA (e.g., [14]).Let us assume that the number of the active UEs, Ut, followsthe Poisson distribution with mean αt. The active M2M UEsparticipate in the random access procedure with the probabilityof the access barring parameter Rt. Because of the character-istics of the Poisson distribution, the number of participatingM2M UEs (i.e., Pt) follows the Poisson distribution with meanRtαt. Then, a participating M2M UE randomly chooses apreamble out of ηn available preambles. The number of M2MUEs selecting preamble b (i.e., Mt,b) also follows the Poissondistribution with mean Rtαt/(ηn) and is independent of Mt,i

for i �= b.Preamble b is detected by the BS if and only if one or more

M2M UEs select preamble b. Therefore, the probability thatpreamble b is detected is

Pr[Mt,b ≥ 1] = 1− exp

(−Rtαt

ηn

). (11)

Since the event that preamble b is detected is independent ofthe event that preamble i is detected for i �= b, the number ofdetected preambles (i.e., V detect

t ) follows the Binomial distri-bution such that

V detectt ∼ Binom

(ηn, 1− exp

(−Rtαt

ηn

)). (12)

Recall that the number of scheduled preambles in cycle t isV schedt = min{V detect

t , d(n, q)}. From (12), we can calculatethe expected number of scheduled preambles as

E[V schedt

]=

ηn∑v=1

min {v, d(n, q)}(ηn

v

){1− exp

(−Rtαt

ηn

)}v

×{exp

(−Rtαt

ηn

)}(ηn−v)

. (13)

The probability that a scheduled preamble is a successpreamble (i.e., the probability that a scheduled preamble is



selected by only one M2M UE) is as follows.

Pr[Mt,b = 1|St,b = 1] = Pr[Mt,b = 1|Mt,b ≥ 1]

=Rtαt

ηn

{exp

(Rtαt

ηn

)− 1

}−1

. (14)

Now, the throughput is calculated as

E [V succt ] =

ηn∑v=1

E[V succt |V sched

t = v]Pr

[V schedt = v

]=

ηn∑v=1

vPr[Mt,b = 1|St,b = 1]Pr[V schedt = v

]= Pr[Mt,b = 1|St,b = 1] · E

[V schedt

]. (15)

From (13)–(15), the throughput is

E [V succt ]=

Rtαt

ηn

{exp

(Rtαt

ηn

)−1

}−1 ηn∑v=1

min {v, d(n, q)}

×(ηn

v

){1− exp

(−Rtαt

ηn

)}v {exp

(−Rtαt

ηn

)}(ηn−v)

.

(16)

The expression for the throughput in (16) is too complex tobe used for the parameter optimization. Therefore, we simplifythe expression by using the following approximation.4

E[V schedt

]=E

[min

{V detectt , d(n, q)

}]� min

{E[V detectt

], d(n, q)

}. (17)

Then, the throughput in (15) can be approximated as

E [V succt ]

� Pr[Mt,b = 1|St,b = 1]min{E[V detectt

], d(n, q)

}= min {E [V one

t ] ,Pr[Mt,b = 1|St,b = 1]d(n, q)}

= min

{Rtαt exp

(−Rtαt

ηn

),

× Rtαt

ηn

{exp

(Rtαt

ηn

)− 1

}−1

d(n, q)

}, (18)

where V onet is the number of preambles, each of which is

selected by only one M2M UE in cycle t (i.e., the number ofpreambles b such that Mt,b = 1).

To make the throughput a smooth function of n, we ap-proximate d(n, q) = (q − n)/δ by taking out a floor function.This approximation is valid since the approximated d(n, q) candeviate from the original value at most by one. Let p denotethe expected number of the participating M2M UEs such thatp = Rtαt. We define a throughput function as

ζ(p, n; q) = min {β(p, n), γ(p, n; q)} , (19)

4This approximation is accurate when V detectt is close to a deterministic

variable (i.e., when the variance of V detectt is relatively small).

Fig. 3. Throughput function according to p and n.

Fig. 4. Comparison between the throughput function obtained by analysis andthe expected throughput obtained by simulation.

where

β(p, n) = p exp

(− p

ηn

), (20)

γ(p, n; q) =p

ηn

{exp

(p

ηn

)− 1

}−1 (q − n

δ

). (21)

Then, the throughput in (18) can be obtained by letting p =Rtαt in the throughput function as E[V succ

t ] � ζ(Rtαt, n; q).In Fig. 3, we present the throughput function in (19) ac-

cording to p and n. For this graph, we set q = 60, η = 4, andδ = 1. To show that the approximation in (17) is acceptable, wepresent Fig. 4 that compares the expected throughput obtainedby analysis (i.e., the throughput function) and by simulation.We can see that the analytic result very closely approximatesthe simulation result.

In the rest of this section, we derive the optimal parametersthat maximize the throughput function in (19). In Section IV-B,we derive the optimal p when n is given. On the other hand, the



optimal n is calculated when p is given in Section IV-C. Finally,we jointly optimize p and n in Section IV-D.

B. Optimization of the Number of Participating M2M UEsGiven the Number of RBs for the PRACH

In this subsection, we find the optimal p that maximize thethroughput function ζ(p, n; q) when n is given. In the followingtheorem, we find p+(n; q) defined as

p+(n; q) = argmaxp

ζ(p, n; q). (22)

Theorem 1: The optimal solution p+(n; q) is calculated as

p+(n; q) = min {p1(n; q), p2(n; q)} , (23)

where

p1(n; q) = ηn, (24)

p2(n; q) = − ηn ln

(1− q − n

ηnδ

). (25)

Proof: Let p1(n; q) denote the optimal point maximizingβ(p, n) over p ≥ 0 when n is given. Then, we can derivep1(n; q) = ηn by differentiating β(p, n) with respect to p andby setting the result equal to zero. We define p2(n; q) as thesolution of the equation β(p, n) = γ(p, n; q) with respect top when n is given. Then, we can calculate that p2(n; q) =−ηn ln(1− (q − n/ηnδ)). The function β(p, n) is an increas-ing function of p when 0 ≤ p ≤ p1(n; q) and is a decreasingfunction of p when p > p1(n; q). On the other hand, γ(p, n; q)is a decreasing function when p ≥ 0.

In the case that p1(n; q) ≥ p2(n; q), we have ζ(p, n; q) ≤γ(p, n; q) ≤ γ(p2(n; q), n; q) = ζ(p2(n; q), n; q) for p ≥p2(n; q) since γ(p, n; q) is a decreasing function. In thiscase, we also have ζ(p, n; q) ≤ β(p, n) ≤ β(p2(n; q), n) =ζ(p2(n; q), n; q) for p ≤ p2(n; q) since β(p, n) is anincreasing function of p when 0 ≤ p ≤ p2(n; q). Therefore,ζ(p2(n; q), n; q) is a maximum value when p1(n; q) ≥p2(n; q).

In the case that p1(n; q) ≤ p2(n; q), we haveζ(p1(n; q), n; q) = β(p1(n; q), n) and β(p1(n; q), n) is amaximum value of β(p, n) over p ≥ 0. Therefore, we haveζ(p1(n; q), n; q) = β(p1(n; q), n) ≥ β(p, n) ≥ ζ(p, n; q) forp ≥ 0. This means that ζ(p1(n; q), n; q) is a maximum valuewhen p1(n; q) ≤ p2(n; q). Finally, we can conclude thatp+(n; q) = min{p1(n; q), p2(n; q)}. �

C. Optimization of the Number of RBs for the PRACH Giventhe Number of Participating M2M UEs

In this subsection, we find the optimal n that maximize thethroughput function in (19) when p is given. The followingtheorem finds n+(p; q) defined as

n+(p; q) = argmaxn

ζ(p, n; q). (26)

Theorem 2: The optimal solution n+(p; q) is calculated as

n+(p; q) = max {n1(p; q), n2(p; q)} , (27)

where

n1(p; q)=

{η

pW0

(−δp

qexp

(−1+ηδ

ηqp

))+1+ηδ

q

}−1

,

(28)

n2(p; q)=

{η

pW0

(− exp

(−1− p

ηq

))+

η

p+

1

q

}−1

.

(29)

In (28) and (29), W0 is the principal branch of the Lambert Wfunction.5

Proof: Let n1(p; q) denote the solution of the equationβ(p, n) = γ(p, n; q) with respect to n given p. We definen2(p; q) as the optimal n maximizing γ(p, n; q) over n ≥ 0when p is given. With some algebraic manipulation, we cancalculate n1(p; q) and n2(p; q) as in (28) and (29), respectively.The function γ(p, n; q) is an increasing function of n when 0 ≤n ≤ n2(n) and is a decreasing function of n when n ≥ n2(n).On the other hand, β(p, n) is an increasing function of n whenn ≥ 0.

In the case that n1(n) ≥ n2(n), we have ζ(p, n; q)≤γ(p, n; q)≤γ(p, n1(p; q); q)=ζ(p, n1(p; q); q) for n≥n1(p; q)since γ(p, n; q) is a decreasing function of n when n ≥n1(p; q). In this case, we also have ζ(p, n; q) ≤ β(p, n) ≤β(p, n1(p; q))=ζ(p, n1(p; q); q) for n≤n1(p; q) since β(p, n)is an increasing function of n. Therefore, ζ(p, n1(p; q); q) is amaximum value when n1(n) ≥ n2(n).

In the case that n1(n) ≤ n2(n), we have ζ(p, n2(p; q); q) =γ(p, n2(p; q); q) and γ(p, n2(p; q); q) is a maximum value ofγ(p, n; q) over n ≥ 0. Therefore, we have ζ(p, n2(p; q); q) =γ(p, n2(p; q); q) ≥ γ(p, n; q)≥ ζ(p, n; q) for n ≥ 0. Thismeans that ζ(p, n2(p; q); q) is a maximum value whenn1(n) ≤ n2(n). Finally, we can conclude that n+(p; q) =max{n1(p; q), n2(p; q)}. �

D. Joint Optimization of the Number of RBs for the PRACHand the Number of Participating M2M UEs

Now, we find the optimal parameters p and n that jointlymaximize the throughput function ζ(p, n; q). That is, we find(p∗(q), n∗(q)) such that

(p∗(q), n∗(q)) = argmax(p,n)

ζ(p, n; q). (30)

The following lemma plays an important role in finding theoptimal parameter.

5The Lambert W function is defined as the inverse relation of function y =x exp(x). With the Lambert W function, x can be expressed as x = W (y). Theprincipal branch of the Lambert W function, W0, is obtained if W is restrictedto a real value satisfying W ≥ −1.



Lemma 1: For the optimal solution (p∗(q), n∗(q)) of theoptimization problem in (30), it is satisfied that

β (p∗(q), n∗(q)) = γ (p∗(q), n∗(q); q) . (31)

Proof: We prove this lemma by showing that there ex-ists (p′, n′) such that ζ(p′, n′; q) > ζ(p, n; q) for given (p, n)such that β(p, n) �= γ(p, n; q). First, we consider the casethat β(p, n) > γ(p, n; q). In this case, ζ(p, n; q) = γ(p, n; q).Since γ(p, n; q) is a strictly decreasing function of a, thereexists ε > 0 such that β(p− ε, n) ≥ γ(p− ε, n; q) and γ(p−ε, n; q) > γ(p, n; q). For such ε, we have ζ(p− ε, n; q) =γ(p− ε, n; q) > γ(p, n; q) = ζ(p, n; q). Second, we considerthe case that β(p, n) < γ(p, n; q). In this case, ζ(p, n; q) =β(p, n). Since β(p, n) is a strictly increasing function of n,there exists ε > 0 such that β(p, n+ ε) ≤ γ(p, n+ ε; q) andβ(p, n+ ε) > β(p, n). For such ε, we have ζ(p, n+ ε, n; q) =β(p, n+ ε) > β(p, n) = ζ(p, n; q). �

From Lemma 1, we can limit the search space for finding theoptimal solution to (p, n) such that β(p, n) = γ(p, n; q). Let usdefine a function p̄ mapping n to the value p̄(n; q) such thatβ(p̄(n; q), n) = γ(p̄(n; q), n; q). From (20) and (21), we cancalculate p̄(n; q) as

p̄(n; q) = −ηn ln

(1− q − n

ηδn

). (32)

The optimal solution n∗(q) is

n∗(q) = argmaxn

ζ (p̄(n; q), n; q) , (33)

where

ζ (p̄(n; q), n; q) =β (p̄(n; q), n)

= − ηn

(1− q−n

ηδn

)ln

(1− q−n

ηδn

). (34)

In addition, we have p∗(q) = p̄(n∗(q); q). In the followingtheorem, we calculate the optimal solution (p∗(q), n∗(q)).

Theorem 3: The optimal solution (p∗(q), n∗(q)) of the opti-mization problem (30) is

p∗(q) =ηq

ηδ + 1, (35)

n∗(q) =q

ηδ + 1

{W0

(− 1

exp(1)· ηδ

ηδ + 1

)+ 1

}−1

. (36)

Proof: We define f(x) = ζ(p̄(x−1; q), x−1; q) and calcu-late the derivative of f(x) with respect to x as

df

dx=

ηδ + 1

δx2ln

(1 +

1

ηδ− qx

ηδ

)+

q

δx. (37)

If we let df/dx = 0, we have

x∗ =ηδ + 1

q

{W0

(− 1

exp(1)· ηδ

ηδ + 1

)+ 1

}. (38)

Since n∗(q) = 1/x∗, we can calculate (36). From (32) and (36),we have p∗(q) = p̄(n∗(q); q) = ηq/(ηδ + 1) as in (35). �

The maximum throughput is defined as

ζ∗(q) = max(p,n)

ζ(p, n; q) = ζ (p∗(q), n∗(q); q) . (39)

The maximum throughput is presented in the followingtheorem.

Theorem 4: The maximum throughput is calculated as

ζ∗(q) = −q

δ·W0

(− 1

exp(1)· ηδ

ηδ + 1

). (40)

Proof: Since we have ζ∗(q) = ζ(p∗(q), n∗(q); q) =β(p∗(q), n∗(q)), we can calculate the maximum throughput bysubstituting p∗(q) in (35) and n∗(q) in (36) into β in (20). �

V. JOINT ADAPTIVE RESOURCE ALLOCATION AND

ACCESS BARRING SCHEME

A. Load Estimation Algorithm

In this section, we propose a joint adaptive resource alloca-tion and access barring scheme based on the analytic resultsderived in the previous section. To this end, we first design aload estimation algorithm that estimates the number of activeM2M UEs attempting to send a data packet in each cycle. Letα̂t denote the estimated number of active M2M UEs at thebeginning of cycle t.

The load estimation algorithm updates α̂t to α̂t+1 based onthe observation in cycle t. The observation in cycle t includesthe number of collision preambles, denoted by V coll

t , and thenumber of unscheduled preambles, denoted by V unsched

t .Suppose that the load estimation algorithm calculates α̂t+1

given V collt and V unsched

t . Under the condition that Ut (i.e., thenumber of the active M2M UEs in cycle t) follows the Poissondistribution with mean α̂t, we can calculate the estimatedexpected number of the active M2M UEs in cycle (t+ 1) as

α̂t+1=E[Ut+1|V coll

t , V unschedt

]=E

[Ut − V succ

t +At|V collt , V unsched

t

]=E

[Ut − Pt|V coll

t , V unschedt

]+ E

[At|V coll

t , V unschedt

]+ E

[Pt − V succ

t |V collt , V unsched

t

]=(1−Rt)α̂t+λ+E

[Pt−V succ

t |V collt , V unsched

t

], (41)

where Pt is the number of the participating M2M UEs, V succt is

number of M2M UEs that successfully transmit a data packet,and At is the number of newly arriving M2M UEs duringcycle t.

In (41), we calculate the expected number of participatingM2M UEs which fail to transmit a data packet, i.e., E[Pt −V succt |V coll

t , V unschedt ]. The number of participating M2M UEs

selecting preamble b (i.e., Mt,b) follows the Poisson distribu-tion with mean Rtα̂t/Bt. Therefore, under the condition thatpreamble b is detected by the BS but is not scheduled, theexpected number of participating M2M UEs selecting preambleb is

E[Mt,b|Mt,b ≥ 1] =Rtα̂t/Bt

1− exp(−Rtα̂t/Bt). (42)



Similarly, under the condition that preamble b is scheduled butis in collision, the expected number of participating M2M UEsselecting preamble b is

E[Mt,b|Mt,b ≥ 2] =Rtα̂t/Bt(1− exp(−Rtα̂t/Bt)

1− (1 +Rtα̂t/Bt) exp(−Rtα̂t/Bt).

(43)

From (41)–(43), we can calculate

α̂t+1 =(1−Rt)α̂t + λ

+Rtα̂t/Bt(1− exp(−Rtα̂t/Bt)

1− (1 +Rtα̂t/Bt) exp(−Rtα̂t/Bt)V collt

+Rtα̂t/Bt

1− exp(−Rtα̂t/Bt)V unschedt . (44)

The BS obtains the knowledge of Rt, Bt, V collt , and V unsched

t

after cycle t. Therefore, the load estimation algorithm in the BScan update α̂t to α̂t+1 after cycle t, based on (44).

B. Deciding Optimal Number of RBs for PRACH and OptimalAccess Barring Parameter

The proposed joint adaptive resource allocation and accessbarring scheme tries to maximize the throughput in each cycle.Before each cycle t begins, the proposed scheme decides thenumber of RBs for PRACH (i.e., Nt) and the access barringparameter (i.e., Rt), when the number of RBs reserved forM2M communications in cycle t (i.e., Qt) and the estimatednumber of active M2M UEs (i.e., α̂t) are given. For doing this,we consider the following overload and underload cases.

• Overload case (α̂t ≥ p∗(Qt)): The estimated number ofactive M2M UEs is higher than the optimal number ofparticipating M2M UEs.

• Underload case (α̂t < p∗(Qt)): The estimated number ofactive M2M UEs is lower than the optimal number ofparticipating M2M UEs.

In the overload case, the access barring scheme should beused to control the number of participating M2M UEs. Thenumber of participating M2M UEs can be estimated as Pt =Rtα̂t, that should be equal to the optimal number of partic-ipating M2M UEs for optimality, i.e., Pt = Rtα̂t = p∗(Qt).Therefore, the access barring parameter is decided as

Rt =p∗(Qt)

α̂t=

1

α̂t

ηQt

ηδ + 1. (45)

On the other hand, Nt should be set to the optimal number ofRBs for the PRACH such that

Nt = n∗(Qt) =Qt

ηδ + 1

{W0

(− 1

exp(1)· ηδ

ηδ + 1

)+ 1

}−1

.

(46)

In the underload case, the access barring scheme is notactivated. That is, the access barring parameter is

Rt = 1. (47)

On the other hand, Nt is decided as the optimal solution pre-sented in Theorem 2. That is, Nt = n+(Pt;Qt) = n+(α̂t;Qt)since Rt = 1. In the underload case, we have n1(α̂t;Qt) ≥n2(α̂t;Qt), which leads to n+(α̂t;Qt) = n1(α̂t;Qt). There-fore, Nt in the underload case is

Nt =n1(α̂t;Qt)

=

{η

α̂tW0

(−δα̂t

Qtexp

(−1+ ηδ

ηQtα̂t

))+1+ηδ

Qt

}−1

. (48)

The capacity of the proposed scheme can be derived from themaximum throughput in Theorem 4. The capacity is defined asthe maximum arrival rate of M2M UEs (i.e., λ) that can stablybe supported by the system. If we assume that the proposedscheme can provide the maximum throughput in all cycles, wecan calculate the capacity, denoted by Ξ, as

Ξ=E [ζ∗(Qt)] = −E[Qt]

δ·W0

(− 1

exp(1)· ηδ

ηδ + 1

). (49)

VI. NUMERICAL RESULTS

A. Analysis and Simulation Results in a Single Cycle

In this subsection, we present analysis and simulation resultsof the proposed hybrid random access and data transmissionprotocol. In this subsection, we aim to show that the analysisresults in Theorems 3 and 4 match the simulation results. Theanalysis results include the optimal number of participatingM2M UEs (i.e., p∗(q) in (35)), the optimal number of RBsallocated for PRACH (i.e., n∗(q) in (36)), and the maximumthroughput (i.e., ζ∗(q) in (40)), where q is the number ofRBs reserved for M2M communications. The analysis resultsare compared with the simulation results. We simulate ourproposed protocol as explained in Section III with all possiblecombinations of parameters to find the optimal parametersachieving the maximum throughput.

Fig. 5 shows the optimal number of participating M2M UEsby analysis and by simulation. This figure is plotted as a func-tion of the number of RBs reserved for M2M communications(i.e., q). We can see that the analysis result p∗(q) well approx-imates the actual optimal number of participating M2M UEs,obtained by simulation. As more RBs are reserved for M2Mcommunications, the optimal number of participating M2MUEs increases since more M2M UEs can be accommodated.

In Fig. 6, we show the optimal number of RBs allocated forPRACH by analysis and by simulation. In this figure, we canalso see that the analysis result n∗(q) well matches the actualoptimal number of RBs allocated for PRACH.

Fig. 7 compares the maximum throughput by analysis andby simulation. The maximum throughput by analysis, ζ∗(q),agrees with the actual maximum throughput obtained bysimulation. We can see that the maximum throughput for δ = 1is higher than that for δ = 3 since only one RB is neededfor transmitting a data packet when δ = 1. The maximumthroughput can also be increased as more preambles can beconstructed from one RB. Therefore, we can see that themaximum throughput for η = 8 is higher than that for η = 4.



Fig. 5. The optimal number of participating M2M UEs within a single cycleby analysis (i.e., p∗(q)) and by simulation, as a function of the number of RBsreserved for M2M communications (i.e., q).

Fig. 6. The optimal number of RBs for the PRACH within a single cycleby analysis (i.e., n∗(q)) and simulation, as a function of the number of RBsreserved for M2M communications (i.e., q).

B. Simulation Results Over Multiple Cycles

In this subsection, we show the performance of the proposedscheme in terms of the throughput and the delay by using thesimulation over multiple cycles. The number of RBs reservedfor M2M communications, Qt, varies over time in this multiplecycle simulation. For each cycle, the simulation randomlydecides Qt out of the uniform distribution ranging from 0 toqmax. Then, the expectation of Qt is E[Qt] = qmax/2. In everycycle, a number of new active M2M UEs arrive at the systemaccording to the Poisson distribution with mean λ.

We compare the proposed scheme with two other schemes,one is the access barring only and the other is the slottedALOHA. The access barring only scheme is basically the sameas the proposed scheme except that the number of RBs allocatedto PRACH, Nt, in the access barring only scheme is fixed to acertain value. In our simulation, we fixedly set Nt = 30 for the

Fig. 7. The maximum throughput within a single cycle by analysis (i.e.,ζ∗(q)) and by simulation, as a function of the number of RBs reserved forM2M communications (i.e., q).

access barring only scheme. The access barring only schemeperforms the access barring by using p+(n; q) in (22). If theestimated number of active M2M UEs, α̂t, exceeds p+(Nt;Qt),the access barring only scheme decides Rt = p+(Nt;Qt)/α̂t.On the other hand, if α̂t ≤ p+(Nt;Qt), the access barring onlyscheme decides Rt = 1.

The slotted ALOHA scheme does not use PRACH, andtherefore all RBs for M2M communications are used as uplinkdata channels. Since there is no PRACH, an active M2MUE using the slotted ALOHA directly sends a data packetwithout transmitting a preamble or receiving an RAR messagein the random access procedure. However, the slotted ALOHAscheme still uses the access barring scheme. Therefore, in theslotted ALOHA scheme, an active M2M UE participates indata transmission with probability Rt, randomly selects onedata channel, and transmits a data packet via the selected datachannel. If more than one M2M UE sends a data packet via thesame data channel, the BS cannot decode any data packet viathat data channel.

The BS tracks the number of active M2M UEs over cyclesby means of the load estimation algorithm. Fig. 8 demonstrateshow well the load estimation algorithm tracks the number ofactive M2M UEs over 100 cycles. In this figure, we can see thatthe actual number of active M2M UEs is very well tracked bythe estimated number, α̂t.

Fig. 9 shows the performance of the load estimation algo-rithm in terms of the normalized mean square error (NMSE). Ifthe NMSE is measured from cycle 1 to cycle T , the NMSE isgiven as

NMSE =1

N

T∑t=1

(Ut − α̂t)2(

1N

∑Tt=1 Ut

)(1N

∑Tt=1 α̂t

) . (50)

In Fig. 9, we can see that the NMSE of the load estimationalgorithm becomes sufficiently low as the arrival rate of M2MUEs increases.



Fig. 8. The estimated number of active M2M UEs (i.e., α̂t) and the actualnumber of active M2M UEs (i.e., Ut) over cycles.

Fig. 9. The normalized mean square error (NMSE) of the load estimationalgorithm as a function of an arrival rate of M2M UEs (i.e., λ).

Figs. 10 and 11 respectively show the expected throughputand the expected delay of the proposed, access barring only,and slotted ALOHA schemes. The expected throughput is theexpected number of successfully transmitted data packets percycle. The expected delay is the expected number of cycles ittakes for an M2M UE to successfully transmit a data packetafter arriving at the system. These graphs are plotted accordingto the arrival rate (i.e., λ), which is an input load to the system.In the simulation, the expected number of RBs reserved forM2M communications (i.e., E[Qt]) is 50, meaning that the Qt israndomly selected out of the uniform distribution ranging from0 to 100.

In Fig. 10, we can see that the expected throughput of eachscheme increases according to the arrival rate λ until it reachesa certain saturation point. This saturation point of the expectedthroughput is a capacity of the respective scheme. The expectedthroughput of each scheme does not drop even when λ is

Fig. 10. The expected throughput over multiple cycles as a function of anarrival rate of M2M UEs (i.e., λ), when the proposed, access barring only, andslotted ALOHA schemes are used.

Fig. 11. The expected delay over multiple cycles as a function of an arrivalrate of M2M UEs (i.e., λ), when the proposed, access barring only, and slottedALOHA schemes are used.

higher than the capacity since excessive collisions are avoideddue to the access barring scheme. In Fig. 11, we can see thatthe expected delay of each scheme drastically increases afterthe arrival rate reaches the capacity of the respective scheme.We can see that the proposed scheme outperforms the accessbarring only and slotted ALOHA schemes in terms of both theexpected throughput and the expected delay.

In Fig. 12, we show the capacity of the proposed, accessbarring only, and slotted ALOHA schemes. The capacity isdefined as the maximum throughput achievable under a suffi-ciently high arrival rate. This graph is plotted by varying theexpected number of RBs reserved for M2M communications(i.e., E[Qt]). We can see that the proposed scheme has thecapacity higher than those of all other schemes.



Fig. 12. The capacity of the proposed, access barring only, and adaptiveresource allocation only schemes according to the expected number of RBsreserved for M2M communications.

Fig. 13. The collision probability over multiple cycles as a function of anarrival rate of M2M UEs (i.e., λ), when the proposed scheme is used.

In Fig. 13, we show the collision probability of the proposedscheme. We can see that the collision probability increases asλ increases. However, at some point the collision probabilitystops increasing due to the access barring that limits the numberof participating devices.

VII. CONCLUSION

In this work, we have proposed a hybrid random access anddata transmission protocol for M2M communications to reduceexcessive signaling overhead. In addition, the joint adaptive re-source allocation and access barring scheme has been proposedto maximize the M2M throughput and to resolve the congestionproblem in the random access procedure. We have derived aclosed-form analytic expression for the expected throughputand have obtained closed-form formulas for the optimal numberof participating M2M UEs and the optimal number of RBs

allocated to PRACH. Based on the simulation, we have shownthat the proposed scheme outperforms the access barring onlyand slotted ALOHA schemes by very wide margin in terms ofthe expected throughput, the expected delay, and the capacity.

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Dimas Tribudi Wiriaatmadja (S’14) received theB.S. degree in electrical engineering from the Uni-versity of Indonesia, Depok, Indonesia, in 2011.He is currently working toward the M.S. degree incomputer science at Seoul National University ofScience and Technology, Seoul, Korea. From 2011to 2013, he was with the Network ManagementSolution, Alstom Grid Co., Ltd., Indonesia. He iscurrently with Seoul National University of Scienceand Technology, working as an Assistant Researcherin the Intelligent Network Laboratory. His research

interests include machine-to-machine communication, radio resource manage-ment, wireless network optimization, smart grid, and vehicular communication.

Kae Won Choi (M’08) received the B.S. degreein civil, urban, and geosystem engineering and theM.S. and Ph.D. degrees in electrical engineering andcomputer science from Seoul National University,Seoul, Korea, in 2001, 2003, and 2007, respectively.From 2008 to 2009, he was with the Telecommu-nication Business, Samsung Electronics Co., Ltd.,Seoul. From 2009 to 2010, he was a Postdoc-toral Researcher with the Department of Electricaland Computer Engineering, University of Manitoba,Winnipeg, MB, Canada. In 2010, he joined the fac-

ulty at Seoul National University of Science and Technology, Seoul, where heis currently an Assistant Professor in the Department of Computer Scienceand Engineering. His research interests include machine-to-machine com-munication, device-to-device communication, cognitive radio, radio resourcemanagement, and wireless network optimization.


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