A Tractable Model of the LTE Signaling and Data...

1 INW2016 SanCandido/Innichen,January13,2016 Jimmy J.Nielsen

ATractableModeloftheLTESignalingandDataLimitationsinMachine-to-MachineCommunications

JimmyJ.Nielsen,[email protected],AalborgUniversity,Denmark

Basedonpublication:G.C.Madueño,J.J.Nielsen,D.M.Kim,N.K.Pratas,Č.Stefanović,P.Popovski,

"AssessmentofLTEWirelessAccessforMonitoringofEnergyDistribution intheSmartGrid",toAppearinIEEEJournalonSelectedAreasinCommunication,June2016.

ThisworkwaspartlyfundedbytheEUprojectSUNSEED,grantno.619437,partlybytheDanishCouncilforIndependentResearchgrantno.DFF-4005-00281“Evolvingwirelesscellularsystemsforsmartgrid

communications”,andpartlyby theDanishHighTechnologyFoundationviatheVirtuosoproject.


CellularM2Mapplicationexample:Real-timesmartdistributiongridmonitoring

§ ImprovedmonitoringtosupportSmartGrid§ Measurements/reportsfromsensorstobackendsystems

• primarilyuplink transmissions• Smallpayloadpackets

2

Telco Network

eNodeB

eNodeB

eNodeB

eSMeSMeSM

eSM

eSMeSM

eSM

SM

SM

eSM

eSMeSMSM

SM

SM

SM

SM

SMSM

DSO Monitoring and Operations Center

DSO State Estimation and Real-time Control

Generation

Transmission

Distribution

Consumers

a) b)

Fig. 1. a) High level architecture of power grid. b) Cellular smart grid with smart meters (SM) and enhanced smart meters (eSM).

provide the standardization bodies and mobile operators withinsights that can influence the relevant M2M standardizationactivities and the M2M-oriented evolution of the cellularnetworks.

The rest of this paper is organized as follows. We begin witha detailed description of LTE access reservation procedure inSection II. In Section III we provide the motivation of thiswork, review the relevant previous works, and outline thecontributions of the paper. The analytical model of LTE accessprocedure, which is the pivotal part of the paper, is provided inSection IV. In Section V we present numerical results, wherethe performance figures obtained with the proposed analyticalmodel are compared to the ones obtained by simulation. Theconclusions are given in Section VI.

We conclude this section by listing in Table I the acronymsthat are used throughout the paper.

II. DETAILED DESCRIPTION OF LTE ACCESS

In this section, we first describe the organization of the LTEaccess resources and channel in the downlink and uplink. Wethen turn to the description of the connection establishment.

A. DownlinkThe downlink resources in LTE in the case of frequency

division duplexing (FDD) are divided into time-frequencyunits, where the smallest unit is denoted as a resource element(RE). Specifically, the time is divided in frames, where everyframe has ten subframes, and each subframe is of durationt

s

= 1ms. An illustration of a subframe is presented in Fig. 2.Each subframe is composed in time by 14 OFDM modulatedsymbols, where the amount of bits of each symbol dependson the modulation used, which could be QPSK, 16QAM or64QAM. The system bandwidth determines the number offrequency units available in each subframe, which is typicallymeasured in resource blocks (RBs), where a RB is composed

TABLE IACRONYMS LIST

Acronym Description

ARP Access Reservation ProcedureCCE Control Channel ElementCFI Control Format IndicatorDER Distributed Energy sourceDSO Distribution System OperatorseSM Enhanced Smart MeterLTE Long Term EvolutionNAS Network Access Stratum

PBCH Physical Broadcast ChannelPCFICH Physical Control Format Indicator ChannelPDCCH Physical Downlink Control ChannelPDSCH Physical Downlink Shared ChannelPHICH Physical Hybrid ARQ ChannelPMU Phasor Measurement UnitPSS Primary Synchronization Signal

PUCCH Physical Uplink Control ChannelPUSCH Physical Uplink Shared Channel

RAR Random Access Response (MSG 2)RB Resource BlockRE Resource Element

RRC Radio Resource ControlSM Smart MeterSSS Secondary Synchronization Signal

WAMS Wide Area Measurement Systems

TABLE IIPDCCH FORMATS IN LTE

Format Purpose No. of CCEs

0 Transmission of resource grants for PUSCH 11 Scheduling PDSCH 22 Same as 1 but with MIMO 43 Transmission of power control commands 8

by 12 frequency units and 14 symbols, i.e., a total of 168REs. The amount of RBs in the system varies from 6 RBs in1.4 MHz system to 100 RBs in 20 MHz system.

In the downlink, there are two main channels; these are thephysical downlink control channel (PDCCH) and the physical


100devices@100kbps≠ [email protected]

Access Reservation Protocol

Data Payload

Dev 2Dev 1

Dev 3Dev 4Dev 5

Dev 7Dev 6

Dev 8Dev 9Dev 10Dev 11Dev 12

time

M2M

User 2User 1

User 3User 4User 5

time

H2x

Large fraction of resourcesis spent on signaling!


4

OFDM Symbols

Slot 0 Slot 1

PUCCH (x=0)Physical Uplink Control Channel


Slot 0 Slot 1

PRACHPhysical Random Access Channel

Uplink Subframe 0 Uplink Subframe 1

PUSCHPhysical Uplink Shared Channel

Resource Block (RB 0)






Fig. 3. Simplified illustration of uplink subframe 0 and subframe 1 organi-zation in a 1.4 MHz system with NCFI = 3.

4MSG4 - Contention Resolution

1 MSG1 - Preamble

3 MSG3 - Connection Request

2MSG2 - Random Access Response

eNodeBSmartMeter Additional Signaling (6 messages)

11 Data Transmission

Connection Release 12

Fig. 4. Message exchange between a smart meter and the eNodeB.

d = 54 are typically available for contention purposes andthe rest are reserved for timing alignment. The contention isslotted ALOHA based [11], [12], but unlike in typical ALOHAscenarios, the eNodeB can only detect which preambles havebeen activated but not if multiple activations (collisions) haveoccurred. In particular, this assumption holds in small/urbancells [13, Sec. 17.5.2.3].4

Via MSG 2, the eNodeB returns a random access response(RAR) to all detected preambles. The contending devices listento the downlink channel, expecting MSG 2 within time periodtRAR. If no MSG 2 is received and the maximum of T MSG 1

4If the cell size is more than twice the distance corresponding to themaximum delay spread, the eNodeB may be able to differentiate the casethat preamble has been activated by two or more users, but only if the usersare separable in terms of the Power Delay Profile [13], [14].

transmissions has not been reached, the device backs off andrestarts the random access procedure after a randomly selectedbackoff interval t

r

2 [0,Wc � 1]. If received, MSG 2 includesuplink grant information that indicates the RB in which theconnection request (MSG 3) should be sent. The connectionrequest specifies the requested service type, e.g., voice call,data transmission, measurement report, etc. When two devicesselect the same preamble (MSG 1), they receive the sameMSG 2 and experience collision when they send their MSG 3sin the same RB.

In contrast to the collisions for MSG 1, the eNodeB is ableto detect collisions for MSG 3. The eNodeB only replies to theMSG 3s that did not experience collision, by sending messageMSG 4 (i.e., RRC Connection Setup). The message MSG 4may carry two different outcomes: either the required RBsare allocated or the request is denied in case of insufficientnetwork resources. The latter is however unlikely in the caseof M2M communications, due to the small payloads. If theMSG 4 is not received within time period tCRT since MSG 1was sent, the random access procedure is restarted. Finally,if a device does not successfully finish all the steps of therandom access procedure within m+1 MSG 1 transmissions,an outage is declared.

After ARP exchange finishes, there is an additional ex-change of MAC messages between the smart meter and theeNodeB, whose main purposes is to establish security andquality of service for the connection, as well as to indicatethe status of the buffer at the device. These extra messagesare detailed further in Table IV.

Besides MAC messages, there are PHY messages includedin the connection establishment [15]. Table IV presents acomplete account of both PHY and MAC messages exchangedduring connection establishment, data report transmission andconnection termination (the PHY messages are indicated ingray). As it can be seen from the table, for every downlinkmessage a downlink grant in the PDCCH is required. Simi-larly, every time a smart meter wishes to transmit in the uplinkafter the ARP, it first need to ask for the uplink resourcesby transmitting a scheduling request in the PUCCH.5 This isfollowed by provision of an uplink grant in the PDCCH bythe eNodeB.

III. MOTIVATION, RELATED WORK AND CONTRIBUTIONS

As already outlined, the traffic profile generated by smart-grid monitoring devices is an example of Machine-to-Machine(M2M) traffic, characterized by a sporadic transmissions ofsmall amounts of data from a very large number of terminals.This is in sharp contrast with the bursty and high data-ratetraffic patterns of the human-centered services.

Another important difference is that smart grid servicestypically require a higher degree of network reliability andavailability than the human-centered services [16]. So far,cellular access has been optimized to human-centered trafficand M2M related standardization efforts came into focus onlyrecently [17].

5We note that the amount of resources reserved for PUCCH is very small forscheduling periodicity above 40 ms [15] and therefore will not be consideredin the following text and analysis.

WhatisperformanceofLTEforthisscenario?

ChallengesofM2Mcommunication§ Forsporadic/randomaccessofM2Mdevices

inLTE,theARPisusedforcontention,resourceallocation,securityprocedures,etc.

§ Possiblebottlenecks ofsignalinganddatainLTEchannels:• PRACH:PhysicalRandomAccessChannel• PDCCH:PhysicalDownlinkControlChannel• PUCCH:PhysicalUplinkControlChannel• PDSCH:PhysicalDownlinkSharedChannel• PUSCH:PhysicalUplinkSharedChannel

[1] J. J. Nielsen, D. M. Kim, G. C. Madueño, N. K. Pratas, P. Popovski, "A Tractable Model of the LTE Access Reservation Procedure for Machine-Type Communications", in proceedings of IEEE Globecom 2015, December 2015.

[2] 3GPP, “TR 36.822: LTE Radio Access Network (RAN) enhancements for diverse data applications, Rel. 11,” Tech. Rep., September 2011.

§ Relatedworkconsiderssomeof these,butnoonehasconsidered themjointlyinthislevelofdetail.

§ WeproposedmodelwithPRACHandPDCCHlimitations inconf.paper[1].§ ImpactofPUCCHcanbeneglectedfortypicalconfigurations accordingto[2].

LTE Access Reservation Protocol (ARP)


DetailedDescriptionofLTEAccess(1)Downlink(FDDcase):§ 10subframes perframe§ 1subframe is1ms§ Eachsubframehas:

• 14OFDMsymbols intime• 6– 100RBs(depending onBW)(1.4– 20MHz)

§ ForM2MwithoutMIMO:• In1.4MHzsystem:max3PDCCHmessagespersubframe.(thisbottleneckwasusedinGlobecom paper)

• PDSCHcarriesdownlinkARP+signaling messages.

• Limitedresources;formassiveaccess,resourcesmaybescarce.

OFDM Symbols







Frequency

PDCCHPhysical Downlink Control Channel

SSSSecondary Synchronization Signal

PSSPrimary Synchronization Signal

PBCHPhysical Broadcast Channel

PDSCHPhysical Downlink Shared Channel

Slot 0 Slot 1Downlink Subframe 0

PCFICHPhysical Control Format Indicator

Channel

PHICHPhysical Hybrid ARQ Channel


DetailedDescriptionofLTEAccess(2)Uplink:§ PUCCHcanbesharedbymultiple

devices,i.e.notabottleneck.§ Whenpresent,PRACH(RAO)

occupies6RBsperiodically:• 1RAOper20subframes upto1RAOin

everysubframe.§ PUSCHisusedforcontroland

data.• Forlargepayload,itmaybealimiting

factor.

OFDM Symbols

Slot 0 Slot 1



Slot 0 Slot 1










RAO: Random Access Opportunity


DetailedstudyofARPandsignaling

Messageoverview:

5

TABLE IVLIST OF MESSAGES EXCHANGED BETWEEN THE SMART METER AND THE ENODEB.

Step Channel Message

MAC Size (Bytes)

Uplink Downlink

AR

P

1 " PRACH MSG 1: Preamble – –2 # PDCCH Downlink Grant – –3 # PDSCH MSG 2: Random Access Response – 84 " PUSCH MSG 3: RRC Connection Request 7 –

5 # PHICH ACK – –6 # PDCCH Downlink Grant – –7 # PDSCH MSG 4: RRC Connection Setup – 388 # PUCCH ACK – –

Add

ition

alSi

gnal

ing

9 # PUCCH Scheduling Request – –10 # PDCCH UL Grant – –11 # PUSCH RRC Connection Setup Complete (+NAS: Service Req. and Buffer Status) 20 –12 # PHICH ACK – –13 # PDCCH Downlink Grant – –14 # PDSCH Security Mode Command – 1115 " PUCCH ACK – –19 " PUCCH Scheduling Request – –20 # PDCCH UL Grant – –21 " PUSCH Security Mode Complete 13 –22 # PHICH ACK – –16 # PDCCH Downlink Grant – –17 # PDSCH RRC Connection Reconfiguration (+NAS: Activate EPS Bearer Context Req.) – 11818 " PUCCH ACK – –23 " PUCCH Scheduling Request – –24 # PDCCH UL Grant – –25 " PUSCH RRC Connection Reconfiguration Complete 10 –26 # PHICH ACK – –

Dat

a

27 " PUCCH Scheduling Request – –28 # PDCCH UL Grant – –29 " PUSCH Report (Data) Variable –

30 # PHICH ACK – –31 # PDCCH Downlink Grant – –32 # PDSCH RRC Connection Release – 10

Due to the sporadic, i.e., intermittent nature of M2M com-munications, it is typically assumed that the M2M deviceswill have to establish the connection to the cellular accessnetwork every time they perform reporting. From Section IIit becomes apparent that connection establishment requiresextensive signaling, both in the uplink and the downlink, andthe total amount of the signaling information that is exchangedmay well over outweigh the information contained in the datareport. Moreover, the total number of resources available in theuplink and downlink is limited, and in the case of a massivenumber of M2M devices, the signaling traffic related to theestablishment of many connections may pose a significantburden to the operation of the access protocol. Thus, it isof paramount importance to consider the whole procedureassociated with the transmission of a data (report) in orderto properly estimate the number of M2M devices that can besupported in the LTE access network.

A. Related Work

Simple models to determine the probability of preamblecollision (MSG 1) in the PRACH channel are presented in3GPP standard documents [18], [19], [20] and in the scientificliterature [21], [22], [23]. Reception of a preamble is basedon energy detection [24] and a detected preamble indicatesthat there is at least one active user that sends that preamble.The drawback is the inability of the receiver to discern ifa preamble has been selected just by a single device or bymultiple devices [14]. More specifically, the eNodeB can onlyinfer whether the preamble is activated, but not how manydevices have simultaneously activated it.

To alleviate the PRACH overload, a group paging is pro-posed [25], where the base station adjusts the group size toprevent preamble collisions and PDCCH limitation. A relatedanalytical model to represent the number of contending, failed,and success uplink attempts was developed, however, the effectof PDCCH resource limitation has not been taken into account.An investigation of the ARP performance considering theeffect of the limitation of PDCCH resources, by modeling


LTEAccessReservationModelAccurateanalyticalmodelofserviceoutageprobability• rapidimplementationandevaluation– twoparts:1. One-shottransmission(a)§ Collisionprobability§ ProbabilityofLTEchannelbottlenecklimitations

2. Fullretransmissionmodel(b)§ Failedtransmissionattemptsareretrieduptom=9times.

IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success


One-shottransmissionOverview

Singletransmissionfailure:§ Independentevents

1. Preamblecollisions:§ Upperbound,d preambles

2. Channelbottlenecks:§ Withspecificqueuemodel

parametersforeachchannel:

13

PUSCH for the required messages. We model this as a sequence of two independent events:

pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�T)

⌘, (1)

where pf(�T) is the probability of a failed UE transmission, pc(�T) is the collision probability in

the preamble contention phase given UE request rate �T, and pe(�T) is the probability of failure

due to starvation of resources in the PDCCH, PDSCH, or PUSCH.

1) Preamble Contention Phase: We start by computing pc(�T). Let d denote the number of

available preambles (d = 54). Let the probability of not selecting the same preamble as one

other UE be 1� 1d

. Then the probability of a UE selecting a preamble that has been selected by

at least one other UE given at NT contending UEs, is:

P (Collision|NT) = 1�✓1� 1

d

◆NT�1

. (2)

Assuming Poisson arrivals with rate �T, then:

pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1

· P(NT= i,�T · �RAO)

#(3)

1�✓1� 1

d

◆�T·�RAO�1

,

where P(NT = i,�T · �RAO) is the probability mass function of the Poisson distribution with

arrival rate �T · �RAO. The inequality comes from applying Jensen’s inequality to the concave

function 1� (1� 1/d)x, where �T is the total arrival rate (including retransmissions), and �RAO

is the average number of subframes between RAOs.6 The computed pc(�T) is thus an upper

bound on the collision probability.

2) Access Granting Phase: The mean number of activated preambles in the contention phase

per RAO, is given by �A. As discussed in Section III, we assume that the eNodeB is unable

to discern between preambles that have been activated by a single user and multiple users,

respectively. This will lead to a higher �A, than in the case where the eNodeB is able to detect

the preamble collisions. The main impact of this assumption is that there will be an increased

rate of AG requests, even though part of these correspond to collided preambles, which even if

accepted will lead to retransmissions. In addition to the rate of activated preambles �A, we also

need the rate of singletons, i.e., non-collided, successful preamble activations denoted by �S.

6E.g., �RAO =1 if 10 RAOs per frame and �RAO =5 if 2 RAOs per frame.

13


pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�T)

⌘, (1)






other UE be 1� 1d




d

◆NT�1

. (2)


pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1


#(3)

1�✓1� 1

d

◆�T·�RAO�1

,















13


pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�T)

⌘, (1)






other UE be 1� 1d




d

◆NT�1

. (2)


pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1


#(3)

1�✓1� 1

d

◆�T·�RAO�1

,















IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success

15

TABLE IVAMOUNT OF CHANNEL RESOURCES USED FOR PDCCH, PDSCH AND PUSCH CHANNELS. FOR SHORT MESSAGE FORMAT,

ONLY BOLD MESSAGES ARE USED (RAR, RRC REQ., RRC COMP., AND DATA).

ARP Additional signaling

RAR

RRC

Request

RRCConnect

RRC

Complete

Reconf.DL

Reconf.UL

SecurityCmd.

SecurityConfig.

SecurityComplete

Data

Channel

PDCCH 1�e��T�RAO�RAO

0 �S �S �S �S �S �S 0 d BdataNfragBRB

ePDSCH d�A

BRARBRB

e 0 �SdBconnBRB

e 0 �SdBr-DLBRB

e 0 �SdBs-cmdBRB

e 0 0 0PUSCH 0 �AdBreq

BRBe 0 �SdBcomp

BRBe 0 �SdBr-UL

BRBe 0 0 �SdBcomp

BRBe �SdBdata

BRBe

PDCCH, PDSCH, and PUSCH, we define pe(�T) from (1) as:

pe(�T) = 1�⇣1� pq(�PDCCH, µPDCCH, Td-PDCCH)

⌘

·⇣1� pq(�PDSCH, µPDSCH, Td-PDCSH)

⌘

·⇣1� pq(�PUSCH, µPUSCH, Td-PUSCH)

⌘, (8)

where the respective �, µ, and Td values are derived in the following. For the � values, we

elaborate in Table IV the amount of resources used in each of the channels for the relevant

messages from Table III. For each, the resources are given in terms of PDCCH, PDSCH, or

PUSCH elements per subframe. The model parameters are described in Table V.

The used M/M/1 model requires a single timeout value to specify the impatience threshold of

the costumers. However, in the modeled LTE access procedure, there are several timers involved

that cover different and sometimes overlapping parts of the message exchange. While this clearly

cannot be modeled very accurately with the used M/M/1 model, we will simply use a typical

minimum timer value for each of the channels. Assuming that LTE has not been designed with

timer values so low that the capacity is limited by timeouts and not by resource scarcity, this

simplifying assumption should not have any significant impact on the results.

a) PDCCH model: The arrival rate for the PDCCH model �PDCCH, which describes the

number of used PDCCH elements per subframe, is given as the sum of the PDCCH row in

Table IV. The service rate µPDCCH is the number of available PDCCH slots per subframe, i.e.,

NPDCCH, and the timer value is the standard RAR timeout:

�PDCCH =1� e��T·�RAO

�RAO+�S(6 + d Bdata

NfragBRBe)

µPDCCH = NPDCCH


ChannelconstraintsPrinciple1. PDDCH,PDSCHandPUSCHhavelimitedresources:§ Eachchannelcanbeseenasqueuesystem:

• servicenodewithservicerate𝜇• Requestarrivalrate𝜆

§ Failureprobability:• Ifrequestnotprocessedwithinshortdeadline,time-outandretry.• Calculatedasprobabilityofimpatientcustomernotbeingserved.

§ ClosedformexpressionisavailableforM/M/1model[28]:

• where𝜌 = %&isqueue utilization factor,andTd istimeoutvalue.

• WhiletheM/D/1(deterministic servicetimes)modelshouldfitbetter,wehavefoundthatinpracticetheM/M/1approximationdeliversindistinguishable results.

IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success

14

The �A and �S can be well approximated, while assuming that the selection of each preamble

by the contending users is independent, by,

�A = [1� P (X = 0)� P (X = 1)] · d/�RAO, (4)

�S =P (X = 1) · d/�RAO, (5)

where P(X = k) is the probability of k successes, which can be well approximated with a

Poisson distribution with arrival rate �pre = �T�RAO/d, i.e.:

P (X = k) ⇡ (�pre)ke��pre

k!. (6)

Since the limitations in the AG phase are primarily given from the demanded resources from

each of the channels PDCCH, PDSCH, and PUSCH and the corresponding timing requirements,

we assume that each of these can be modeled as a separate queue with impatient costumers. That

is, we assume that the loss probability pq(�A) can be seen as the long-run fraction of costumers

that are lost in a queuing system with impatient costumers [26].

Based on the message exchange diagram in Section III-C, we specify in the following text the

arrival rate, service rate and the maximum latency for each of the channels PDCCH, PDSCH,

and PUSCH.

In general, since LTE uses fixed size time slots, the most obvious approach would be to use

an M/D/1 model structure, as presented in [26]. Unfortunately, the expression to compute the

fraction of lost customers pq(�, µ, Td) for the M/D/1 queue does not have a closed form solution.

However the equivalent expression for the M/M/1 queue has a closed form solution. Through an

extensive study, we have found that with the parameter ranges that we use, there is no noticeable

difference in the results. Thus, in the following we use the M/M/1 model to compute pq(�, µ, Td)

as:

pq(�, µ, Td) =(1� ⇢) · ⇢ · ⌦1� ⇢2 · ⌦ , with ⌦ = e�µ·(1�⇢)·⌧q , (7)

where ⇢ = �

µ

is the queue load, µ is the service rate, with ⌧q = Td � 1µ

and Td is the max waiting

time.

Assuming we can use the M/M/1 model structure to obtain the failure probabilities of the[28] A. G. De Kok and H. Tijms, “A queueing system with impatient customers,” Journal of Applied Probability, vol. 22, no. 3, pp. 688–696, Sept. 1985.


ChannelconstraintsParametersPDCCH:

PDSCH:

PUSCH:

§ Thehighlevelofdetailinthemodelrequiresmanyparameters.

IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success

8

where P(X = k) is the probability of k successes, which canbe well approximated with a Poisson distribution with arrivalrate �pre = �T�RAO/d, i.e.:

P (X = k) ⇡(�pre)ke��pre

k!. (6)

Since the limitations in the AG phase are primarily givenfrom the demanded resources from each of the channelsPDCCH, PDSCH, and PUSCH and the corresponding timingrequirements, we assume that each of these can be modeled asa separate queue with impatient costumers. That is, we assumethat the loss probability pq(�A) can be seen as the long-runfraction of costumers that are lost in a queuing system withimpatient costumers [33].

Based on the message exchange diagram in Section II-C,we specify in the following text the arrival rate, service rateand the maximum latency for each of the channels PDCCH,PDSCH, and PUSCH.

In general, since LTE uses fixed size time slots, the mostobvious approach would be to use an M/D/1 model structurewhere service times are deterministic, as presented in [33].Unfortunately, the expression to compute the fraction of lostcustomers pq(�, µ, Td) for the M/D/1 queue does not havea closed form solution. However, the equivalent expressionfor the M/M/1 queue, which assumes exponential durationservice intervals, does have a closed form solution. Throughan extensive study, we have found that with the parameterranges that we use, there is no noticeable difference in theresults. Furthermore, and most importantly, our results withthis model fit well to simulation results, as shown in sec. V-B.Thus, in the following we use the M/M/1 model to computepq(�, µ, Td) as:

pq(�, µ, Td) =(1� ⇢) · ⇢ · ⌦1� ⇢

2 · ⌦ , with ⌦ = e

�µ·(1�⇢)·⌧q, (7)

where ⇢ = �

µ

is the queue load, µ is the service rate, with⌧q = Td � 1

µ

and Td is the max waiting time.Assuming we can use the M/M/1 model structure to obtain

the failure probabilities of the PDCCH, PDSCH, and PUSCH,we define pe(�T) from (1) as:


⌘


⌘


⌘, (8)

where the respective �, µ, and Td values are derived in thefollowing. For the � values, we elaborate in Table VI theamount of resources used in each of the channels for therelevant messages from Table IV. For each, the resources aregiven in terms of PDCCH, PDSCH, or PUSCH elements persubframe. The model parameters are described in Table VII.

The used M/M/1 model requires a single timeout value tospecify the impatience threshold of the costumers. However,in the modeled LTE access procedure, there are several timersinvolved that cover different and sometimes overlapping partsof the message exchange. While this clearly cannot be modeledvery accurately with the M/M/1 model used here, we will

simply use a typical minimum timer value for each of thechannels. Assuming that LTE has not been designed with timervalues so low that the capacity is limited by timeouts and notby resource scarcity, this simplifying assumption should nothave any significant impact on the results.

a) PDCCH model: The arrival rate for the PDCCHmodel �PDCCH, which describes the number of used PDCCHelements per subframe, is given as the sum of the PDCCHrow in Table VI. The service rate µPDCCH is the number ofavailable PDCCH slots per subframe, i.e., NPDCCH, and thetimer value is the standard RAR timeout:

�PDCCH =1� e

��T·�RAO

�RAO+�S(6 +

⇠Bdata

NfragBRB

⇡)

µPDCCH = NPDCCH

Td-PDCCH = 10,

where dxe is the smallest integer not less than x.b) PDSCH model: Similarly, the arrival rate for the

PDSCH model is the sum of the corresponding row in Ta-ble VI, the service rate is the number of available PDSCHelements per subframe, and the timer value is set to 40, whichis a typical minimum value of the PDSCH related timers.

�PDSCH=

⇠�ABRAR

BRB

⇡+�S

✓⇠Bconn

BRB

⇡+

⇠Br-DL

BRB

⇡+

⇠Bs-cmd

BRB

⇡◆

µPDSCH = NDLRB

Td-PDSCH = 40.

c) PUSCH model: Finally, as above, the arrival rate forthe PUSCH model is the sum of the corresponding row inTable VI, the service rate is the number of available PUSCHelements per subframe subtracted the resources used for RAOs,and the timer value is set to 40, which is a typical minimumvalue of the PUSCH related timers.

�PUSCH =�A

⇠Breq

BRB

⇡

+�S

✓⇠Bcomp

BRB

⇡+

⇠Br-UL

BRB

⇡+

⇠Bs-comp

BRB

⇡+

⇠Bdata

BRB

⇡◆

µPUSCH =NULRB � 6 · 10

�RAO

Td-PUSCH =40.

B. m-Retransmissions Model

During the ARP, UEs may experience failures of the trans-mitted packets (MSG1 and MSG3) and the received packets(MSG2 and MSG4). When a failure occurs with probabilitypf(�T), the total arrival rate �T changes to represent also theadditional arrivals of retransmissions. Further, these additionalarrivals affect the probability of failure again. To modelthis behavior, we apply the two-dimensional Markov chainapproach first presented in [34]. The LTE adapted version ofthis model have already been proposed in [31], [35] and in thiswork we consider an extended version of the model in [31] toexplicitly model the transmissions of MSG1 and MSG3.

8



k!. (6)




pq(�, µ, Td) =(1� ⇢) · ⇢ · ⌦1� ⇢

2 · ⌦ , with ⌦ = e

�µ·(1�⇢)·⌧q, (7)

where ⇢ = �

µ


µ




⌘


⌘


⌘, (8)





�PDCCH =1� e

��T·�RAO

�RAO+�S(6 +

⇠Bdata

NfragBRB

⇡)

µPDCCH = NPDCCH

Td-PDCCH = 10,



�PDSCH=

⇠�ABRAR

BRB

⇡+�S

✓⇠Bconn

BRB

⇡+

⇠Br-DL

BRB

⇡+

⇠Bs-cmd

BRB

⇡◆

µPDSCH = NDLRB

Td-PDSCH = 40.


�PUSCH =�A

⇠Breq

BRB

⇡

+�S

✓⇠Bcomp

BRB

⇡+

⇠Br-UL

BRB

⇡+

⇠Bs-comp

BRB

⇡+

⇠Bdata

BRB

⇡◆


�RAO

Td-PUSCH =40.



8



k!. (6)




pq(�, µ, Td) =(1� ⇢) · ⇢ · ⌦1� ⇢

2 · ⌦ , with ⌦ = e

�µ·(1�⇢)·⌧q, (7)

where ⇢ = �

µ


µ




⌘


⌘


⌘, (8)





�PDCCH =1� e

��T·�RAO

�RAO+�S(6 +

⇠Bdata

NfragBRB

⇡)

µPDCCH = NPDCCH

Td-PDCCH = 10,



�PDSCH=

⇠�ABRAR

BRB

⇡+�S

✓⇠Bconn

BRB

⇡+

⇠Br-DL

BRB

⇡+

⇠Bs-cmd

BRB

⇡◆

µPDSCH = NDLRB

Td-PDSCH = 40.


�PUSCH =�A

⇠Breq

BRB

⇡

+�S

✓⇠Bcomp

BRB

⇡+

⇠Br-UL

BRB

⇡+

⇠Bs-comp

BRB

⇡+

⇠Bdata

BRB

⇡◆


�RAO

Td-PUSCH =40.



9

TABLE VIAMOUNT OF CHANNEL RESOURCES USED FOR PDCCH, PDSCH AND PUSCH CHANNELS. FOR SHORT MESSAGE FORMAT, ONLY BOLD MESSAGES ARE

USED (RAR, RRC REQ., RRC COMP., AND DATA).

ARP Additional signaling

Channel RAR

RRC

Request

RRCConnect

RRC

Complete

Reconf.DL

Reconf.UL

SecurityCmd.

SecurityConfig.

SecurityComplete

Data

PDCCH 1�e��T�RAO�RAO

0 �S �S �S �S �S �S 0 d BdataNfragBRB

ePDSCH d�A

BRARBRB

e 0 �SdBconnBRB

e 0 �SdBr-DLBRB

e 0 �SdBs-cmdBRB

e 0 0 0

PUSCH 0 �AdBreqBRB

e 0 �SdBcompBRB

e 0 �SdBr-ULBRB

e 0 0 �SdBcompBRB

e �SdBdataBRB

e

1, 0 1, 1 1, 2 1,𝑊𝑐 − 2 1,𝑊𝑐 − 1"

𝑚, 0 𝑚, 1 𝑚, 2 𝑚,𝑊𝑐 − 2 𝑚,𝑊𝑐 − 1"

𝑖 − 1, 0

𝑖, 0 𝑖, 1 𝑖, 2 𝑖,𝑊𝑐 − 2 𝑖,𝑊𝑐 − 1""/c cp W

"/c cp W

"/c cp W

"/c cp W

"

"

" /c cp W0, 0

1 cp−

𝐶𝑅 1

1 ep−

ep

Connect

𝐶𝑅 𝑖 − 1

𝐶𝑅 𝑖

𝐶𝑅 𝑚

off on1 p−onp𝐶𝑅 0

1 cp−

1 cp−

1 cp−

1 cp−

/e cp W

/e cp W

/e cp W

/e cp W

/e cp W

drop

cp

1

Fig. 6. Markov chain model for m retransmissions during the ARP.

TABLE VIIVARIABLE DEFINITIONS

Variable Value Description

BRAR 8 number of bytes used for the RAR messageBRB 36 number of bytes per resource blockBreq 7 size of RRC request message in bytesBconn 38 size of RRC connect message in bytesBcomp 20 size of RRC complete message in bytesBr-DL 118 size of RRC reconfigure DL message in bytesBr-UL 10 size of RRC reconfigure UL message in bytesBs-cmd 11 size of security command message in bytesBs-comp 13 size of security complete message in bytesBdata Variable size of the data payload in bytesNPDCCH Variable number of PDCCH pointers per subframeNDLRB Variable number of resource blocks in PDSCHNULRB Variable number of resource blocks in PUSCHNfrag 6 fragmentation threshold in RBs

Fig. 6 shows the structure of the Markov chain model form retransmissions during the ARP. The uplink traffic at UEis generated with probability pon. The UE enters the initial

transmission state {0, 0} from the off state:

P (0, 0| off) = pon,

where pon is the traffic generation probability defined as pon =1� e

��I .

The state depicted {i, k} represents the ith preamble re-transmission attempt and kth backoff counter. Retransmissionattempts are allowed up to m times. The maximum backoffwindow size is denoted by W

c

. If a preamble transmission isnot successful, the backoff counter is increased and a randombackoff state is entered with probability:

P ( i, k| i� 1, 0) =p

c

W

c

, 0 k W

c

� 1, 1 i m,

where p

c

denotes the collision probability of the preambletransmission.

The CR(i) state represents the connect request attempt afterthe success of the ith preamble transmission attempt. Thetransition probability is:

P (CR(i)| i, 0) = 1� p

c

, 0 i m.

If the connect request attempt succeeds, the UE will be in


m-retransmissions§ Fromsteadystateprobabilitiesb*:

§ Iterativeupdatingoffixedpointequationtofind𝜆':

21

Using (18), the value of �T can be obtained by solving the following iterative equation:

�T = NTX(�T) · �I = �I1� (p

e

(1� pc

) + pc

)m+1

1� (pe

(1� pc

) + pc

), (19)

where �I is constant but pc and pe are both functions of �T as defined in (3) and (8).

V. SYSTEM PERFORMANCE EVALUATION

In this section we first describe the used traffic models. Thereafter we present and discuss

numerical results, where we compare results from our analytical model to the simulation results.

A. Model of the Smart Grid Traffic

At the time of writing, there is no standardized traffic model that could be used to describe

reporting activities of the eSMs. In the following, we develop a model by considering the typical

smart metering traffic models and enhancing them in order to achieve PMU-like functionalities

that eSMs are expected to have.

In the literature there are different examples of traffic models for smart meters, such as [29],

[30], [31], [32]. Of these, the OpenSG Smart Grid Networks System Requirements Specification

(described in [29]) from the Utilities Communications Architecture (UCA) user group is the

most coherent and detailed network requirement specification. This specification describes the

typical configuration where billing reports are collected as often as every 1 hour for industrial

smart meters and every 4 hours for residential smart meters. While this is sufficient for billing

purposes, such low reporting frequency does not allow real-time monitoring and control. A way

to enable this, as proposed and analysed in our work in [16], would be to drastically increase

the reporting frequency of all smart meters so that reports are collected, e.g., every 10 seconds.

While such a configuration is not described in OpenSG [29], it is mentioned that on-demand

meter read response messages are 100 bytes, wherefore we will use this value in the following

evaluation.

Besides the basic measurements of consumption and production, the distribution system op-

erators need to collect more detailed information of the distribution grid behavior in the form

of power phasors from certain, strategically chosen, measurement points. As an example in the

following numerical results, we assume that every 10 seconds an eSM sends a measurement

report that consist of concatenated PMU measurements (1 Hz sample rate) from the preceding

10 second measurement interval. The samples are, as specified in PMU standards IEEE 1588 and

!

!

!

!

f/ cp W

!

f/ cp W

!

f/ cp W

!

f/ cp W

!

!

!

f/ cp W

f1 p−

Connect offon

1 p−onp

drop

fp

1

Fig. 3. Markov Chain backoff model to estimate number of requiredtransmissions. The states in the red dashed box are used to calculate NTX.


When UEs are allowed to make retransmissions the proba-bility of an UE becoming in outage is the probability that noneof the allowed m+1 transmissions attempts are successful.

When retransmissions are allowed (m > 0), the total arrivalrate �T must include the extra arrivals caused by the UEs’retransmissions. The number of retransmissions �R is howevera result of the limit m and transmission error probabilitypf, which in turn depends on the number of retransmissions�R. This chicken and egg problem can be solved iterativelyusing a derivative of the Bianchi model [16] applied to oursystem model. Specifically, we are using a model adapted toLTE, with a structure similar to the one presented in [17].The following derivations of the number of transmissions andoutage probabilities have, to the best of our knowledge, notbeen presented previously.

The mean number of required transmissions NTX and outageprobability Poutage, are computed with help of the Markovchain model depicted in Fig. 3. In the Markov chain model, thestate index {i, k} denotes the ith transmission attempt stageand kth backoff counter. The number of allowed retransmis-sions is then given by m.

Whenever the one-shot transmission is successful, depictedin Fig. 2(a), the UE enters the connect state:

P (connect| i, 0) = 1� pf, 0 i m.

Where, pf is short for pf(�T). Whenever the one-shot accessfails, the UE increases the backoff counter:

P ( i, k| i� 1, 0) =pf

Wc

,

where 0 k Wc

� 1 and 1 i m.At the last stage of the Markov chain, the UE enters the

drop state if the transmission fails:

P (drop|m, 0) = pf(�T).

The UE enters the off state after the connect or the drop states,with probability:

P (off| drop) = P (off| connect) = 1.

From the off state, the node enters the first transmissionstate {0, 0} with probability pon:

P (0, 0| off) = pon.

where the probability pon is defined as pon = 1� e��I .Let b

i,k

be the steady state probability that a UE is at state{i, k}. Then b

i,k

can be derived as:

bi,k

=Wc�k

Wcpfbi�1,0=

Wc�k

Wcpifb0,0=

Wc�k

Wcpifponboff, (7)

for 1 i m and 0 k Wc � 1.Let bconnect be the steady state probability that a node is at

connect state:

bconnect =mX

i=0

(1� pf) bi,0 =mX

i=0

(1� pf) pi

fponboff

=�1� pm+1

f�ponboff.

By imposing the probability normalization condition, asdetailed in Appendix A, we find boff as:

boff =2 (1� pf)

2 (1� pf) (1 + 2pon) + pon (Wc + 1) pf (1� pmf ).

Since a transmission will eventually either finish success-fully in the connect state or unsuccessfully in the drop state,the outage probability can be computed as:

Poutage =bdrop

bdrop + bconnect= pm+1

f , (8)

where bdrop and bconnect, whose derivations are shown in theAppendix A, can be computed as:

bconnect=2 (1�pf)

�1�pm+1

f�pon

2 (1�pf) (1+2pon)+pon (Wc+1) pf (1�pmf ), (9)

bdrop =2 (1�pf) p

m+1f pon

2 (1�pf) (1+2pon)+pon (Wc+1) pf (1�pmf ). (10)

The number of required transmissions can be estimated fromthe steady state probabilities, keeping in mind that b

i,0/b0,0represents the probability of using i+1 or more transmissionattempts to deliver a packet, and b

m,0/b0,0 is the probabilityof using exactly m+1 transmission attempts:

NTX(�T)=

✓m�1Pi=0

(i+ 1) · (bi,0 � b

i+1,0)

◆+ (m+ 1) · b

m,0

b0,0

=(1�pf)m�1X

i=0

(i+1)pif+(m+1) pmf =1� pm+1

f1� pf

.

(11)

From the number of transmissions, the value of �T can besolved iteratively using the fixed point equation:

�T = NTX(�T) · �I = �I1� pf(�T)m+1

1� pf(�T). (12)

!

!

!

!

f/ cp W

!

f/ cp W

!

f/ cp W

!

f/ cp W

!

!

!

f/ cp W

f1 p−

Connect offon

1 p−onp

drop

fp

1







P (connect| i, 0) = 1� pf, 0 i m.


P ( i, k| i� 1, 0) =pf

Wc

,

where 0 k Wc



P (drop|m, 0) = pf(�T).




P (0, 0| off) = pon.


i,k


i,k

can be derived as:

bi,k

=Wc�k

Wcpfbi�1,0=

Wc�k

Wcpifb0,0=

Wc�k

Wcpifponboff, (7)


connect state:

bconnect =mX

i=0

(1� pf) bi,0 =mX

i=0

(1� pf) pi

fponboff

=�1� pm+1

f�ponboff.


boff =2 (1� pf)



Poutage =bdrop


f , (8)


bconnect=2 (1�pf)

�1�pm+1

f�pon


bdrop =2 (1�pf) p

m+1f pon





NTX(�T)=

✓m�1Pi=0

(i+ 1) · (bi,0 � b

i+1,0)

◆+ (m+ 1) · b

m,0

b0,0

=(1�pf)m�1X

i=0

(i+1)pif+(m+1) pmf =1� pm+1

f1� pf

.

(11)


�T = NTX(�T) · �I = �I1� pf(�T)m+1

1� pf(�T). (12)

!

!

!

!

f/ cp W

!

f/ cp W

!

f/ cp W

!

f/ cp W

!

!

!

f/ cp W

f1 p−

Connect offon

1 p−onp

drop

fp

1







P (connect| i, 0) = 1� pf, 0 i m.


P ( i, k| i� 1, 0) =pf

Wc

,

where 0 k Wc



P (drop|m, 0) = pf(�T).




P (0, 0| off) = pon.


i,k


i,k

can be derived as:

bi,k

=Wc�k

Wcpfbi�1,0=

Wc�k

Wcpifb0,0=

Wc�k

Wcpifponboff, (7)


connect state:

bconnect =mX

i=0

(1� pf) bi,0 =mX

i=0

(1� pf) pi

fponboff

=�1� pm+1

f�ponboff.


boff =2 (1� pf)



Poutage =bdrop


f , (8)


bconnect=2 (1�pf)

�1�pm+1

f�pon


bdrop =2 (1�pf) p

m+1f pon





NTX(�T)=

✓m�1Pi=0

(i+ 1) · (bi,0 � b

i+1,0)

◆+ (m+ 1) · b

m,0

b0,0

=(1�pf)m�1X

i=0

(i+1)pif+(m+1) pmf =1� pm+1

f1� pf

.

(11)


�T = NTX(�T) · �I = �I1� pf(�T)m+1

1� pf(�T). (12)

IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success

1, 0 1, 1 1, 2 1,𝑊𝑐 − 2 1,𝑊𝑐 − 1"

𝑚, 0 𝑚, 1 𝑚, 2 𝑚,𝑊𝑐 − 2 𝑚,𝑊𝑐 − 1"

𝑖 − 1, 0

𝑖, 0 𝑖, 1 𝑖, 2 𝑖,𝑊𝑐 − 2 𝑖,𝑊𝑐 − 1""/c cp W

"/c cp W

"/c cp W

"/c cp W

"

"

" /c cp W0, 0

1 cp−

𝐶𝑅 1

1 ep−

ep

Connect

𝐶𝑅 𝑖 − 1

𝐶𝑅 𝑖

𝐶𝑅 𝑚

off on1 p−onp𝐶𝑅 0

1 cp−

1 cp−

1 cp−

1 cp−

/e cp W

/e cp W

/e cp W

/e cp W

/e cp W

drop

cp

1

Based on LTE-adapted version of Bianchi’s backoff model, by X. Yang, A. Fapojuwo, and E. Egbogah, “Performance Analysis and Parameter Optimization of Random Access Backoff Algorithm in LTE,” in Proc. of the IEEE Vehicular Technology Conference (VTC Fall 2012), Sept. 2012.


Evaluationscenario

Trafficmodel:§ EachdevicehasPoisson

trafficgenerator:• 𝜆)

*++ = 10 sinterval

• 𝜆. = ∑ 𝜆)*++0

)12§ Packetsizes

• 100bytes• 1Kbytes

Verification/validation:§ ComparisontoMatlab

simulationthatimplementstheLTEaccessreservationprotocol[11],[12].

LTEconfiguration:

IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success

[11] 3GPP, “TS 36.321 E-UTRA medium access control (MAC) protocol specification,” Tech. Rep., 2015.

[12] 3GPP, “TS 36.213 E-UTRA physical layer procedures,” Tech. Rep., 2015.

23

TABLE VILTE SIMULATION AND MODEL PARAMETERS

Parameter Value

Preambles per RAO (d) 54Subframes between RAOs (�RAO) 20 or 5Max number of retransmissions (m) 0 or 9CFI Value 3 [19]Number of CCEs (µ) 6 or 21System bandwidth 1.4 MHz or 5 MHzeNodeB processing time 3 msUE processing time 3 msMSG 2 window (tRAR) 10 msContention time-out (tCRT) 40 msBackoff limit (Wc) 20 msRest of Messages window 40 ms

Arrivals/s 0 500 1000 1500 2000 2500 3000 3500 4000

P Out

age

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1Sim: 1.4 MHz - ARP + Data (100 bytes)Ana: 1.4 MHz - ARP + Data (100 bytes)Sim: 1.4 MHz - ARP + Data (1 kbyte)Ana: 1.4 MHz - ARP + Data (1 kbyte)Sim: 5 MHz - ARP + Data (100 bytes)Ana: 5 MHz - ARP + Data (100 bytes)Sim: 5 MHz - ARP + Data (1 kbyte)Ana: 5 MHz - ARP + Data (1 kbyte)

Fig. 7. Probability of outage in LTE with respect the number of M2M arrivals per second in a 1.4 MHz and 5 MHz systemfor different models, payloads and number of RAOs.

transmission starts. That is, we have only the messages shown in bold text in Table IV7. Fig. 7

shows the outage probability Poutage for 1.4 MHz and 5 MHz systems, both for SM and eSM

traffic models. It can be seen that the analytical model is very capable of capturing the outage

7The case where the data transmission occurs immediately after the ARP, without the additional signaling denoted in Table III,is denoted as lightweight-signaling access and corresponds to an extreme case of signaling overhead reduction, beyond whathas been proposed in 3GPP [6], [35].


Results§ Simulationandmodel

resultsfitclosely.• Both100bytesand1kbytespackets.

§ MAClayer(PUSCH)limitationisclearwhencomparing100bytesto1kbytes:• 1.4MHz:1000à 200arr/s• 5MHz:3900à 800arr/s

Arrivals/s 0 500 1000 1500 2000 2500 3000 3500 4000

P Out

age

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1Sim: 1.4 MHz - ARP + Data (100 bytes)Ana: 1.4 MHz - ARP + Data (100 bytes)Sim: 1.4 MHz - ARP + Data (1 kbyte)Ana: 1.4 MHz - ARP + Data (1 kbyte)Sim: 5 MHz - ARP + Data (100 bytes)Ana: 5 MHz - ARP + Data (100 bytes)Sim: 5 MHz - ARP + Data (1 kbyte)Ana: 5 MHz - ARP + Data (1 kbyte)


Results§ Simulationandmodel

resultsfitclosely.• Bothwithandwithoutsignaling.

§ Additionalsignalinghaslargeimpactonperformance.• Almosta3xreduction ifomitted!

• LTEforM2Mneedslesssignaling.

4

OFDM Symbols

Slot 0 Slot 1



Slot 0 Slot 1










Fig. 3. Simplified illustration of uplink subframe 0 and subframe 1 organi-zation in a 1.4 MHz system with NCFI = 3.

4MSG4 - Contention Resolution

1 MSG1 - Preamble

3 MSG3 - Connection Request

2MSG2 - Random Access Response

eNodeBSmartMeter Additional Signaling (6 messages)

11 Data Transmission

Connection Release 12

Fig. 4. Message exchange between a smart meter and the eNodeB.

d = 54 are typically available for contention purposes andthe rest are reserved for timing alignment. The contention isslotted ALOHA based [11], [12], but unlike in typical ALOHAscenarios, the eNodeB can only detect which preambles havebeen activated but not if multiple activations (collisions) haveoccurred. In particular, this assumption holds in small/urbancells [13, Sec. 17.5.2.3].4

Via MSG 2, the eNodeB returns a random access response(RAR) to all detected preambles. The contending devices listento the downlink channel, expecting MSG 2 within time periodtRAR. If no MSG 2 is received and the maximum of T MSG 1

4If the cell size is more than twice the distance corresponding to themaximum delay spread, the eNodeB may be able to differentiate the casethat preamble has been activated by two or more users, but only if the usersare separable in terms of the Power Delay Profile [13], [14].

transmissions has not been reached, the device backs off andrestarts the random access procedure after a randomly selectedbackoff interval t

r

2 [0,Wc � 1]. If received, MSG 2 includesuplink grant information that indicates the RB in which theconnection request (MSG 3) should be sent. The connectionrequest specifies the requested service type, e.g., voice call,data transmission, measurement report, etc. When two devicesselect the same preamble (MSG 1), they receive the sameMSG 2 and experience collision when they send their MSG 3sin the same RB.

In contrast to the collisions for MSG 1, the eNodeB is ableto detect collisions for MSG 3. The eNodeB only replies to theMSG 3s that did not experience collision, by sending messageMSG 4 (i.e., RRC Connection Setup). The message MSG 4may carry two different outcomes: either the required RBsare allocated or the request is denied in case of insufficientnetwork resources. The latter is however unlikely in the caseof M2M communications, due to the small payloads. If theMSG 4 is not received within time period tCRT since MSG 1was sent, the random access procedure is restarted. Finally,if a device does not successfully finish all the steps of therandom access procedure within m+1 MSG 1 transmissions,an outage is declared.

After ARP exchange finishes, there is an additional ex-change of MAC messages between the smart meter and theeNodeB, whose main purposes is to establish security andquality of service for the connection, as well as to indicatethe status of the buffer at the device. These extra messagesare detailed further in Table IV.

Besides MAC messages, there are PHY messages includedin the connection establishment [15]. Table IV presents acomplete account of both PHY and MAC messages exchangedduring connection establishment, data report transmission andconnection termination (the PHY messages are indicated ingray). As it can be seen from the table, for every downlinkmessage a downlink grant in the PDCCH is required. Simi-larly, every time a smart meter wishes to transmit in the uplinkafter the ARP, it first need to ask for the uplink resourcesby transmitting a scheduling request in the PUCCH.5 This isfollowed by provision of an uplink grant in the PDCCH bythe eNodeB.

III. MOTIVATION, RELATED WORK AND CONTRIBUTIONS

As already outlined, the traffic profile generated by smart-grid monitoring devices is an example of Machine-to-Machine(M2M) traffic, characterized by a sporadic transmissions ofsmall amounts of data from a very large number of terminals.This is in sharp contrast with the bursty and high data-ratetraffic patterns of the human-centered services.

Another important difference is that smart grid servicestypically require a higher degree of network reliability andavailability than the human-centered services [16]. So far,cellular access has been optimized to human-centered trafficand M2M related standardization efforts came into focus onlyrecently [17].

5We note that the amount of resources reserved for PUCCH is very small forscheduling periodicity above 40 ms [15] and therefore will not be consideredin the following text and analysis.

Packet size is 100 bytes

Arrivals/s 0 500 1000 1500 2000 2500 3000 3500 4000

P Out

age

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Sim: 1.4 MHz - ARP + DataAna: 1.4 MHz - ARP + DataSim: 1.4 MHz - ARP + Signaling + DataAna: 1.4 MHz - ARP + Signaling + DataSim: 5 MHz - ARP + DataAna: 5 MHz - ARP + DataSim: 5 MHz - ARP + Signaling + DataAna: 5 MHz - ARP + Signaling + Data

Signaling impact

Signaling Impact


Results:NumberofRAOs§ FormassiveM2M

(smallpayload),highnumberofRAOsistheoptimalsolution.

§ However,forlargepayload(1kbytes),thefewestpossibleRAOsisoptimal.

Arrivals/s 300 350 400 450 500 550 600 650 700 750 800

P Out

age

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1δRAO = 10δRAO = 5δRAO = 2δRAO = 1

Bandwidth is 5 MHz, 1000 bytes packets


Results:ARPonlyvs PHYandMAC§ 100bytes

• PDCCHlimits(PHY/signaling)

§ 1kbytes• PUSCHlimitsduetodata.

§ ImportanttoaccountforPHYandMAClimitations!

Arrivals/s ×1040 0.5 1 1.5 2 2.5 3 3.5 4

P Out

age

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1100 bytes1 kbyte100 bytes and 1000 bytes (ideal PHY and MAC)

2 RAOs per 10 subframes


Conclusion

1. Necessarytotakeintoaccountchannellimitations:§ M2M(smallpayload):PRACH andPDCCHlimits.§ Largepayload:PUSCHlimits.

2. Rapidimplementation(comparedtosimulations)andclick-speedevaluationofoutagebreakpoint.

3. SignalingafterARPhasbigimpactonM2Mperformance.

§ Reducedsignalingshouldbeinvestigated.


Backupslides


Collisionprobability§ Availablepreambles:𝑑 = 54§ Prob.ofnotselectingsamepreambleasoneotherUEis:1 − 2

7.

§ ThentheprobabilityofaUEselectingapreamblethathasbeenselectedbyatleastoneotherUE,givenNT contendingUEs,is:

§ AssumingPoissonarrivalswithrateλT,then:

§ where istheprobabilitymassfunctionofthePoissondistributionwitharrivalrate𝜆' · 𝛿:;<.

should be sent. The connection request specifies the requestedservice type, e.g., voice call, data transmission, measurementreport, etc. In case of collision the devices receive the sameMSG 2, resulting in their MSG 3s colliding in the RB.

In contrast to the collisions of MSG 1, the eNodeB is ableto detect collisions of MSG 3. The eNodeB only replies tothe MSG 3s that did not experience collision, by sendingmessage MSG 4, with which the required RBs are allocatedor the request is denied in case of insufficient resources.The latter is however unlikely in the case of MTC, due tothe small payloads. If the MSG 4 is not received withintCRT since MSG 1 was sent, the random access procedureis restarted. Finally, if a device does not successfully finish allthe steps of the random access procedure within m+1 MSG 1transmissions, an outage is declared.

III. MODELING THE ACCESS RESERVATION PROTOCOL

We now go to the analysis of the access reservation pro-cedure. First, we model the One-shot transmission and thenextend it to the m-Retransmissions model. The numericalresults cover the complete model, as depicted in Fig. 2.

A. One-Shot Transmission Model

We are interested in characterizing how often a transmissionfrom a UE fails. This happens when the transmission is notsuccessful in both the preamble contention and AG phases,i.e., a request from the UE must not experience a preamblecollision and the uplink grant must not become stale anddropped. We model this as two independent events:

pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�A)

⌘, (1)

where pc(�T) is the collision probability in the preamblecontention phase given UE request rate �T, while pe(�A) isthe probability of the uplink grant being dropped from the AGqueue given preamble activation rate �A.

1) Preamble Contention Phase: We start by computingpc(�T). Let d denote the number of available preambles(d = 54). Let the probability of not selecting the samepreamble as one other UE be 1 � 1

d

. Then the probability ofa UE selecting a preamble that has been selected by at leastone other UE, given NT contending UEs, is:


d

◆NT�1

. (2)


pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1


#(3)

1�✓1� 1

d

◆�T·�RAO�1

,

where P(NT = i,�T · �RAO) is the probability mass functionof the Poisson distribution with arrival rate �T · �RAO. Theinequality comes from applying Jensen’s inequality to the con-cave function 1�(1� 1/d)x, where �T is the total arrival rate(including retransmissions), and �RAO is the average number

of subframes between RAOs.2 The computed pc(�T) is thusan upper bound on the collision probability.

2) Access Granting Phase: The mean number of activatedpreambles in the contention phase per RAO, is given by �A. Asdiscussed in Section II, we assume that the eNodeB is unableto discern between preambles that have been activated by asingle user and multiple users, respectively. This will lead to ahigher �A, than in the case where the eNodeB is able to detectthe preamble collisions. The main impact of this assumptionis that there will be an increased rate of AG requests, eventhough part of these correspond to collided preambles, whicheven if accepted will lead to retransmissions.

The �A can be well approximated, while assuming thatthe selection of each preamble by the contending users isindependent, by,

�A = [1� P (X = 0)� P (X = 1)] · d, (4)

where P(X = k) is the probability of k successes, which canbe well approximated with a Poisson distribution with arrivalrate �T/d, i.e.:

P (X = k) ⇡ (�T/d)ke��T/d

k!. (5)

To compute the outage probability due to the limitation inthe AG phase, i.e., due to the maximum number of uplinkgrants per subframe and a maximum waiting time of tRARsubframes, we consider that this subsystem can be modeled asa queuing system. We assume that the loss probability pe(�A)can be seen as the long-run fraction of costumers that are lostin a queuing system with impatient costumers [15].

In LTE, pending uplink grants are served with a determin-istic time interval (1 subframe) between each serving slot [8].A straightforward approach would be to use an M/D/1 modelstructure, as presented in [15], in order to compute the dropprobability. Unfortunately, the expression to compute pe(�A)for the M/D/1 queue does not have a closed-form solution.However the equivalent expression for the M/M/1 queue in[15] has a closed-form solution, see eq. (6). We have comparedthe results of the two model types and found no noticeabledifference in the computed outage numbers in practice. Thus,in the following we use the M/M/1 model to compute pe(�A):

pe(�A) =(1� ⇢) · ⇢ · ⌦1� ⇢2 · ⌦ , with ⌦ = e�µ·(1�⇢)·⌧q . (6)

where ⇢ = �Aµ

is the queue load, µ is the number of uplinkgrants per RAR (µ = 3), with ⌧q = Td � 1

µ

and Td is the maxwaiting time (in terms of requests) in the uplink grant queue,i.e., Td = µ · tRAR.

The fact that we are using an M/M/1 model instead of anM/D/1 model, may cause a discrepancy between the simulationand model results when the queue becomes congested (⇢ > 1).However, we are interested in the switching point (⇢ = 1) fromwhich we then estimate accurately the outage breaking point,as shown in the results in section IV.


13


pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�T)

⌘, (1)






other UE be 1� 1d




d

◆NT�1

. (2)


pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1


#(3)

1�✓1� 1

d

◆�T·�RAO�1

,





















pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�A)

⌘, (1)



d



d

◆NT�1

. (2)


pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1


#(3)

1�✓1� 1

d

◆�T·�RAO�1

,





�A = [1� P (X = 0)� P (X = 1)] · d, (4)


P (X = k) ⇡ (�T/d)ke��T/d

k!. (5)



pe(�A) =(1� ⇢) · ⇢ · ⌦1� ⇢2 · ⌦ , with ⌦ = e�µ·(1�⇢)·⌧q . (6)

where ⇢ = �Aµ


µ




IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success


AccessGrantingphase

§ Approximationofrateofactivatedpreambles𝜆;:• Assumingindependentpreambleselection:

• AssumingPoissondist.,withrate%= 7> :

IdlePopulation

Backlogged

PRACH Data Phase

λI Access Granting

(a)

(b)

λT

λR

NTx< TYes

No

λA

Failure

Success







pf(�T) = 1�⇣1� pc(�T)

⌘⇣1� pe(�A)

⌘, (1)



d



d

◆NT�1

. (2)


pc(�T) =+1X

i=1

"1�

✓1� 1

d

◆i�1


#(3)

1�✓1� 1

d

◆�T·�RAO�1

,





�A = [1� P (X = 0)� P (X = 1)] · d, (4)


P (X = k) ⇡ (�T/d)ke��T/d

k!. (5)



pe(�A) =(1� ⇢) · ⇢ · ⌦1� ⇢2 · ⌦ , with ⌦ = e�µ·(1�⇢)·⌧q . (6)

where ⇢ = �Aµ


µ




15



the preamble collisions. The main impact of this assumption is that there will be an increased rate

of access granted requests, even though part of these correspond to collided preambles, which

even if accepted will lead to retransmissions. In addition to the rate of activated preambles �A,

we also need the rate of singletons, i.e., non-collided, successful preamble activations denoted

by �S.

The �A and �S can be well approximated, while assuming that the selection of each preamble

by the contending users is independent, by,

�A = [1� P (X = 0)] · d/�RAO, (4)

�S =P (X = 1) · d/�RAO, (5)

where P(X = k) is the probability of k successes, which can be well approximated with a

Poisson distribution with arrival rate �pre = �T�RAO/d, i.e.:

P (X = k) ⇡ (�pre)ke��pre

k!. (6)

Since the limitations in the AG phase are primarily given from the demanded resources from

each of the channels PDCCH, PDSCH, and PUSCH and the corresponding timing requirements,

we assume that each of these can be modeled as a separate queue with impatient costumers. That

is, we assume that the loss probability pq(�A) can be seen as the long-run fraction of costumers

that are lost in a queuing system with impatient costumers [33].

Based on the message exchange diagram in Section II-C, we specify in the following text the

arrival rate, service rate and the maximum latency for each of the channels PDCCH, PDSCH,

and PUSCH.

In general, since LTE uses fixed size time slots, the most obvious approach would be to use an

M/D/1 model structure where service times are deterministic, as presented in [33]. Unfortunately,

the expression to compute the fraction of lost customers pq(�, µ, Td) for the M/D/1 queue does

not have a closed form solution. However, the equivalent expression for the M/M/1 queue, which

assumes exponential duration service intervals, does have a closed form solution. Through an

extensive study, we have found that with the parameter ranges that we use, there is no noticeable

difference in the results. Furthermore, and most importantly, our results with this model fit well

A Tractable Model of the LTE Signaling and Data...

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