Bandwidth Allocation with Half-Duplex Stationsin IEEE 802.16 Wireless Networks

Andrea Bacioccola, Claudio Cicconetti, Student Member, IEEE,

Alessandro Erta, Luciano Lenzini, and Enzo Mingozzi, Member, IEEE

Abstract—IEEE 802.16 is a recent IEEE standard for broadband wireless access networks. In IEEE 802.16 networks, the Medium

Access Control (MAC) protocol is centralized and explicitly supports quality of service (QoS). That is to say, access to the medium by a

number of Subscriber Stations (SSs) is centrally controlled by one Base Station (BS), which is responsible for allocating bandwidth to

several MAC connections in order to provide them with the negotiated QoS guarantees. However, although the network can be

operated in Frequency Division Duplex (FDD) mode (that is, transmissions from the BS (downlink) and SSs (uplink) occur on separate

frequency channels), the standard supports SSs with half-duplex capabilities. This means that they are equipped with a single radio

transceiver which can be used either to transmit in the uplink direction or to receive in the downlink direction. This may severely hamper

the capacity to support QoS. Therefore, in order to allocate bandwidth, an IEEE 802.16 BS has to solve two related issues: 1) how it

can schedule bandwidth grants to SSs in order to meet the QoS requirements of their connections and 2) how it can coordinate the

uplink and downlink scheduled grants so as to support half-duplex capabilities. In this paper, we derive sufficient conditions for a set of

scheduled grants to be allocated so that the transmission of each half-duplex SS does not overlap with its reception. Based on this, we

propose a grant allocation algorithm, namely, the Half-Duplex Allocation (HDA) algorithm, which always produces a feasible grant

allocation provided that the sufficient conditions are met. HDA has a computation complexity of OðnÞ, where n is the number of grants

to be allocated. Finally, we show that the definition of HDA allows us to address the two issues mentioned above by following a pipeline

approach. This is when scheduling and allocation are implemented by separate and independently running algorithms, which are just

loosely coupled with each other. We show via extensive simulations that the performance of SSs with half-duplex capabilities, in terms

of the delay of real-time and non-real-time interactive traffic, using HDA almost perfectly matches that of full-duplex SSs, whereas an

alternative approach, based on the static partitioning of half-duplex SSs into separate groups, which are allocated alternately, is shown

to degrade the performance.

Index Terms—IEEE 802.16, broadband wireless access, quality of service, bandwidth allocation, half-duplex transmission.

Ç

1 INTRODUCTION

INDUSTRY and research communities are investing con-siderable effort in the convergence of multimedia services

(for example, voice over IP (VoIP), video, and massiveonline gaming) and ubiquitous instant access, which, bynecessity, depends on the use of Broadband WirelessAccess (BWA) technologies [1]. The IEEE 802.16 standardfor BWA has been developed by IEEE [13]. Since 2001, theWorldwide Interoperability for Microwave Access (Wi-MAX) forum [23], a nonprofit organization with over400 partners, has been working to promote and certify thecompatibility and interoperability of IEEE 802.16 for fixedand mobile BWAs.

An IEEE 802.16 network consists of a number ofSubscriber Stations (SSs) served by a Base Station (BS).According to the standard, time is partitioned into frames offixed duration. Within each frame, transmissions occur inboth directions: from the BS to the SSs (downlink direction)

and from each SS to the BS (uplink direction). In order tosupport bidirectional transmissions, IEEE 802.16 specifiestwo alternative duplex modes [5]. The first is FrequencyDivision Duplex (FDD), where uplink and downlinktransmissions occur simultaneously on separate frequen-cies. The second is Time Division Duplex (TDD), whereuplink and downlink transmissions alternate within thetime frame and share the same frequencies. Regardless ofthe duplex mode, an SS can have either full-duplex or half-duplex transmission capabilities. A full-duplex SS (FD-SS)can simultaneously listen to the downlink channel whiletransmitting data, whereas a half-duplex SS (HD-SS) cannotreceive while transmitting, that is, uplink and downlinktransmissions from/to an HD-SS cannot overlap in time.We refer to this as the half-duplex constraint.

Despite this constraint, IEEE 802.16 FDD systems withHD-SSs are expected to be widely used solutions for anumber of reasons [2]. First, most licensed bands intendedfor data applications operate with FDD systems in mind.Second, providing wireless communication devices withfull-duplex capabilities is challenging. In fact, when thewireless transceiver is transmitting data, a large fraction ofthe signal energy leaks into the receive path. The trans-mitted and received power levels can differ by severalorders of magnitude and, therefore, the impact of theenergy leakage can be significant. FD-SSs are thus moreexpensive to design and manufacture than HD-SSs, and thelatter seem to offer a very attractive solution for user

1384 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

. A. Bacioccola, C. Cicconetti, L. Lenzini, and E. Mingozzi are with theDipartimento di Ingegneria dell’Informazione, University of Pisa, ViaDiotisalvi, 2—56122 Pisa, Italy.E-mail: {a.bacioccola, c.cicconetti, l.lenzini, e.mingozzi}@iet.unipi.it.

. A. Erta is with the IMT Lucca Institute for Advanced Studies, Via S.Micheletto 3—55100 Lucca, Italy. E-mail: a.erta@imtlucca.it.

Manuscript received 22 Aug. 2005; revised 30 Jan. 2007; accepted 2 Apr.2007; published online 17 Apr. 2007.For information on obtaining reprints of this article, please send e-mail to:tmc@computer.org, and reference IEEECS Log Number TMC-0246-0805.Digital Object Identifier no. 10.1109/TMC.2007.1064.

1536-1233/07/$25.00 � 2007 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

radio devices. Finally, up until the beginning of 2007, mostWiMAX-certified SSs supported only half-duplex opera-tions when operated in FDD mode.

Irrespective of the duplex mode and the SS transmissioncapabilities, IEEE 802.16 Medium Access Control (MAC) iscentralized and connection oriented: All data communica-tions for both transport and control are carried out in aunidirectional connection. SSs notify the BS of the numberof bytes to be sent by a connection through specific MACheaders. The BS controls access to the medium by broad-casting a number of bandwidth grants at the beginning ofeach frame. Each bandwidth grant specifies which SSs aregoing to receive data from the BS (downlink grants) orwhich ones are allowed to transmit data to the BS (uplinkgrants) in the forthcoming frame. Bandwidth grants alsospecify when in the frame and for how long an SS willreceive/transmit data. As specified in the IEEE 802.16standard, the BS is responsible for providing connectionswith quality-of-service (QoS) guarantees. Therefore, the BShas to implement a scheduling function to grant adequatedownlink and uplink bandwidth to each SS according to thenegotiated QoS of the admitted connections.

When implementing the BS scheduling function in IEEE802.16 FDD systems that support HD-SSs, two related issuesneed to be tackled. The first is how we can grant bandwidthin each frame and in both the uplink and the downlinkdirections so as to provide the admitted connections withthe negotiated level of QoS. The second issue is how we cancoordinate the downlink and uplink bandwidth grants intime so as to also comply with the half-duplex constraint foreach HD-SS. In this respect, it is worth noting that thestandard does not specify any mandatory or informativesolution: IEEE-802.16-compliant device manufacturers arethus free to develop their own solutions. In this paper, wepropose a framework for solving the above issues, which isbased on a pipeline approach: Bandwidth granting is firstperformed by determining the duration of each uplink anddownlink grant, irrespective of the actual allocation in thetime frame. The latter is then performed in its entirety in asubsequent step. To this aim, we devise sufficient condi-tions to be met when granting bandwidth, which guaranteethat the time allocation of grants will always be feasible

without violating the half-duplex constraint. In addition, wepropose a grant allocation algorithm, namely, the Half-Duplex Allocation algorithm (HDA),1 which arranges thegrants scheduled to both FD-SSs and HD-SSs in the frame.Furthermore, we prove HDA to be 1) optimal in the sensethat, if there is a feasible allocation of a set of scheduledgrants, then HDA is always able to find it, and 2) compu-tationally efficient, since grant allocation is completed inOðnÞ steps, where n is the number of grants.

The rest of the paper is organized as follows: In Section 2,we describe the aspects of the IEEE 802.16 MAC protocolthat are relevant to this study. In Section 3, we provide adetailed rationale and introduce the pipeline approach. InSection 4, we describe HDA and formally prove itsproperties. In Section 5, we present an alternative approachto “work around” the half-duplex constraint. In Section 6,the performance of HD-SSs using HDA is comparedthrough simulation to that obtained with the aforemen-tioned alternative approach and FD-SSs. Conclusions aredrawn in Section 7.

2 IEEE 802.16 MAC

In this section, we describe those aspects of the IEEE 802.16MAC protocol that are specifically relevant to this study.We thus focus on the Point-to-Multipoint (PMP) modewith a centralized BS operating in FDD using theWirelessMAN-OFDM physical layer, which is the mostpromising air interface for supporting Non-Line-of-Sight(NLOS) operations in fixed BWA networks [25]. In thiscontext, the basic time allocation unit is the OFDM symbol,which is made up of 256 subcarriers according to thestandard Fast Fourier Transform (FFT) size. The interestedreader can find a technical introduction to the OFDMsystem of the IEEE 802.16 in [16].

As already mentioned, time is partitioned into frames offixed duration. Since the duplex mode is FDD, uplink anddownlink transmissions occur simultaneously on separatefrequencies. The frame structure is shown in Fig. 1. In thedownlink subframe, the BS transmits MAC Protocol DataUnits (PDUs). BS transmission is broadcast; thus, all SSs

BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1385

1. HDA is under a patent owned by Nokia Corp.

Fig. 1. FDD frame structure with IEEE 802.16.

listen to the data transmitted by the BS. However, an SS isentitled to only process the burst of PDUs that is directed toitself. On the other hand, in the uplink subframe, each SStransmits multiple bursts of MAC PDUs to the BS in a TimeDivision Multiple Access (TDMA) manner. A MAC PDUconsists of one or more MAC Service Data Units (SDUs)which are used to convey data from upper layers, forexample, Internet Protocol version 4 (IPv4) datagrams orEthernet frames. MAC SDUs can be fragmented orconcatenated by the sending entity, either SS or BS, toefficiently exploit the available capacity. DL-MAP and UL-MAP messages (or maps), which are advertised by the BS atthe beginning of each frame, contain the time boundariesof downlink and uplink grants addressed to differentSSs. More specifically, a downlink grant in the DL-MAPannounces the transmission by the BS of a burst of PDUsaddressed to a given SS. An uplink grant in the UL-MAP,on the other hand, announces a time interval inside theuplink subframe within which a given SS is allowed totransmit a burst of PDUs.

As shown in Fig. 1, the DL-MAP is prepended by aphysical long preamble (two OFDM symbols), which isneeded for synchronization. Each uplink burst starts with aphysical short preamble (one OFDM symbol), which allowsthe BS to synchronize its receiver with the subsequenttransmission of data from the SS. The uplink subframe isdelayed with respect to the beginning of the downlinksubframe by a fixed amount of time, called the uplinkallocation start time, so as to give SSs enough time to decodethe UL-MAP and take appropriate decisions. IEEE 802.16specifies that this value must be at least as long as themaximum Round-Trip Time (RTT) delay but not longerthan the frame duration. As an example, in Fig. 1, theuplink allocation start time is equal to the frame durationand, thus, the beginning of the uplink subframe n overlapswith the beginning of the downlink subframe nþ 1.

All SSs, both HD-SS and FD-SS, synchronize themselveswith the BS by means of the long preamble transmitted atthe beginning of the downlink subframe so as to retrieveinformation from DL-MAP and UL-MAP messages. FD-SSskeep themselves synchronized to the downlink channel bycontinuously listening to the BS’s transmissions. On theother hand, an HD-SS is synchronized with the downlinkchannel only as far as the beginning of its own uplink grant,if any. At this point, in fact, the HD-SS has to switch itsradio transceiver from receiving to transmitting modes,thus losing synchronization with the downlink channel.Even though HD-SS switches back to the receiving modeafter transmission, synchronization with the downlinkchannel is lost and cannot be restored unless the BStransmits a new physical preamble (illustrated in Fig. 1).Therefore, the BS is required to add a physical shortpreamble to each downlink burst that is addressed to anHD-SS whose uplink grant was scheduled after theoccurrence of the beginning of the last downlink subframe.On the other hand, physical preambles are never added todownlink grants addressed to FD-SSs.

In order to support QoS at the connection level,applications are grouped by the standard into four classes,called scheduling services in IEEE 802.16 terminology:Unsolicited Grant Service (UGS), real-time Polling Service(rtPS), non-rtPS (nrtPS), and Best Effort (BE). Each schedul-ing service defines a mandatory set of QoS parameters such

as the Minimum Reserved Traffic Rate, the MaximumLatency, and the Unsolicited Polling Interval, which istailored to meet the guarantees required by the applicationsthat the scheduling service is designed for. The detaileddifferences among these scheduling services can be found,for example, in [8], and are outside the scope of this work.However, since rtPS and BE are analyzed in the perfor-mance evaluation in Section 6, we briefly report their mostimportant features. The rtPS scheduling service is designedto support real-time applications with stringent delayrequirements that generate variable size data packets atperiodic intervals such as Moving Pictures Expert Group(MPEG) video and VoIP with silence suppression. In fact, aminimum reserved rate is specified for each connection. Inaddition, for uplink rtPS connections only, the BS periodi-cally polls each rtPS connection. This is in order to becomeaware of the amount of data waiting for transmission at theconnection buffers, which reside at the SSs, and to scheduleuplink grants accordingly. The BE scheduling service, onthe other hand, is envisaged for use by applications that donot pose any specific delay constraints such as Webbrowsing and e-mail transfer. Unlike rtPS, uplink BEconnections request bandwidth from the BS by means of acontention-based mechanism that occurs in specificallyallocated time slots of the uplink subframe and is notifiedby the BS through the UL-MAP. When a collision occurs,because different SSs transmit a bandwidth request in thesame slot, SSs employ a truncated binary exponentialbackoff mechanism so as to reduce the chance of collisionwhen they reiterate the bandwidth request transmission.

Finally, the IEEE 802.16 standard specifies a rateadaptation procedure to be employed by the BS and SSsto maximize data transmission efficiency [10]. This involvesselecting the Modulation and Coding Scheme (MCS) usedto receive from (or transmit to) any SS among a set ofpossible combinations periodically advertised by the BS.

3 RATIONALE

One of the main responsibilities of the BS is to guaranteeQoS to admitted connections, both downlink and uplink,according to the QoS requirements of the applicationsspecified by the scheduling services introduced in Sec-tion 2. To achieve this, downlink and uplink grants in eachframe must be appropriately scheduled to SSs based onboth the current traffic load of each connection and theavailable resources. We refer to the scheduling functioninside the BS as the functional module in charge ofperforming this task, that is, to define at the beginning ofeach frame the start time and the duration of eachbandwidth grant, and, therefore, the content of maps. Asalready mentioned, the specification of the algorithms tobe implemented by the scheduling function at the BS isbeyond the scope of the standard and is thus left up to themanufacturers [13, p. 139].

When the FDD mode is used, since transmissions occuron separate frequencies, there are actually two separatetransmission resources to be scheduled in every frame, thatis, the uplink and the downlink subframes. An obviousconstraint for the scheduling function in this case is that theoverall amount of bandwidth granted in a downlink oruplink subframe, that is, the sum of the respective grantdurations as announced in the maps, cannot be greater than

1386 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

the length of the subframe itself.2 Furthermore, when onlyFD-SSs are present in the system, there is no constraint onthe relative time location of the downlink and uplink grantsaddressed to the same SS since the latter can manage thesimultaneous transmission and reception of bursts.

It follows that, with FDD and FD-SSs, the only nontrivialtask to be performed by the BS scheduling function is todetermine the duration of each uplink and/or downlinkgrant to address to each SS since any time allocation of thegrants in the respective subframes will be feasible. There-fore, the scheduling function could be implemented using apipeline approach, as depicted in Fig. 2, where thescheduling function is partitioned into two main subfunc-tions, namely, the grant scheduler and the grant allocator. Thegrant scheduler is responsible for determining the durationof each grant in the respective subframe.3 The output ofthe grant scheduler is then fed to the grant allocator, whichis responsible both for determining the start time of eachgrant in the respective subframe and for finalizing thecontent of the maps to be transmitted by the BS.

Since bandwidth is scheduled on a frame-by-framebasis, QoS guarantees should be expressed with a timegranularity not smaller than the frame duration. In fact,several values are allowed by the standard for the latter(ranging from 2.5 to 20 ms), and the network operator can

choose the one that best fits the service that it is planning tooffer. It follows that, with the pipeline approach in mind,QoS provisioning only depends on the algorithm imple-mented in the grant scheduler. This is the main advantageof this approach since the task of scheduling bandwidth forQoS support is confined to a well-identified functionalsubmodule and is naturally abstracted from the detailsoriginating from the grant allocation within the frame.Furthermore, it is easy to see how such an isolation allowsfor implementing scheduling algorithms as a result of thesimple adaptation of well-known algorithms alreadyproposed in the context of wired networks, where thisdiscipline has been extensively studied in the recent past[21], [22]. Finally, the pipeline approach has a definiteadvantage as far as the implementation is concerned. Infact, map production is a real-time task with a harddeadline, the latter being the beginning of the subsequentframe. If scheduling and allocation can actually beimplemented by independent subtasks interworking con-currently according to a pipeline scheme, then the time thatcan be dedicated by each subtask to accomplish its work inevery frame is basically doubled. This is because the grantscheduler can start working on the next frame, whereas thegrant allocator is still allocating the current one. Therefore,either a less powerful processing hardware can be usedinside the BS with the same scheduling algorithm, or withthe same hardware, more complex scheduling algorithmscan be implemented.

However, with FDD and HD-SSs, the pipeline approachdevised in Fig. 2 cannot be implemented “as is.” In fact, theduration of the grants, as determined by the grantscheduler, may be such that there is no way of allocatingthem in the current frame without violating the half-duplexconstraint. For example, if the grant scheduler selected bothan uplink grant and a downlink grant to the same HD-SS ina frame, and the sum of the duration of the two grantsexceeds the frame duration, then the grant allocator isclearly not able to produce any valid map. This examplewould be illustrated in Fig. 3, where the uplink anddownlink grants addressed to SS 1 would overlap over

BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1387

Fig. 2. Grant scheduling and allocation in FDD.

2. To be precise, the overhead due to map transmissions should also betaken into account for the downlink subframe. However, this is not relevantfor the current discussion and, thus, we assume for simplicity’s sake thatthe overhead due to map transmissions is negligible.

3. In doing so, it must explicitly take into account the QoS requirementsof the admitted connections. In addition, it could also consider other systemfactors such as the modulation used by each SS and take the appropriateaction regardless of the allocation problem.

Fig. 3. Unfeasible grant scheduling in FDD.

time regardless of the allocation algorithm. It is worthnoting, as we prove numerically in Section 6, that thescheduling of a station, both uplink and downlink, in thesame frame is a typical case when QoS guarantees have tobe provided. In conclusion, whereas the grant schedulerand allocator operations are completely decoupled fromeach other when only FD-SSs are considered, they actuallybecome tightly coupled when HD-SSs are present as well.

Many solutions can be devised to work around thisproblem. One solution could be to abandon the pipelineapproach and implement the scheduling function withalgorithms that jointly define the duration and start time ofeach grant. This approach could be described as producingthe final maps through a number of successive iterationsinvolving the scheduler and the allocator depicted in Fig. 2based on the exchange of their intermediate results.However, the advantages of the pipeline approach dis-cussed above would be withdrawn as well. On the otherhand, one could try to find sufficient conditions to impose onthe grant scheduler so that the grant allocator could alwaysfind a feasible grant allocation. For example, one couldtrivially impose that an HD-SS could only be grantedbandwidth in one direction in each frame. This wouldremove the burden of coping with the half-duplex con-straint explicitly.

However, such sufficient conditions should be carefullyselected since they could greatly affect the capability of thegrant scheduler to provide the admitted connections withthe required QoS guarantees. We could formulate such arequirement by stating that, if the pipeline approach isfollowed, then the sufficient conditions imposed on theoutput of the grant scheduler should be as loose as possible.On the other hand, it is straightforward to identify thenecessary conditions for the grants’ duration defined by thegrant scheduler so that the grant allocation is feasible.Specifically, such necessary conditions are that the overallbandwidth, both downlink and uplink, granted to each HD-SS in each frame must not exceed the frame duration.4

The main contribution of this paper is providing a formalproof that the above-mentioned necessary conditions are alsosufficient to guarantee that scheduled grants can be allocatedin the respective subframes without violating the half-duplex constraint. In this respect, such sufficient conditionsare the loosest possible because they are also necessary; thatis, they are essential to all other sets of conditions that couldbe devised. Furthermore, based on the above proof, wepropose an algorithm for the grant allocator, namely, theHDA algorithm, which can always arrange the scheduledgrants in the respective subframes provided that sufficientconditions are met. Thus, HDA can be employed in thegrant allocator, whatever algorithm is implemented in thegrant scheduler. This means that a pipeline approach canalso be adopted in the case of HD-SSs, where grantscheduling and allocation are only loosely coupled.

In the next section, we describe HDA and prove that itcan allocate any set of downlink and uplink grants in therespective subframes without violating the half-duplexconstraint, provided that the necessary conditions hold.

4 HDA ALGORITHM

In this section, we describe HDA and prove its formalproperties. First, we introduce the notation and assump-tions that will be used in the rest of the section. We thenprove that the necessary conditions are also sufficient for a setof unicast5 grants addressed to HD-SSs to be allocated in aframe without violating the half-duplex constraint. Theproof of one of the main theoretical results, namely,Lemma 1, enables us to define the HDA algorithm. Tosimplify the notations, hereafter, we assume that all grantsare addressed to HD-SSs (hence, we refer to them as SSs),and the uplink allocation start time is equal to the frameduration. The solution for the general case, where FD-SSsare also present and uplink and downlink subframes arenot aligned over time, is reported at the end of the section.

4.1 Definitions and Assumptions

We define the available frame duration (T , in time units) asthe frame duration minus the duration of MAC messages,which are broadcast by the BS at the beginning of thedownlink subframe for management purposes, and do notconvey MAC SDUs. MAC messages include the UL- andDL-MAPs, which were described in Section 2, as well asseveral messages that have not been reported since theirfunctions are beyond the scope of this paper. All SSs needto listen to those messages whose transmission durationmay vary frame by frame. Thus, the overlapping portion ofthe uplink frame cannot be used for uplink grants, whichare accounted for by the above definition of T .

Without loss of generality, we assume that each SS isscheduled exactly one grant for each direction per frame.In fact, should an SS be scheduled more than one grantin the same direction, they could all be equivalentlyaggregated into a single grant whose duration is the sumof the durations of the grants originally scheduled.However, should no grant be scheduled to an SS in onedirection, we equivalently assume that a grant of nullduration has been scheduled instead. We also assume thatthe grant duration includes any protocol overhead such asthe synchronization preamble.

Let n be the number of SSs scheduled in the currentframe. The grant allocated to SS i within the frame ofavailable duration T is uniquely identified by any two ofthe following quantities: the start time sxi , the finish time fxi ,and the duration xi, where x 2 fd; ug represents either thedownlink or the uplink direction. It is straightforward toderive the relationships between the three quantities asfollows:

fxi ¼ sxi þ xi�� ��

T

sxi ¼ fxi � xi�� ��

T

xi ¼ fxi � sxi�� ��

T;

8><>:

where the modulo operator jxjT is defined based onEuclid’s Theorem, as reported in [3]; that is, jxjT ¼x� bx=Tc � T: The notation is summarized in Table 1 andillustrated in Fig. 4.

1388 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

4. Without losing generality, we refer to the case where the uplinkallocation start time is equal to the frame duration and, thus, uplink anddownlink subframes perfectly overlap in time.

5. The results reported in this section cannot be straightforwardlyextended to multicast connections. However, the main challenge withmulticast is to schedule grants by taking into account the different physicalprofiles of the SSs which participate in a multicast session since theydynamically adapt their modulation and coding according to physical-layermeasurements. Hence, we consider unicast connections only.

We now provide a set of definitions and preliminaryresults, which basically formalize the problem of grantallocation.

Definition 1. A set U ¼ sui ; ui� �� �

ðD ¼ sdi ; di� �� �

Þ ofuplink (downlink) allocated grants is said to be feasibleiff for any time instant t 2 ½0; T �, there exists at most onegrant ðsuj ; ujÞ � U ððsdj ; djÞ � DÞ, 1 � j � n, such that

jt� suj jT < uj ðjt� sdj jT < djÞ: ð1Þ

Inequality (1) means “the time instant t lies betweenthe start and the end times of the uplink (downlink) grantaddressed to SS j.” Therefore, the definition aboveformally states the intuitive concept that an allocation isfeasible iff the uplink and downlink allocated grants ofany SS do not overlap in time.

Proposition 1. A set U of uplink grants is feasible iffjsui � fuj jT þ ui þ uj � T , 1 � i, j � n, i 6¼ j. A set D ofdownlink grants is feasible iff jsdi � fdj jT þ di þ dj � T ,1 � i, j � n, i 6¼ j.

Proof. The proof is straightforward, considering that

1. jsui � fuj jT is the time interval between the end ofone grant and the beginning of the next,

2. ui is the grant scheduled starting from sui onwardand uj is the grant scheduled starting from fujbackward, and

3. if the sum of the three is not greater than T , thengrants ui and uj do not overlap.

The same line of reasoning also applies to downlinkgrants. tuFrom Proposition 1, if U ðDÞ is a feasible set of uplink

(downlink) grants, then �iui � T ð�idi � T Þ.Definition 2. A pair fU;Dg of uplink and downlink sets is said

to be feasible iff for any SS i and time instant t 2 ½0; T � suchthat t� sui

�� ��T< ui, it is t� sdi

�� ��T� di. In other words, the

uplink and downlink grants for the same SS do not overlapover time and hence do not violate the half-duplex constraint.

The following results can be easily proved:

Proposition 2. A pair fU;Dg of uplink and downlink feasiblesets is feasible iff

sdi � fui�� ��

Tþui þ di � T; 1 � i � n: ð2Þ

Thus, fU;Dg is not feasible if any of the followingconditions is false:

Pni¼1

ui � TPni¼1

di � Tui þ di � T 1 � i � n:

8>>>><>>>>:

ð3Þ

Proposition 3. Given a feasible pair fU;Dg, any pair fUt;Dtgsuch that Ut ¼ fðjsui þ tjT ; uiÞg and Dt ¼ fðjsdi þ tjT ; diÞg,where t 2 IR, is also feasible. Thus, a feasible pair fU;Dg is

uniquely identified, except for a constant value.

4.2 Theoretical Results

The following lemma will be used to prove Theorem 1:

Lemma 1. Let U be a feasible set of uplink grants. Let ~D ¼dk 2 IR dk � 0j ; 1 � k � nf g be a set of n nonnegative real

numbers and let X be defined as follows:

X ¼� x 2 IR maxi

Xik¼1

dk � sui

!� x�min

i

Xi�1

k¼1

dk � fui þ T !�����

( ):

ð4Þ

IfPn

k¼1 dk � T and ui þ di � T , 1 � i � n, then X 6¼ �.

Proof. Without losing generality, we assume that i < j,sui � suj : Furthermore, based on Proposition 3, we assume

that su1 ¼ 0, which yields sui � fui for any i. Proving the

thesis is equivalent to proving that

mini

Xi�1

k¼1

dk � fui þ T !

�maxi

Xik¼1

dk � sui

!� 0;

i.e., for any i, j, 1 � i, j � n, it must be

Xj�1

k¼1

dk � fuj þ T �Xik¼1

dk � sui

!� 0:

We consider three possible cases:

Case 1. i > j. It is

Xj�1

k¼1

dk � fuj þ T �Xik¼1

dk � sui

!¼ T �

Xik¼j

dk þ sui � fuj � 0

by hypothesis since �ik¼jdk � �n

k¼1dk � T for any i > j

and sui � fuj because of the feasibility of U .

Case 2. i < j. It is

Xj�1

k¼1

dk�fuj þ T�Xik¼1

dk � sui

!¼ T� fuj � sui

� �þXj�1

k¼iþ1

dk � 0

since fuj � sui for any i < j and fuj � sui � T by assumption.

BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1389

TABLE 1Glossary

Fig. 4. Notations.

Case 3. i ¼ j. It is

Xi�1

k¼1

dk � fui þ T �Xik¼1

dk � sui

!¼ T � ui � di � 0

by hypothesis for any i, which concludes the proof. tuTheorem 1, which is the main theoretical contribution,

proves that the necessary conditions that must be met bya set of grants addressed to SSs in order to be feasible arealso sufficient.

Theorem 1. Let U be a feasible set of uplink grants and let fdigbe a set of grants. A set of downlink grants D such that thepair fU;Dg is feasible always exists iff �n

i¼1di � T andui þ di � T , 1 � i � n.

Proof. If part (sufficient condition). Without losing general-ity, we assume that i < j, sui � suj . Furthermore, basedon Proposition 3, we assume that su1 ¼ 0, which yieldssui � fui for any i. Let us consider a set of downlink grantsD such that

sdi ¼Xi�1

k¼1

dk � x�����

�����T

ð5Þ

for any x 2 X, where X is defined according to (4). Notethat the hypotheses of Lemma 1 are satisfied and, hence,X 6¼ �; that is, the downlink set of grants is well defined.It is straightforward to prove that D is feasible.

To complete the proof, we show that the pair fU;Dg isfeasible by using Proposition 2. By substituting (5) into(2), we obtain

sdi � fui�� ��

Tþui þ di ¼

Xi�1

k¼1

dk � fui � x�����

�����T

þui þ di: ð6Þ

Now, by the definition of X, it follows that

Xik¼1

dk � sui � x �Xi�1

k¼1

dk � sui � ui þ T

for any x 2 X. Hence, x can be rewritten as

x ¼Xik¼1

dk � sui þ y ð7Þ

provided that 0 � y � T � ui � di. Substituting (7) into(6) yields

sdi � fui�� ��

Tþui þ di

¼Xi�1

k¼1

dk �Xik¼1

dk

!þ sui � sui� �

� ui � y�����

�����T

þui þ di

¼ �di � ui � yj jTþui þ di¼ T � di � ui � yþ ui þ di¼ T � y � T:

ð8Þ

Equation (8) holds for any i, 1 � i � n, which completesthe proof.

Only if part (necessary condition). This immediatelyfollows from Propositions 1 and 2. tu

4.3 HDA Algorithm

Based on the constructive proof of Lemma 1, we devised analgorithm, called HDA, to allocate a set of uplink anddownlink grants fuig [ fdig such that the half-duplexconstraint is satisfied provided that the necessary condi-tions are met. HDA, whose correctness is proved byTheorem 1, consists of three steps:

Step 1. Set the start and finish times of the uplink grantof each SS i as follows:

su1 ¼ 0fu1 ¼ su1 þ u1

and

sui ¼ fui�1

fui ¼ sui þ ui;

1 < i � n:

In other words, place the uplink grants contiguously fromthe beginning of the uplink frame. This initial allocation ofuplink grants will not be changed.

Step 2. Temporarily set the start and finish times of thedownlink grant of SS i as follows:

sd1 ¼ 0fd1 ¼ sd1 þ d1

and

sdi ¼ fdi�1

fdi ¼ sdi þ di;

1 < i � n:

Step 3. The allocation so far may not comply with thehalf-duplex constraint. Select an offset �x, which will be usedto update the allocation of the downlink grants, so that theresulting allocation complies with the half-duplex con-straint. Left-shift each downlink grant in a circular way(that is, modulo T ) by �x. To do this, update the start andfinish times of the downlink grant of each SS i as follows:

sd1 ¼ ��xj jTfd1 ¼ sd1 þ d1

and

sdi ¼ fdi�1

�� ��T

fdi ¼ sdi þ di�� ��

T;

1 < i � n:

Based on Lemma 1, we can select �x in the range X definedby (4), which is proved to be nonempty. It is worth notingthat any value in X provides the same guarantees, in termsof the feasibility of a set of input grants, as any other valuein the same range. For instance, in the pseudocodedescribed below, we chose �x as the lower bound of X; thatis, �x ¼ minðXÞ ¼ maxið

Pik¼1 dk � sui Þ.

The pseudocode of HDA is reported in Fig. 5.After the initialization of local variables sum and x, the

final allocation of the uplink grants is settled by placingthem contiguously at the beginning of the uplink subframe(lines 1-7). This is done by setting the start time of the firstuplink grant to zero (line 4) and that of any other grant tothe finish time of its previous grant (line 5). Finish times arecomputed as the sum of the start time and the grantduration (line 6). The same operation is carried out fordownlink grants (lines 8-12). Unlike the uplink, the down-link allocation is only temporary. In step 3, we compute thevalue of the offset x that will be used to left-shift thedownlink grants to produce an allocation that complieswith the half-duplex constraint (lines 13-16). Finally, thedownlink temporary allocation is “left-shifted” in a circularway by the modulo (mod) operator (lines 17-21), as definedabove [3]. More specifically, the start time of the firstdownlink grant is brought forward by T-x time units (line18), and the start time of any other downlink grant is set tothe finish time of its previous grant (line 19). Finish timesare computed as the sum of the start time and the grantduration (line 20).

The computational complexity of HDA can be derived asfollows: The body of each for loop includes elementary

1390 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

operations that are performed at a constant time withrespect to the number of grants to allocate (say, n). Sinceeach for loop consists of OðnÞ iterations, the computationcomplexity of the whole procedure is OðnÞ.

4.4 HDA Extension to the Case of Mixed HD-SSsand FD-SSs

When both HD-SSs and FD-SSs are present in the networkand require grant allocation in the same frame, a straight-forward solution is to treat FD-SSs as if they were half-duplex and therefore apply HDA to both. However, withsuch an approach, the sum of the downlink and uplinkgrants addressed to each FD-SS is enforced to be smallerthan the frame duration, which is not necessary. A moreefficient implementation of the grant allocator, which stillcomplies with the pipeline approach devised in Section 3, isgiven as follows:

1. (Grant scheduler) Schedule uplink and downlinkgrants to HD-SSs and FD-SSs such that 1) the sumof the uplink and downlink grants of any HD-SSis smaller than or equal to the frame duration and2) the sum of all uplink (downlink) grants issmaller than or equal to the frame duration.

2. (Grant allocator) Allocate grants addressed to HD-SSsby using HDA as if they were the only ones.

3. (Grant allocator) Allocate grants addressed to FD-SSsin the remaining portion of the uplink and downlinksubframes.

In step 1, the duration of downlink grants addressed toFD-SSs does not include the time needed to transmit aphysical preamble, which is never required for resynchro-nization. Step 2 always succeeds because the sufficientconditions expressed by (3) hold for the subset of scheduled

grants addressed to HD-SSs. The remaining capacity instep 3 is certainly sufficient for FD-SS grants since theoverall sum of grant durations (including both HD-SSs andFD-SSs) in each direction, as produced by the grantscheduler, cannot exceed the frame duration. Finally, notethat it is possible to allocate FD-SSs uplink grants at theexact beginning of the uplink subframe, that is, partiallyoverlapping with the MAC messages broadcast in downlinkby the BS, thus making use of the bandwidth, which, bydefinition, is not available to HD-SSs.

4.5 HDA Extension to Not Time-Aligned Uplink andDownlink Frames

HDA can also be extended to take into account the generalcase where uplink and downlink subframes are notperfectly aligned in time; that is, the uplink allocation starttime is equal to T 0 < T . Fig. 6 illustrates this scenario,where subframes are numbered according to the maprelevance; that is, the downlink subframe x hosts the UL-MAP containing the timetable of uplink grants in subframex. Let us consider uplink and downlink subframes n. Let t0be the start time of downlink subframe n, which is thuslogically split into two sections: The first section begins at t0and ends at t0 þ T 0 when the uplink subframe n begins,whereas the second section begins at t0 þ T 0 and ends att0 þ T . Therefore, the duration of the first section is T 0 andthat of the second section is T � T 0. Note that the uplinkand downlink grants of the first section belong to frames nand n� 1, respectively, whereas those of the second sectionbelong to frame n only. For this reason, it is not possible torun a single instance of HDA over the whole downlink oruplink subframe. Therefore, an instance of HDA is carriedout for each section, where the necessary and sufficientconditions for a feasible grant allocation in (3) are modifiedas follows:

BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1391

Fig. 5. Pseudocode of HDA.

first

section:

Pmi¼1

ui � T 0

Pmi¼1

di � T 0

ui þ di � T 0 1 � i � m;

8>>>><>>>>:

second

section:

Pki¼1

ui � T � T 0

Pki¼1

di � T � T 0

ui þ di � T � T 0 1 � i � k;

8>>>><>>>>:

where m and k are the numbers of grants in the first andsecond sections, respectively. In the pipeline approach, aninstance of the grant scheduler is carried out for eachsection. Finally, note that the duration of maps is subtractedfrom the available frame duration in the first section only.

5 ALTERNATIVE APPROACHES TO THE

HALF-DUPLEX PROBLEM

In the literature, several studies have investigated theperformance of IEEE 802.16. However, to the best of ourknowledge, there is no previous work that explicitly dealswith the allocation of grants for HD-SSs within IEEE 802.16frames. The only reference that we are aware of is [19],where a way of “working around” the half-duplex con-straint is proposed: partitioning the HD-SSs into two sets,which are then served alternately in the downlink anduplink subframes. A detailed description is provided in thenext section. With regard to the performance evaluationstudies of IEEE 802.16, we carried out a detailed simulationanalysis of FD-SSs operated in the FDD mode, which can befound in [9]. In the same context, solutions for packetscheduling with rtPS/nrtPS/BE scheduling services havebeen proposed [6], [20], [26], whereas UGS is considered in[7] and [27]. The performance with the TDD mode wasanalyzed in [12], whereas Hoymann [14] performed a hybridanalytic-simulative analysis of the effect on the systemperformance of several MAC mechanisms, including packetfragmentation and OFDM symbol padding. Finally, thephysical layer of IEEE 802.16 has been investigated in recentsurvey papers [11], [16].

5.1 Odd/Even Static Allocation (SA)

We will now describe the approach proposed in [19],hereafter referred to as the odd/even Static Allocation (SA). SAworks by partitioning the set of HD-SSs into two subsets,

which are referred to as odd and even subsets, respectively.Let us assume that frames are numbered: The odd subsetcontains HD-SSs that transmit in odd-numbered frames andreceive in even-numbered frames, whereas the even subsetcontains HD-SSs that transmit in even-numbered framesand receive in odd-numbered frames. Each HD-SS belongsto exactly one of the above subsets. Therefore, the over-lapping of uplink and downlink grants addressed to thesame HD-SS is prevented from occurring a priori by meansof a static allocation of each HD-SS to only one of thesubsets.

Despite its simplicity, SA has the following disadvan-tages: First, SA only works with an uplink allocation starttime equal to the frame duration. Otherwise, it would not bepossible to keep the odd and even sets of HD-SSs separatedat each frame. Second, SA imposes a tighter constraint onthe grant scheduler with respect to HDA: In addition to thenecessary conditions, the grant scheduler has to enforce thatthe sum of the grants scheduled to an HD-SS over any twoconsecutive frames in one direction does not exceed theframe duration. For instance, with SA, it is not possible toschedule the whole channel bandwidth to an HD-SS in onedirection. Finally, SA is based on a static partitioning of theHD-SSs into odd/even sets, which may become imbalancedin terms of their traffic load. Thus, network resources wouldnot be shared fairly among connections that belong to SSs indifferent sets. However, perfect load balancing is difficult toachieve in practice, even though dynamic partitioning isapplied on a short time scale (that is, the grant schedulerdynamically moves SSs back and forth in order to balancethe current load in the two sets). In fact, besides theamount of complexity that this would inject into the grantscheduler, uplink and downlink MCSs of an SS aregenerally different. Therefore, a partition that would resultin a perfect load balance in one direction would most likelyimply an imbalanced partition in the opposite direction.

6 PERFORMANCE ANALYSIS

In this section, we show the effectiveness of HDA with HD-SSs under realistic traffic conditions through extensivesimulation. Results obtained with HD-SSs via SA and withFD-SSs are considered as a benchmark. The evaluatedscenarios are based on the business opportunity of employ-ing IEEE 802.16 as the last-mile Internet access technologyfor residential and Small and Medium Enterprises (SME)subscribers as envisaged by the WiMAX forum [24].

1392 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

Fig. 6. HDA with the uplink allocation start time smaller than the frame duration.

6.1 Simulation Environment

The network parameters used in the simulations arereported in Table 2. The simulated air interface is theWirelessMAN-OFDM, operating in the FDD duplexingmode, with 7-MHz channel bandwidth and uplink alloca-tion start time equal to the frame duration.

BS scheduling was performed according to the pipelineapproach devised in Section 3. As in [9], we selected DeficitRound Robin (DRR) [21] as the BS’s downlink grantscheduler since it combines the ability to provide fairqueuing, in the presence of variable length packets, withsimplicity of implementation. DRR assumes that the size ofthe head-of-line packet is known at each packet queue;thus, it cannot be used by the BS to schedule transmissionsin the uplink direction. In fact, with regard to the uplinkdirection, the BS can only estimate the overall amount ofbacklog of each connection and not the size of eachbacklogged packet. Therefore, we selected Weighted RoundRobin (WRR) [15] as the uplink grant scheduler in our IEEE802.16 simulator. Both HDA and SA were implemented asthe BS’s grant allocator. Last, we adopted DRR as thescheduling algorithm running at each SS. The uplinkcapacity, which is assigned by the BS on a frame-by-framebasis, is thus shared fairly among each SS connection inproportion to their minimum reserved rates.

Although the accurate modeling of channel conditions iscritical when simulating wireless networks in terms ofprovisioning and resource management, this study focusesonly on those aspects related to the MAC layer. We thusassumed ideal channel conditions, that is, with no packetcorruption due to the wireless channel. Furthermore, wesimulated a steady state of the system where the set ofadmitted connections does not change.

The simulations were carried out using an event-drivenad hoc simulator from the 802.16 MAC protocol written inC++. We implemented the MAC layer of SSs and the BS,including all procedures and functions for uplink/down-link data transmission and uplink bandwidth requests/grants. A detailed description of our design choices andimplementation of the IEEE 802.16 standard can be found in[8] and [9]. Statistical analysis of the simulation output wascarried out using independent replications [17]. We ran20 independent replications whose duration dependedon the traffic source employed (detailed below). In all thesimulation runs, we estimated the 95 percent confidenceinterval for each performance measure. Confidence inter-vals were not drawn when negligible.

6.2 Traffic Models and Workload Characterization

We simulated bidirectional6 multimedia and data traffic,namely, VoIP and Web, respectively. VoIP was modeled asan ON/OFF source with Voice Activity Detection (VAD).Packets were generated only during the ON period. Theduration of the ON and OFF periods was distributedexponentially [4]. Data traffic was modeled as a Websource, generating variable size packets at variable inter-arrival times [18]. The packet size was distributed as atruncated Pareto random variable with the location of7.3 Kbytes, shape of 1.1, and cutoff of 150 Kbytes. Packetinterarrival time was distributed exponentially with themean equal to 1 sec. VoIP and Web connections hadseparate buffers, which hold up to 10 Kbytes and500 Kbytes, respectively, which were large enough toprevent buffer overflow in all the simulated scenarios.The VoIP and Web traffic characterizations are reported inTable 3.

The performance was assessed using the followingmetrics: The transfer delay (or delay for short) is defined asthe time interval between the instant when a packet arrivesat the MAC layer of the source node (SS/BS) and the timethat this packet is completely delivered to the next protocollayer of the destination node (BS/SS). Both the averageand the Cumulative Distribution Function (CDF) areestimated. The delay variation is the difference betweenthe 99th percentile of the delay and the packet transmis-sion time, that is, the time that it takes for a packet ofminimum length to be transmitted over the air. This metricis of paramount importance for VoIP traffic and should bekept as small as possible so as to satisfy the QoS perceivedby the users of VoIP applications. Web traffic, on the otherhand, though interactive, has less stringent delay require-ments and is thus evaluated by means of the averagedelay. Last, we measured the number of SSs served in bothdirections within the same frame, that is, the number ofSSs that have at least one downlink and one uplink grantsin the downlink and uplink subframes occurring at thesame time. The latter helps quantify the impact of the half-duplex constraint on the grant scheduler operation.

We set up each replication of the simulation scenario asfollows: We provided each SS with a random number ofconnections. The number of connections was selectedaccording to a geometric distribution with ratio 0.5 truncatedat 9. In terms of the workload, we assumed that eachconnection carries aggregate traffic from a random numberof basic sources, either Web or VoIP, depending on thescenario, whose characterization and average rate arereported in Table 3. The number of sources was sampledfrom a geometric distribution with ratio 0.5 truncated at 9.Furthermore, the MCS of each SS was uniformly distributedin the set {QPSK-3/4, 16-QAM-1/2, 64-QAM-2/3}, whichentails encoding 24, 48, and 72 bytes per OFDM symbol,respectively. With regard to SA, each SS was randomlyplaced into the odd or even set with equal probability.

6.3 Simulation Results

In this section, we analyze the results obtained with HD-SSs, both HDA and SA, and FD-SSs in simulation scenarioswith the following network parameters and workloadconfiguration: 1) different types of traffic (that is, VoIP

BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1393

6. Uplink and downlink sessions were not correlated.

TABLE 2Network Parameters

and Web), 2) increasing numbers of SSs from 10 to 60, and3) varied frame durations (that is, 5 ms, 10 ms, and 20 ms).

We start with the VoIP traffic with a frame durationequal to 20 ms. Table 4 reports the average number of SSsthat were served in both directions within the same framefor FD-SSs (or FD) and HD-SSs with HDA and SA,respectively. It is important to remember that, in general,the output of the BS grant schedulers (that is, DRR/WRR)depends on several factors, for example, traffic character-ization, QoS parameters, and frame duration. Additionally,the grant schedulers are subject to the half-duplex con-straint, which only holds for HD-SS. Therefore, thedifference between the results from the FD case (whenonly QoS-related requirements are considered by the grantscheduler) and the HDA and SA cases (when the half-duplex constraint is also applied) can be considered as ameasure of the impact of the half-duplex constraint on theoperation of the grant scheduler. As can be seen, whenHDA is employed as a grant allocator, in practice, the half-duplex constraint does not affect the grant scheduleroperation; that is, the difference between the HDA andFD results is negligible irrespective of the number of SSs inthe network. This metric is always zero in the SA case,where no HD-SS is ever scheduled a downlink grant and anuplink grant in the same frame.

We will now analyze the delay variation of uplink anddownlink connections, as reported in Fig. 7. As can be seen,each curve consists of two phases. In the first phase, that is,when the number of SSs is smaller than or equal to x (inuplink, x ¼ 32 with SA and x ¼ 38 with HDA/FD, whereas,in downlink, x ¼ 32 with SA and x ¼ 42 with HDA/FD),the delay variation is almost stable. In the second phase,that is, when the number of SSs increases further, there is asteep increase in the delay variation which would sig-nificantly degrade the quality perceived by the users ofVoIP applications. This is clearly due to the uplink and

downlink subframes being saturated by the overall offeredload; that is, the system is overloaded. The number of SSsthat saturate the subframes with SA is smaller than it iswith HDA/FD, which can be explained as follows: Underthe realistic assumption that SSs are not identical, the odd/even sets of SA may become imperfectly balanced. Thus,the cumulative offered SS load of one set may not be thesame as the other set. However, this does not mean that thelightly loaded set performs significantly better in terms ofthe delay variation, as the latter is almost constant withrespect to the number of SSs. The performance of theheavily loaded set overly degrades when the overallsubframe capacity is exceeded. This is an inherent propertyof SA, where the half-duplex constraint is worked aroundby partitioning the SSs into two sets in a static manner sincethis operation may privilege one set over the other. Byusing HDA, this unfairness is avoided a priori as each HD-SS can be served in any frame. In fact, the HDA and FDcurves almost overlap.

With regard to the difference between FD and HDA, thedelay variation of downlink connections with HDA isslightly greater than with FD. This is because the formerincurs the additional overhead of prepending each down-link burst with a physical preamble so as to allow any SStransmitting in the same frame to resynchronize with thetransmission from the BS, as described in Section 2. There-fore, even though the half-duplex constraint does notsignificantly impact the decisions of the BS’s grant schedu-ler, the net capacity available in the downlink subframe fordata transmission with HDA is slightly smaller than withFD. As far as the uplink is concerned, the HDA and FDcurves almost overlap because each uplink grant needs to be

1394 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

TABLE 3Workload Characterization

TABLE 4Average Number of SSs Served in

Both Directions within the Same Frame

Fig. 7. Delay variation of VoIP connections versus the number of SSs.

prepended by a physical preamble, regardless of the half-duplex capabilities of the SS, as described in Section 2. Thesmall difference seen in Fig. 7 is due to the fact that FD-SSscan exploit the full duration of the uplink subframe. Thisincludes the interval when the BS is transmitting the DL-MAP and UL-MAP, which is unavailable for HD-SSs.

Last, both the uplink and the downlink SA curves lieabove the respective HDA/FD curves, where the offset is atleast equal to the frame duration, that is, 20 ms. This isbecause VoIP connections cannot be served at each framewith SA due to the odd/even constraint. In other words,there are cases when the BS’s grant scheduler has a VoIPpacket enqueued at a downlink connection (or a pendingbandwidth request from an uplink connection), but itcannot schedule a downlink (uplink) grant until the nextframe, as the SS of the connection belongs to the “wrong”set. This behavior is investigated further below. It was alsoverified with a frame duration equal to 5 ms and 10 ms;however, the results are not reported for reasons of space.

In Figs. 8 and 9, we report the CDF of the delay ofdownlink and uplink connections with 30 SSs, that is,before the steep increase in delay variation. Let us considerthe downlink first. The HDA and FD curves almost overlap,with FD incurring a slightly smaller delay than HDA due tothe additional overhead that the latter incurs, as discussedabove. The SA curve diverges from the HDA/FD curves assome packets are delayed due to the odd/even eligibility ofthe destination SS in a given frame, even though there is

enough capacity to transmit them. This effect is amplified inthe uplink case due to the bandwidth request mechanism.Since VoIP applications are served using the rtPS schedul-ing service, the BS polls all connections at regular intervalsequal to the interarrival time of packets, that is, 20 ms. Byresponding to these polls, the BS becomes aware of theamount of data waiting for transmission at the connectionbuffers and schedules uplink grants accordingly. With SA,both when polling a connection and when scheduling theuplink grant, the BS is subject to odd/even partitioning.This explains why the tail of the uplink curve is morepronounced than the tail of the downlink curve. Inaddition, the bandwidth request mechanism justifies theminimum delay of about 30 ms experienced with bothHDA/FD and SA.

To conclude the analysis of VoIP traffic, we will nowinvestigate how the frame duration impacts on the delayvariation of downlink and uplink connections, plotted inFig. 10. For simplicity’s sake, we only report HDA, since thesame conclusions can be drawn from the analysis with FDand SA. As can be seen, the shorter the frame duration, thesmaller the delay variation. In downlink, this is because anySDU enqueued at the BS after the DL-MAP has been senthas to wait until the next frame before it can be scheduledfor transmission. In uplink, the frame duration has an evenstronger impact than in downlink because of the bandwidthrequest mechanism. In fact, the delay of an SDU includesthe latency that the SS experiences for an opportunity tosend a bandwidth request to the BS. This becomes greater asthe frame duration increases, in addition to the time neededby the BS to schedule an uplink grant to the SS, which is atleast the duration of one frame.

However, in both directions, the subframe capacitybecomes saturated with a smaller number of SSs when theframe duration becomes shorter, which can be explained asfollows: In downlink, this is because there is a fixed controloverhead per frame due to the transmission of the DL-MAPand UL-MAP messages, including the long physicalpreamble. This overhead consumes an increasing amountof net capacity available for data transmission when theframe duration is shorter. With regard to the uplink, withshorter frame durations, the BS reacts more promptly to thebandwidth requests sent by the connections. This decreasesthe delays but increases the number of uplink grants thateach connection is scheduled on average in a time unit,

BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1395

Fig. 8. CDF of the delay of downlink VoIP connections with 30 SSs.

Fig. 9. CDF of the delay of uplink VoIP connections with 30 SSs.

Fig. 10. Delay variation of VoIP connections versus the number of SSs

(HDA only).

which subsequently increases the overhead due to physicalpreambles.

We will now discuss the results obtained with Webtraffic with a frame duration equal to 20 ms. Fig. 11 showsthe average delay of downlink and uplink connections.Basically, the same conclusions as those with VoIP trafficcan be drawn in this case; that is, the difference betweenthe FD and HDA curves is negligible and increasesslightly when the offered load increases, whereas the SAcurves lie significantly above the respective FD/HDAcurves. Again, this is due to the odd/even constraint onthe grant scheduler imposed by SA in terms of thetransmission of data and bandwidth requests (uplinkonly). It is worth noting that, unlike for VoIP, the uplinksubframe becomes saturated with a smaller number of SSsthan with the uplink subframe. This is because part of theuplink subframe is reserved by the BS for the transmissionof bandwidth requests in a contention-based manner. Thisthen reduces the capacity available in the uplink withrespect to downlink.

We conclude our analysis of Web traffic by analyzing theCDF of the buffer occupancy of downlink and uplinkconnections before the steep increase in average delays, thatis, with 36 and 52 SSs in the uplink and downlinkdirections, respectively. As shown in Fig. 12, the SA curvesalways lie below the respective HDA/FD curves. Thismight become an issue if the IEEE 802.16 devices hadlimited buffer capacity, in which case, SA would experiencea higher drop rate than HDA/FD due to buffer overflow.Moreover, if a transport protocol like Transmission ControlProtocol (TCP) is used, then there is a degradation ofperformance both in terms of delay, since packets need beretransmitted, and throughput due to the congestioncontrol mechanisms.

7 CONCLUSIONS

In this paper, we have proposed a pipeline approach togrant bandwidth at the BS of an IEEE 802.16 FDD networkwith half-duplex SSs. This approach is based on anallocation algorithm, namely, the HDA algorithm, whichis responsible for finalizing the content of DL-MAPs andUL-MAPs, once the size of the grants has been determinedby the grant scheduler. We have proved that HDA isoptimal in the sense that there is no set of downlink anduplink grants that meet the necessary conditions for the

allocation to be feasible and that cannot be allocated byHDA. The computational complexity of HDA is OðnÞ,where n is the number of the grants to be allocated.

We have investigated the performance of HDA by usingan extensive simulation analysis with VoIP and Web trafficunder varied load conditions and with different framedurations. The results have shown that the performance ofHD-SSs in terms of the most relevant metrics of each traffictype is almost equal to that of FD-SSs. The negligibleperformance degradation in downlink was due to theadditional overhead of HDA, which adds a physicalpreamble to each downlink grant. The performancedegradation in uplink was due to the inability of HD-SSsto transmit while the BS is broadcasting the DL-MAPsand UL-MAPs. Furthermore, we have compared HDA toan alternative approach, namely, SA, where HD-SSs arestatically partitioned into two groups served by the grantscheduler alternately in the downlink and uplink sub-frames. We have shown how the SA approach performsworse than HDA, especially when the SSs are not identical,in terms of offered load and transmission rate.

REFERENCES

[1] D.I. Axiotis, T. Al-Gizawi, K. Peppas, E.N. Protonotarios, F.I.Lazarakis, C. Papadias, and P.I. Philippopoulos, “Services inInterworking 3G and WLAN Environments,” IEEE WirelessComm., vol. 11, no. 5, pp. 14-20, 2004.

[2] B. Bisla, R. Eline, and L.M. Franca-Neto, “RF System and CircuitChallenges for WiMAX,” Intel Technology J., vol. 8, no. 3, pp. 189-200, 2004.

[3] R.T. Boute, “The Euclidean Definition of the Functions Div andMod,” ACM Trans. Programming Languages and Systems, vol. 14,no. 2, pp. 127-144, 1992.

[4] P.T. Brady, “A Model for Generating On-Off Speech Patterns inTwo-Way Conversation,” Bell System Technical J., vol. 48, pp. 2445-2472, 1969.

[5] P.W.C. Chan, E.S. Lo, R.R. Wang, E.K.S. Au, V.K.N. Lau, R.S.Cheng, W.H. Mow, R.D. Murch, and K.B. Letaief, “The EvolutionPath of 4G Networks: FDD or TDD?” IEEE Comm., vol. 44, no. 12,pp. 42-50, 2006.

[6] J. Chen, W. Jiao, and H. Wang, “A Service Flow ManagementStrategy for IEEE 802.16 Broadband Wireless Access Systems inTDD Mode,” Proc. IEEE Int’l Conf. Comm. (ICC ’05), pp. 3422-3426,May 2005.

[7] D.-H. Cho, J.-H. Song, M.-S. Kim, and K.-J. Han, “PerformanceAnalysis of the IEEE 802.16 Wireless Metropolitan Area Net-work,” Proc. First Int’l Conf. Distributed Frameworks for MultimediaApplications (DFMA ’05), pp. 130-137, Feb. 2005.

1396 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007

Fig. 11. Average delay of Web connections versus the number of SSs. Fig. 12. CDF of the buffer occupancy of Web connections with 36 (52)

SSs in uplink (downlink).

[8] C. Cicconetti, C. Eklund, L. Lenzini, and E. Mingozzi, “Quality ofService Support in IEEE 802.16 Networks,” IEEE Network, vol. 20,no. 2, pp. 50-55, 2006.

[9] C. Cicconetti, A. Erta, L. Lenzini, and E. Mingozzi, “PerformanceEvaluation of the IEEE 802.16 MAC for QoS Support,” IEEE Trans.Mobile Computing, vol. 6, no. 1, pp. 26-38, 2007.

[10] C. Eklund, R.B. Marks, K.L. Stanwood, and S. Wang, “IEEEStandard 802.16: A Technical Overview of the WirelessMAN AirInterface for Broadband Wireless Access,” IEEE Comm. Magazine,vol. 40, no. 6, pp. 98-107, 2002.

[11] A. Ghosh, D.R. Wolter, J.G. Andrews, and R. Chen, “BroadbandWireless Access with WiMax/802.16: Current Performance Bench-marks and Future Potential,” IEEE Comm., vol. 43, no. 2, pp. 129-136, 2005.

[12] O. Gusak, N. Oliver, and K. Sohraby, “Performance Evaluation ofthe 802.16 Medium Access Control Layer,” Lecture Notes onComputer Science, vol. 3280, pp. 228-237, 2004.

[13] IEEE 802.16-2004, IEEE Standard for Local and Metropolitan AreaNetworks—Air Interface for Fixed Broadband Wireless Access Systems(Part 16), IEEE, Oct. 2004.

[14] C. Hoymann, “Analysis and Performance Evaluation of theOFDM-Based Metropolitan Area Network IEEE 802.16,” ComputerNetworks, vol. 49, no. 3, pp. 341-363, 2005.

[15] M. Katevenis, S. Sidiropoulos, and C. Courcoubetis, “WeightedRound-Robin Cell Multiplexing in a General-Purpose ATMSwitch Chip,” IEEE J. Selected Areas in Comm., vol. 9, no. 8,pp. 1265-1279, 1991.

[16] I. Koffman and V. Roman, “Broadband Wireless Access SolutionsBased on OFDM Access in IEEE 802.16,” IEEE Comm., vol. 40,no. 4, pp. 96-103, 2002.

[17] A.M. Law and W.D. Kelton, Simulation Modeling and Analysis,third ed. McGraw-Hill, 2000.

[18] “Evaluation Methods for High Speed Downlink Packet Access(HSDPA),” TSG-R1 document TSGR#14(00)0909, Motorola, 2000.

[19] J.F. Mollenauer, J. Klein, and B. Petry, “An Efficient Media AccessControl Protocol for Broadband Wireless Access Systems,” IEEE802.16 Broadband Wireless Access Working Group, Oct. 1999.

[20] M. Settembre, M. Puleri, S. Garritano, P. Testa, R. Albanese, M.Mancini, and V. Lo Curto, “Performance Analysis of an EfficientPacket-Based IEEE 802.16 MAC Supporting Adaptive Modulationand Coding,” Proc. Seventh IEEE Int’l Symp. Computer Networks(ISCN ’06), pp. 11-16, June 16-18,2006.

[21] M. Shreedhar and G. Varghese, “Efficient Fair Queueing UsingDeficit Round Robin,” IEEE/ACM Trans. Networking, vol. 4, no. 3,pp. 375-385, 1996.

[22] D. Stiliadis and A. Varma, “Latency-Rate Servers: A GeneralModel for Analysis of Traffic Scheduling Algorithms,” IEEE/ACMTrans. Networking, vol. 6, pp. 675-689, 1998.

[23] WiMAX Forum, http://www.wimaxforum.org/, 2007.[24] WiMAX Forum, “Business Case Models for Fixed Broadband

Wireless Access Based on WiMAX Technology and the 802.16Standard,” Oct. 2004.

[25] WiMAX Forum, “Initial Certification Profiles and the EuropeanRegulatory Framework,” WiMAX Forum Regulatory WorkingGroup, Sept. 2004.

[26] K. Wongthavarawat and A. Ganz, “Packet Scheduling for QoSSupport in IEEE 802.16 Broadband Wireless Access Systems,” Int’lJ. Comm. Systems, vol. 16, no. 1, pp. 81-96, 2003.

[27] Y. Yao and J. Sun, “Study of UGS Grant Synchronization for802.16,” Proc. Ninth IEEE Int’l Symp. Consumer Electronics (ISCE’05), pp. 105-110, June 2005.

Andrea Bacioccola received the master’sdegree (magna cum laude) in computer systemsengineering from the University of Pisa, Italy, inDecember 2005. He is currently a PhD studentat the University of Pisa. In 2004, he spent fourmonths at the Nokia Research Center inHelsinki, where he worked on scheduling algo-rithms for IEEE 802.16 wireless networks. Hismain research areas are quality of service inwireless multiservice networks, network simula-

tion, and performance evaluation.

Claudio Cicconetti received the bachelor’sdegree in computer systems engineering fromthe University of Pisa, Italy, in October 2003. Heis currently pursuing the PhD degree at thesame university. His research interests includequality of service in IEEE 802.16 and IEEE802.11 wireless networks, medium access con-trol protocols for mobile computing, and wirelessmesh networks. He is involved in the EuQoS(End-to-end Quality of Service support over

heterogeneous networks) project, which participates in the EU Informa-tion Society Technologies (IST) Programme. He has served as amember of the organizing committee of the First InternationalConference on Performance Evaluation Methodologies and Tools(VALUETOOLS 2006). He is a student member of the IEEE.

Alessandro Erta received the bachelor’s de-gree (cum laude) in computer systems engineer-ing from the University of Pisa, Italy, in February2005. During his master’s thesis, he joined theNokia Research Center, Helsinki, where hedesigned and evaluated solutions for the IEEE802.16/WiMAX standard. He is currently a PhDstudent at the Institutions, Markets, Technolo-gies (IMT) Lucca Institute for Advanced Studies.He has been involved in the national project

NADIR and in projects supported by private companies (Telecom ItaliaLab, Nokia). His research interests include quality of service in wirelessnetworks, the design and performance evaluation of medium accesscontrol (MAC) protocols, and scheduling algorithms for wirelessnetworks and wireless mesh networks.

Luciano Lenzini holds a degree in physics fromthe University of Pisa, Italy. He joined CNUCE,Italian National Research Council (CNR), in1970. In 1994, he joined the Department ofInformation Engineering, University of Pisa, as afull professor. He is currently on the editorialboards of Computer Networks and the Journal ofCommunications and Networks. He served aschairman for the 1992 IEEE Workshop onMetropolitan Area Networks and for the 2002

European Wireless Conference (EW ’02). He has directed severalnational and international projects in the area of computer networking.His current research interests include the design and performanceevaluation of medium access control (MAC) protocols for wirelessnetworks and the quality-of-service provision in integrated and differ-entiated services networks.

Enzo Mingozzi received the Laurea (cumlaude) and PhD degrees in computer systemsengineering from the University of Pisa in 1995and 2000, respectively. He has been an associ-ate professor with the Faculty of Engineering,University of Pisa, Italy, since January 2005. Hisresearch activities span several areas, includingdesign and performance evaluation of multipleaccess protocols for wireless networks, quality-of-service (QoS) provisioning, and service inte-

gration in Internet Protocol (IP) networks. He has been involved inseveral national (FIRB, PRIN) and international (Eurescom, IST)projects, as well as research projects supported by private industries(Telecom Italia Lab and Nokia). He also actively took part in thestandardization process of HIPERLAN/2 and HIPERACCESS networksin the framework of the ETSI project Broadband Radio Access Networks(BRAN). He is a member of the IEEE and the IEEE Computer Society.

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BACIOCCOLA ET AL.: BANDWIDTH ALLOCATION WITH HALF-DUPLEX STATIONS IN IEEE 802.16 WIRELESS NETWORKS 1397