Bandwidth Allocation with Half-Duplex Stations in IEEE ... - IEEE Xplore

3 downloads 1197 Views 2MB Size Report
Access Control (MAC) protocol is centralized and explicitly supports quality of ... uplink and downlink scheduled grants so as to support half-duplex capabilities.
1384

IEEE TRANSACTIONS ON MOBILE COMPUTING,

VOL. 6, NO. 12,

DECEMBER 2007

Bandwidth Allocation with Half-Duplex Stations in 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

I

NDUSTRY and research communities are investing considerable effort in the convergence of multimedia services (for example, voice over IP (VoIP), video, and massive online gaming) and ubiquitous instant access, which, by necessity, depends on the use of Broadband Wireless Access (BWA) technologies [1]. The IEEE 802.16 standard for BWA has been developed by IEEE [13]. Since 2001, the Worldwide Interoperability for Microwave Access (WiMAX) forum [23], a nonprofit organization with over 400 partners, has been working to promote and certify the compatibility and interoperability of IEEE 802.16 for fixed and mobile BWAs. An IEEE 802.16 network consists of a number of Subscriber Stations (SSs) served by a Base Station (BS). According to the standard, time is partitioned into frames of fixed duration. Within each frame, transmissions occur in both directions: from the BS to the SSs (downlink direction)

. A. Bacioccola, C. Cicconetti, L. Lenzini, and E. Mingozzi are with the Dipartimento di Ingegneria dell’Informazione, University of Pisa, Via Diotisalvi, 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: [email protected]. 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: [email protected], and reference IEEECS Log Number TMC-0246-0805. Digital Object Identifier no. 10.1109/TMC.2007.1064. 1536-1233/07/$25.00 ß 2007 IEEE

and from each SS to the BS (uplink direction). In order to support bidirectional transmissions, IEEE 802.16 specifies two alternative duplex modes [5]. The first is Frequency Division Duplex (FDD), where uplink and downlink transmissions occur simultaneously on separate frequencies. The second is Time Division Duplex (TDD), where uplink and downlink transmissions alternate within the time frame and share the same frequencies. Regardless of the duplex mode, an SS can have either full-duplex or halfduplex transmission capabilities. A full-duplex SS (FD-SS) can simultaneously listen to the downlink channel while transmitting data, whereas a half-duplex SS (HD-SS) cannot receive while transmitting, that is, uplink and downlink transmissions 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 with HD-SSs are expected to be widely used solutions for a number of reasons [2]. First, most licensed bands intended for data applications operate with FDD systems in mind. Second, providing wireless communication devices with full-duplex capabilities is challenging. In fact, when the wireless transceiver is transmitting data, a large fraction of the signal energy leaks into the receive path. The transmitted and received power levels can differ by several orders of magnitude and, therefore, the impact of the energy leakage can be significant. FD-SSs are thus more expensive to design and manufacture than HD-SSs, and the latter seem to offer a very attractive solution for user Published by the IEEE CS, CASS, ComSoc, IES, & SPS

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

1385

Fig. 1. FDD frame structure with IEEE 802.16.

radio devices. Finally, up until the beginning of 2007, most WiMAX-certified SSs supported only half-duplex operations when operated in FDD mode. Irrespective of the duplex mode and the SS transmission capabilities, IEEE 802.16 Medium Access Control (MAC) is centralized and connection oriented: All data communications for both transport and control are carried out in a unidirectional connection. SSs notify the BS of the number of bytes to be sent by a connection through specific MAC headers. The BS controls access to the medium by broadcasting a number of bandwidth grants at the beginning of each frame. Each bandwidth grant specifies which SSs are going to receive data from the BS (downlink grants) or which ones are allowed to transmit data to the BS (uplink grants) in the forthcoming frame. Bandwidth grants also specify when in the frame and for how long an SS will receive/transmit data. As specified in the IEEE 802.16 standard, the BS is responsible for providing connections with quality-of-service (QoS) guarantees. Therefore, the BS has to implement a scheduling function to grant adequate downlink and uplink bandwidth to each SS according to the negotiated QoS of the admitted connections. When implementing the BS scheduling function in IEEE 802.16 FDD systems that support HD-SSs, two related issues need to be tackled. The first is how we can grant bandwidth in each frame and in both the uplink and the downlink directions so as to provide the admitted connections with the negotiated level of QoS. The second issue is how we can coordinate the downlink and uplink bandwidth grants in time so as to also comply with the half-duplex constraint for each HD-SS. In this respect, it is worth noting that the standard does not specify any mandatory or informative solution: IEEE-802.16-compliant device manufacturers are thus free to develop their own solutions. In this paper, we propose a framework for solving the above issues, which is based on a pipeline approach: Bandwidth granting is first performed by determining the duration of each uplink and downlink grant, irrespective of the actual allocation in the time frame. The latter is then performed in its entirety in a subsequent step. To this aim, we devise sufficient conditions to be met when granting bandwidth, which guarantee that the time allocation of grants will always be feasible

without violating the half-duplex constraint. In addition, we propose a grant allocation algorithm, namely, the HalfDuplex Allocation algorithm (HDA),1 which arranges the grants scheduled to both FD-SSs and HD-SSs in the frame. Furthermore, we prove HDA to be 1) optimal in the sense that, if there is a feasible allocation of a set of scheduled grants, then HDA is always able to find it, and 2) computationally efficient, since grant allocation is completed in OðnÞ 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 protocol that are relevant to this study. In Section 3, we provide a detailed rationale and introduce the pipeline approach. In Section 4, we describe HDA and formally prove its properties. In Section 5, we present an alternative approach to “work around” the half-duplex constraint. In Section 6, the performance of HD-SSs using HDA is compared through simulation to that obtained with the aforementioned alternative approach and FD-SSs. Conclusions are drawn in Section 7.

2

IEEE 802.16 MAC

In this section, we describe those aspects of the IEEE 802.16 MAC protocol that are specifically relevant to this study. We thus focus on the Point-to-Multipoint (PMP) mode with a centralized BS operating in FDD using the WirelessMAN-OFDM physical layer, which is the most promising air interface for supporting Non-Line-of-Sight (NLOS) operations in fixed BWA networks [25]. In this context, the basic time allocation unit is the OFDM symbol, which is made up of 256 subcarriers according to the standard Fast Fourier Transform (FFT) size. The interested reader can find a technical introduction to the OFDM system of the IEEE 802.16 in [16]. As already mentioned, time is partitioned into frames of fixed duration. Since the duplex mode is FDD, uplink and downlink transmissions occur simultaneously on separate frequencies. The frame structure is shown in Fig. 1. In the downlink subframe, the BS transmits MAC Protocol Data Units (PDUs). BS transmission is broadcast; thus, all SSs 1. HDA is under a patent owned by Nokia Corp.

1386

IEEE TRANSACTIONS ON MOBILE COMPUTING,

listen to the data transmitted by the BS. However, an SS is entitled to only process the burst of PDUs that is directed to itself. On the other hand, in the uplink subframe, each SS transmits multiple bursts of MAC PDUs to the BS in a Time Division Multiple Access (TDMA) manner. A MAC PDU consists of one or more MAC Service Data Units (SDUs) which are used to convey data from upper layers, for example, Internet Protocol version 4 (IPv4) datagrams or Ethernet frames. MAC SDUs can be fragmented or concatenated by the sending entity, either SS or BS, to efficiently exploit the available capacity. DL-MAP and ULMAP messages (or maps), which are advertised by the BS at the beginning of each frame, contain the time boundaries of downlink and uplink grants addressed to different SSs. More specifically, a downlink grant in the DL-MAP announces the transmission by the BS of a burst of PDUs addressed to a given SS. An uplink grant in the UL-MAP, on the other hand, announces a time interval inside the uplink subframe within which a given SS is allowed to transmit a burst of PDUs. As shown in Fig. 1, the DL-MAP is prepended by a physical long preamble (two OFDM symbols), which is needed for synchronization. Each uplink burst starts with a physical short preamble (one OFDM symbol), which allows the BS to synchronize its receiver with the subsequent transmission of data from the SS. The uplink subframe is delayed with respect to the beginning of the downlink subframe by a fixed amount of time, called the uplink allocation start time, so as to give SSs enough time to decode the UL-MAP and take appropriate decisions. IEEE 802.16 specifies that this value must be at least as long as the maximum Round-Trip Time (RTT) delay but not longer than the frame duration. As an example, in Fig. 1, the uplink allocation start time is equal to the frame duration and, thus, the beginning of the uplink subframe n overlaps with the beginning of the downlink subframe n þ 1. All SSs, both HD-SS and FD-SS, synchronize themselves with the BS by means of the long preamble transmitted at the beginning of the downlink subframe so as to retrieve information from DL-MAP and UL-MAP messages. FD-SSs keep themselves synchronized to the downlink channel by continuously listening to the BS’s transmissions. On the other hand, an HD-SS is synchronized with the downlink channel only as far as the beginning of its own uplink grant, if any. At this point, in fact, the HD-SS has to switch its radio transceiver from receiving to transmitting modes, thus losing synchronization with the downlink channel. Even though HD-SS switches back to the receiving mode after transmission, synchronization with the downlink channel is lost and cannot be restored unless the BS transmits a new physical preamble (illustrated in Fig. 1). Therefore, the BS is required to add a physical short preamble to each downlink burst that is addressed to an HD-SS whose uplink grant was scheduled after the occurrence of the beginning of the last downlink subframe. On the other hand, physical preambles are never added to downlink 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 scheduling service defines a mandatory set of QoS parameters such

VOL. 6, NO. 12,

DECEMBER 2007

as the Minimum Reserved Traffic Rate, the Maximum Latency, and the Unsolicited Polling Interval, which is tailored to meet the guarantees required by the applications that the scheduling service is designed for. The detailed differences 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 performance evaluation in Section 6, we briefly report their most important features. The rtPS scheduling service is designed to support real-time applications with stringent delay requirements that generate variable size data packets at periodic intervals such as Moving Pictures Expert Group (MPEG) video and VoIP with silence suppression. In fact, a minimum reserved rate is specified for each connection. In addition, for uplink rtPS connections only, the BS periodically polls each rtPS connection. This is in order to become aware of the amount of data waiting for transmission at the connection buffers, which reside at the SSs, and to schedule uplink grants accordingly. The BE scheduling service, on the other hand, is envisaged for use by applications that do not pose any specific delay constraints such as Web browsing and e-mail transfer. Unlike rtPS, uplink BE connections request bandwidth from the BS by means of a contention-based mechanism that occurs in specifically allocated time slots of the uplink subframe and is notified by the BS through the UL-MAP. When a collision occurs, because different SSs transmit a bandwidth request in the same slot, SSs employ a truncated binary exponential backoff mechanism so as to reduce the chance of collision when they reiterate the bandwidth request transmission. Finally, the IEEE 802.16 standard specifies a rate adaptation procedure to be employed by the BS and SSs to maximize data transmission efficiency [10]. This involves selecting the Modulation and Coding Scheme (MCS) used to receive from (or transmit to) any SS among a set of possible combinations periodically advertised by the BS.

3

RATIONALE

One of the main responsibilities of the BS is to guarantee QoS to admitted connections, both downlink and uplink, according to the QoS requirements of the applications specified by the scheduling services introduced in Section 2. To achieve this, downlink and uplink grants in each frame must be appropriately scheduled to SSs based on both the current traffic load of each connection and the available resources. We refer to the scheduling function inside the BS as the functional module in charge of performing this task, that is, to define at the beginning of each frame the start time and the duration of each bandwidth grant, and, therefore, the content of maps. As already mentioned, the specification of the algorithms to be implemented by the scheduling function at the BS is beyond the scope of the standard and is thus left up to the manufacturers [13, p. 139]. When the FDD mode is used, since transmissions occur on separate frequencies, there are actually two separate transmission resources to be scheduled in every frame, that is, the uplink and the downlink subframes. An obvious constraint for the scheduling function in this case is that the overall amount of bandwidth granted in a downlink or uplink subframe, that is, the sum of the respective grant durations as announced in the maps, cannot be greater than

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

1387

Fig. 3. Unfeasible grant scheduling in FDD.

Fig. 2. Grant scheduling and allocation in FDD.

the length of the subframe itself.2 Furthermore, when only FD-SSs are present in the system, there is no constraint on the relative time location of the downlink and uplink grants addressed to the same SS since the latter can manage the simultaneous transmission and reception of bursts. It follows that, with FDD and FD-SSs, the only nontrivial task to be performed by the BS scheduling function is to determine the duration of each uplink and/or downlink grant to address to each SS since any time allocation of the grants in the respective subframes will be feasible. Therefore, the scheduling function could be implemented using a pipeline approach, as depicted in Fig. 2, where the scheduling function is partitioned into two main subfunctions, namely, the grant scheduler and the grant allocator. The grant scheduler is responsible for determining the duration of each grant in the respective subframe.3 The output of the grant scheduler is then fed to the grant allocator, which is responsible both for determining the start time of each grant in the respective subframe and for finalizing the content of the maps to be transmitted by the BS. Since bandwidth is scheduled on a frame-by-frame basis, QoS guarantees should be expressed with a time granularity 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 2. To be precise, the overhead due to map transmissions should also be taken into account for the downlink subframe. However, this is not relevant for the current discussion and, thus, we assume for simplicity’s sake that the overhead due to map transmissions is negligible. 3. In doing so, it must explicitly take into account the QoS requirements of the admitted connections. In addition, it could also consider other system factors such as the modulation used by each SS and take the appropriate action regardless of the allocation problem.

choose the one that best fits the service that it is planning to offer. It follows that, with the pipeline approach in mind, QoS provisioning only depends on the algorithm implemented in the grant scheduler. This is the main advantage of this approach since the task of scheduling bandwidth for QoS support is confined to a well-identified functional submodule and is naturally abstracted from the details originating from the grant allocation within the frame. Furthermore, it is easy to see how such an isolation allows for implementing scheduling algorithms as a result of the simple adaptation of well-known algorithms already proposed in the context of wired networks, where this discipline has been extensively studied in the recent past [21], [22]. Finally, the pipeline approach has a definite advantage as far as the implementation is concerned. In fact, map production is a real-time task with a hard deadline, the latter being the beginning of the subsequent frame. If scheduling and allocation can actually be implemented by independent subtasks interworking concurrently according to a pipeline scheme, then the time that can be dedicated by each subtask to accomplish its work in every frame is basically doubled. This is because the grant scheduler can start working on the next frame, whereas the grant allocator is still allocating the current one. Therefore, either a less powerful processing hardware can be used inside the BS with the same scheduling algorithm, or with the same hardware, more complex scheduling algorithms can be implemented. However, with FDD and HD-SSs, the pipeline approach devised in Fig. 2 cannot be implemented “as is.” In fact, the duration of the grants, as determined by the grant scheduler, may be such that there is no way of allocating them in the current frame without violating the half-duplex constraint. For example, if the grant scheduler selected both an uplink grant and a downlink grant to the same HD-SS in a frame, and the sum of the duration of the two grants exceeds the frame duration, then the grant allocator is clearly not able to produce any valid map. This example would be illustrated in Fig. 3, where the uplink and downlink grants addressed to SS 1 would overlap over

1388

IEEE TRANSACTIONS ON MOBILE COMPUTING,

time regardless of the allocation algorithm. It is worth noting, as we prove numerically in Section 6, that the scheduling of a station, both uplink and downlink, in the same frame is a typical case when QoS guarantees have to be provided. In conclusion, whereas the grant scheduler and allocator operations are completely decoupled from each other when only FD-SSs are considered, they actually become tightly coupled when HD-SSs are present as well. Many solutions can be devised to work around this problem. One solution could be to abandon the pipeline approach and implement the scheduling function with algorithms that jointly define the duration and start time of each grant. This approach could be described as producing the final maps through a number of successive iterations involving the scheduler and the allocator depicted in Fig. 2 based on the exchange of their intermediate results. However, the advantages of the pipeline approach discussed above would be withdrawn as well. On the other hand, one could try to find sufficient conditions to impose on the grant scheduler so that the grant allocator could always find a feasible grant allocation. For example, one could trivially impose that an HD-SS could only be granted bandwidth in one direction in each frame. This would remove the burden of coping with the half-duplex constraint explicitly. However, such sufficient conditions should be carefully selected since they could greatly affect the capability of the grant scheduler to provide the admitted connections with the required QoS guarantees. We could formulate such a requirement by stating that, if the pipeline approach is followed, then the sufficient conditions imposed on the output of the grant scheduler should be as loose as possible. On the other hand, it is straightforward to identify the necessary conditions for the grants’ duration defined by the grant scheduler so that the grant allocation is feasible. Specifically, such necessary conditions are that the overall bandwidth, both downlink and uplink, granted to each HDSS in each frame must not exceed the frame duration.4 The main contribution of this paper is providing a formal proof that the above-mentioned necessary conditions are also sufficient to guarantee that scheduled grants can be allocated in the respective subframes without violating the halfduplex constraint. In this respect, such sufficient conditions are the loosest possible because they are also necessary; that is, they are essential to all other sets of conditions that could be devised. Furthermore, based on the above proof, we propose an algorithm for the grant allocator, namely, the HDA algorithm, which can always arrange the scheduled grants in the respective subframes provided that sufficient conditions are met. Thus, HDA can be employed in the grant allocator, whatever algorithm is implemented in the grant scheduler. This means that a pipeline approach can also be adopted in the case of HD-SSs, where grant scheduling and allocation are only loosely coupled. In the next section, we describe HDA and prove that it can allocate any set of downlink and uplink grants in the respective subframes without violating the half-duplex constraint, provided that the necessary conditions hold. 4. Without losing generality, we refer to the case where the uplink allocation start time is equal to the frame duration and, thus, uplink and downlink subframes perfectly overlap in time.

4

VOL. 6, NO. 12,

DECEMBER 2007

HDA ALGORITHM

In this section, we describe HDA and prove its formal properties. First, we introduce the notation and assumptions that will be used in the rest of the section. We then prove that the necessary conditions are also sufficient for a set of unicast5 grants addressed to HD-SSs to be allocated in a frame without violating the half-duplex constraint. The proof of one of the main theoretical results, namely, Lemma 1, enables us to define the HDA algorithm. To simplify the notations, hereafter, we assume that all grants are addressed to HD-SSs (hence, we refer to them as SSs), and the uplink allocation start time is equal to the frame duration. The solution for the general case, where FD-SSs are also present and uplink and downlink subframes are not 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) as the frame duration minus the duration of MAC messages, which are broadcast by the BS at the beginning of the downlink subframe for management purposes, and do not convey MAC SDUs. MAC messages include the UL- and DL-MAPs, which were described in Section 2, as well as several messages that have not been reported since their functions are beyond the scope of this paper. All SSs need to listen to those messages whose transmission duration may vary frame by frame. Thus, the overlapping portion of the uplink frame cannot be used for uplink grants, which are accounted for by the above definition of T . Without loss of generality, we assume that each SS is scheduled exactly one grant for each direction per frame. In fact, should an SS be scheduled more than one grant in the same direction, they could all be equivalently aggregated into a single grant whose duration is the sum of the durations of the grants originally scheduled. However, should no grant be scheduled to an SS in one direction, we equivalently assume that a grant of null duration has been scheduled instead. We also assume that the grant duration includes any protocol overhead such as the synchronization preamble. Let n be the number of SSs scheduled in the current frame. The grant allocated to SS i within the frame of available duration T is uniquely identified by any two of the following quantities: the start time sxi , the finish time fix , and the duration xi , where x 2 fd; ug represents either the downlink or the uplink direction. It is straightforward to derive the relationships between the three quantities as follows: 8  x  x > < fi ¼ si þ xi T sx ¼ f x  xi T > i  ix : xi ¼ fi  sxi T ; where the modulo operator jxjT is defined based on Euclid’s Theorem, as reported in [3]; that is, jxjT ¼ x  bx=T c  T : The notation is summarized in Table 1 and illustrated in Fig. 4. 5. The results reported in this section cannot be straightforwardly extended to multicast connections. However, the main challenge with multicast is to schedule grants by taking into account the different physical profiles of the SSs which participate in a multicast session since they dynamically adapt their modulation and coding according to physical-layer measurements. Hence, we consider unicast connections only.

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

1389

TABLE 1 Glossary

Fig. 4. Notations.

8 > > > > < > > > > : We now provide a set of definitions and preliminary results, which basically formalize the problem of grant allocation.     Definition 1. A set U ¼ sui ; ui ðD ¼ sdi ; di Þ of uplink (downlink) allocated grants is said to be feasible iff for any time instant t 2 ½0; T , there exists at most one grant ðsuj ; uj Þ  U ððsdj ; dj Þ  DÞ, 1  j  n, such that jt  suj jT < uj ðjt  sdj jT < dj Þ:

ð1Þ

Inequality (1) means “the time instant t lies between the start and the end times of the uplink (downlink) grant addressed to SS j.” Therefore, the definition above formally states the intuitive concept that an allocation is feasible iff the uplink and downlink allocated grants of any SS do not overlap in time. Proposition 1. A set U of uplink grants is feasible iff jsui  fju jT þ ui þ uj  T , 1  i, j  n, i 6¼ j. A set D of downlink grants is feasible iff jsdi  fjd jT þ di þ dj  T , 1  i, j  n, i 6¼ j. Proof. The proof is straightforward, considering that jsui  fju jT is the time interval between the end of one grant and the beginning of the next, 2. ui is the grant scheduled starting from sui onward and uj is the grant scheduled starting from fju backward, and 3. if the sum of the three is not greater than T , then grants ui and uj do not overlap. The same line of reasoning also applies to downlink grants. u t 1.

From Proposition 1, if U ðDÞ is a feasible set of uplink (downlink) grants, then i ui  T ði di  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  such that t  sui T < ui , it is t  sdi T  di . In other words, the uplink and downlink grants for the same SS do not overlap over 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 feasible sets is feasible iff  d  s  f u  þui þ di  T ; 1  i  n: ð2Þ i i T Thus, fU; Dg is not feasible if any of the following conditions is false:

n P i¼1 n P

ui  T ð3Þ

di  T

i¼1

ui þ d i  T

1  i  n:

Proposition 3. Given a feasible pair fU; Dg, any pair fUt ; Dt g such that Ut ¼ fðjsui þ tjT ; ui Þg and Dt ¼ fðjsdi þ tjT ; di Þg, 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: ~¼ Lemma 1. Let U be a feasible set of uplink grants. Let D fdk 2 IRjdk  0; 1  k  ng be a set of n nonnegative real numbers and let X be defined as follows:  ! ( !)  i i1 X X   u u dk  si  x  min dk  fi þ T : X ¼ x 2 IRmax i  i k¼1 k¼1 ð4Þ If

Pn

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  fiu for any i. Proving the thesis is equivalent to proving that ! ! i1 i X X u u dk  fi þ T  max dk  si  0; min i

i

k¼1

k¼1

i.e., for any i, j, 1  i, j  n, it must be ! j1 i X X dk  fju þ T  dk  sui  0: k¼1

k¼1

We consider three possible cases: Case 1. i > j. It is ! j1 i i X X X u u d k  fj þ T  dk  si ¼ T  dk þ sui  fju  0 k¼1

k¼1

k¼j

ik¼j dk

nk¼1 dk

  T for any i > j by hypothesis since and sui  fju because of the feasibility of U. Case 2. i < j. It is ! j1 j1 i   X X X u u dk fj þ T  dk  si ¼ T  fju  sui þ dk  0 k¼1

k¼1

k¼iþ1

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

1390

IEEE TRANSACTIONS ON MOBILE COMPUTING,

Case 3. i ¼ j. It is i1 X

dk  fiu þ T 

k¼1

i X

! dk  sui

¼ T  ui  di  0

k¼1

by hypothesis for any i, which concludes the proof.

u t

Theorem 1, which is the main theoretical contribution, proves that the necessary conditions that must be met by a set of grants addressed to SSs in order to be feasible are also sufficient. Theorem 1. Let U be a feasible set of uplink grants and let fdi g be a set of grants. A set of downlink grants D such that the pair fU; Dg is feasible always exists iff ni¼1 di  T and ui þ di  T , 1  i  n. Proof. If part (sufficient condition). Without losing generality, we assume that i < j , sui  suj . Furthermore, based on Proposition 3, we assume that su1 ¼ 0, which yields sui  fiu for any i. Let us consider a set of downlink grants D such that   X  i1   d d k  x ð5Þ si ¼   k¼1  T

for any x 2 X, where X is defined according to (4). Note that 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 is feasible by using Proposition 2. By substituting (5) into (2), we obtain   X  i1  d   u s  f u  þui þ di ¼  dk  fi  x þui þ di : ð6Þ i i T  k¼1  T

Now, by the definition of X, it follows that i X

dk  sui  x 

k¼1

i1 X

dk  sui  ui þ T

k¼1

for any x 2 X. Hence, x can be rewritten as x¼

i X

dk  sui þ y

ð7Þ

k¼1

provided that 0  y  T  ui  di . Substituting (7) into (6) yields  d  s  f u  þui þ di i i T   !   X i1 i X  u    u ¼ dk  dk þ si  si  ui  y þui þ di   k¼1 k¼1 T

¼ jdi  ui  yjT þui þ di ¼ T  di  ui  y þ ui þ di ¼ T  y  T: ð8Þ Equation (8) holds for any i, 1  i  n, which completes the proof. Only if part (necessary condition). This immediately follows from Propositions 1 and 2. u t

VOL. 6, NO. 12,

DECEMBER 2007

4.3 HDA Algorithm Based on the constructive proof of Lemma 1, we devised an algorithm, called HDA, to allocate a set of uplink and downlink grants fui g [ fdi g such that the half-duplex constraint is satisfied provided that the necessary conditions are met. HDA, whose correctness is proved by Theorem 1, consists of three steps: Step 1. Set the start and finish times of the uplink grant of each SS i as follows: u u u si ¼ fi1 s1 ¼ 0 1 < i  n: and u u u fi ¼ sui þ ui ; f1 ¼ s1 þ u1 In other words, place the uplink grants contiguously from the beginning of the uplink frame. This initial allocation of uplink grants will not be changed. Step 2. Temporarily set the start and finish times of the downlink grant of SS i as follows: d d d si ¼ fi1 s1 ¼ 0 1 < i  n: and d d d fi ¼ sdi þ di ; f1 ¼ s1 þ d1 Step 3. The allocation so far may not comply with the half-duplex constraint. Select an offset x, which will be used to update the allocation of the downlink grants, so that the resulting allocation complies with the half-duplex constraint. Left-shift each downlink grant in a circular way (that is, modulo T ) by x. To do this, update the start and finish times of the downlink grant of each SS i as follows: d  d  d si ¼ fi1 T  s1 ¼ j xjT 1 < i  n: and f1d ¼ sd1 þ d1 fid ¼ sdi þ di T ; Based on Lemma 1, we can select x in the range X defined by (4), which is proved to be nonempty. It is worth noting that any value in X provides the same guarantees, in terms of the feasibility of a set of input grants, as any other value in the same range. For instance, in the pseudocode described below, we chose P x as the lower bound of X; that is, x ¼ minðXÞ ¼ maxi ð ik¼1 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 placing them contiguously at the beginning of the uplink subframe (lines 1-7). This is done by setting the start time of the first uplink grant to zero (line 4) and that of any other grant to the finish time of its previous grant (line 5). Finish times are computed as the sum of the start time and the grant duration (line 6). The same operation is carried out for downlink grants (lines 8-12). Unlike the uplink, the downlink allocation is only temporary. In step 3, we compute the value of the offset x that will be used to left-shift the downlink grants to produce an allocation that complies with the half-duplex constraint (lines 13-16). Finally, the downlink temporary allocation is “left-shifted” in a circular way by the modulo (mod) operator (lines 17-21), as defined above [3]. More specifically, the start time of the first downlink grant is brought forward by T-x time units (line 18), and the start time of any other downlink grant is set to the finish time of its previous grant (line 19). Finish times are computed as the sum of the start time and the grant duration (line 20). The computational complexity of HDA can be derived as follows: The body of each for loop includes elementary

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

1391

Fig. 5. Pseudocode of HDA.

operations that are performed at a constant time with respect to the number of grants to allocate (say, n). Since each for loop consists of OðnÞ iterations, the computation complexity of the whole procedure is OðnÞ.

4.4

HDA Extension to the Case of Mixed HD-SSs and FD-SSs When both HD-SSs and FD-SSs are present in the network and require grant allocation in the same frame, a straightforward solution is to treat FD-SSs as if they were halfduplex and therefore apply HDA to both. However, with such an approach, the sum of the downlink and uplink grants addressed to each FD-SS is enforced to be smaller than the frame duration, which is not necessary. A more efficient implementation of the grant allocator, which still complies with the pipeline approach devised in Section 3, is given as follows: (Grant scheduler) Schedule uplink and downlink grants to HD-SSs and FD-SSs such that 1) the sum of the uplink and downlink grants of any HD-SS is smaller than or equal to the frame duration and 2) the sum of all uplink (downlink) grants is smaller than or equal to the frame duration. 2. (Grant allocator) Allocate grants addressed to HD-SSs by using HDA as if they were the only ones. 3. (Grant allocator) Allocate grants addressed to FD-SSs in the remaining portion of the uplink and downlink subframes. In step 1, the duration of downlink grants addressed to FD-SSs does not include the time needed to transmit a physical preamble, which is never required for resynchronization. Step 2 always succeeds because the sufficient conditions expressed by (3) hold for the subset of scheduled 1.

grants addressed to HD-SSs. The remaining capacity in step 3 is certainly sufficient for FD-SS grants since the overall sum of grant durations (including both HD-SSs and FD-SSs) in each direction, as produced by the grant scheduler, cannot exceed the frame duration. Finally, note that it is possible to allocate FD-SSs uplink grants at the exact beginning of the uplink subframe, that is, partially overlapping with the MAC messages broadcast in downlink by the BS, thus making use of the bandwidth, which, by definition, is not available to HD-SSs.

4.5

HDA Extension to Not Time-Aligned Uplink and Downlink Frames HDA can also be extended to take into account the general case where uplink and downlink subframes are not perfectly aligned in time; that is, the uplink allocation start time is equal to T 0 < T . Fig. 6 illustrates this scenario, where subframes are numbered according to the map relevance; that is, the downlink subframe x hosts the ULMAP containing the timetable of uplink grants in subframe x. Let us consider uplink and downlink subframes n. Let t0 be the start time of downlink subframe n, which is thus logically split into two sections: The first section begins at t0 and ends at t0 þ T 0 when the uplink subframe n begins, whereas the second section begins at t0 þ T 0 and ends at t0 þ T . Therefore, the duration of the first section is T 0 and that of the second section is T  T 0 . Note that the uplink and downlink grants of the first section belong to frames n and n  1, respectively, whereas those of the second section belong to frame n only. For this reason, it is not possible to run a single instance of HDA over the whole downlink or uplink subframe. Therefore, an instance of HDA is carried out for each section, where the necessary and sufficient conditions for a feasible grant allocation in (3) are modified as follows:

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.

first

8 > > > >
> > > :

second

8 > > > >
> > > :

m P i¼1 m P

ui  T 0 di  T 0

i¼1

ui þ di  T 0 k P i¼1 k P

1  i  m;

ui  T  T 0 di  T  T 0

i¼1

ui þ di  T  T 0

1  i  k;

where m and k are the numbers of grants in the first and second sections, respectively. In the pipeline approach, an instance of the grant scheduler is carried out for each section. Finally, note that the duration of maps is subtracted from the available frame duration in the first section only.

5

ALTERNATIVE APPROACHES HALF-DUPLEX PROBLEM

TO THE

In the literature, several studies have investigated the performance of IEEE 802.16. However, to the best of our knowledge, there is no previous work that explicitly deals with the allocation of grants for HD-SSs within IEEE 802.16 frames. The only reference that we are aware of is [19], where a way of “working around” the half-duplex constraint is proposed: partitioning the HD-SSs into two sets, which are then served alternately in the downlink and uplink subframes. A detailed description is provided in the next section. With regard to the performance evaluation studies of IEEE 802.16, we carried out a detailed simulation analysis of FD-SSs operated in the FDD mode, which can be found in [9]. In the same context, solutions for packet scheduling with rtPS/nrtPS/BE scheduling services have been proposed [6], [20], [26], whereas UGS is considered in [7] and [27]. The performance with the TDD mode was analyzed in [12], whereas Hoymann [14] performed a hybrid analytic-simulative analysis of the effect on the system performance of several MAC mechanisms, including packet fragmentation and OFDM symbol padding. Finally, the physical layer of IEEE 802.16 has been investigated in recent survey 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). SA works 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 subset contains HD-SSs that transmit in odd-numbered frames and receive in even-numbered frames, whereas the even subset contains HD-SSs that transmit in even-numbered frames and receive in odd-numbered frames. Each HD-SS belongs to exactly one of the above subsets. Therefore, the overlapping of uplink and downlink grants addressed to the same HD-SS is prevented from occurring a priori by means of a static allocation of each HD-SS to only one of the subsets. Despite its simplicity, SA has the following disadvantages: First, SA only works with an uplink allocation start time equal to the frame duration. Otherwise, it would not be possible to keep the odd and even sets of HD-SSs separated at each frame. Second, SA imposes a tighter constraint on the grant scheduler with respect to HDA: In addition to the necessary conditions, the grant scheduler has to enforce that the sum of the grants scheduled to an HD-SS over any two consecutive frames in one direction does not exceed the frame duration. For instance, with SA, it is not possible to schedule the whole channel bandwidth to an HD-SS in one direction. Finally, SA is based on a static partitioning of the HD-SSs into odd/even sets, which may become imbalanced in terms of their traffic load. Thus, network resources would not be shared fairly among connections that belong to SSs in different sets. However, perfect load balancing is difficult to achieve in practice, even though dynamic partitioning is applied on a short time scale (that is, the grant scheduler dynamically moves SSs back and forth in order to balance the current load in the two sets). In fact, besides the amount of complexity that this would inject into the grant scheduler, uplink and downlink MCSs of an SS are generally different. Therefore, a partition that would result in a perfect load balance in one direction would most likely imply an imbalanced partition in the opposite direction.

6

PERFORMANCE ANALYSIS

In this section, we show the effectiveness of HDA with HDSSs under realistic traffic conditions through extensive simulation. Results obtained with HD-SSs via SA and with FD-SSs are considered as a benchmark. The evaluated scenarios are based on the business opportunity of employing IEEE 802.16 as the last-mile Internet access technology for residential and Small and Medium Enterprises (SME) subscribers as envisaged by the WiMAX forum [24].

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

TABLE 2 Network Parameters

6.1 Simulation Environment The network parameters used in the simulations are reported in Table 2. The simulated air interface is the WirelessMAN-OFDM, operating in the FDD duplexing mode, with 7-MHz channel bandwidth and uplink allocation start time equal to the frame duration. BS scheduling was performed according to the pipeline approach devised in Section 3. As in [9], we selected Deficit Round Robin (DRR) [21] as the BS’s downlink grant scheduler since it combines the ability to provide fair queuing, in the presence of variable length packets, with simplicity of implementation. DRR assumes that the size of the head-of-line packet is known at each packet queue; thus, it cannot be used by the BS to schedule transmissions in the uplink direction. In fact, with regard to the uplink direction, the BS can only estimate the overall amount of backlog of each connection and not the size of each backlogged packet. Therefore, we selected Weighted Round Robin (WRR) [15] as the uplink grant scheduler in our IEEE 802.16 simulator. Both HDA and SA were implemented as the BS’s grant allocator. Last, we adopted DRR as the scheduling algorithm running at each SS. The uplink capacity, which is assigned by the BS on a frame-by-frame basis, is thus shared fairly among each SS connection in proportion to their minimum reserved rates. Although the accurate modeling of channel conditions is critical when simulating wireless networks in terms of provisioning and resource management, this study focuses only on those aspects related to the MAC layer. We thus assumed ideal channel conditions, that is, with no packet corruption due to the wireless channel. Furthermore, we simulated a steady state of the system where the set of admitted connections does not change. The simulations were carried out using an event-driven ad hoc simulator from the 802.16 MAC protocol written in C++. We implemented the MAC layer of SSs and the BS, including all procedures and functions for uplink/downlink data transmission and uplink bandwidth requests/ grants. A detailed description of our design choices and implementation of the IEEE 802.16 standard can be found in [8] and [9]. Statistical analysis of the simulation output was carried out using independent replications [17]. We ran 20 independent replications whose duration depended on the traffic source employed (detailed below). In all the simulation runs, we estimated the 95 percent confidence interval for each performance measure. Confidence intervals were not drawn when negligible.

1393

6.2 Traffic Models and Workload Characterization We simulated bidirectional6 multimedia and data traffic, namely, VoIP and Web, respectively. VoIP was modeled as an ON/OFF source with Voice Activity Detection (VAD). Packets were generated only during the ON period. The duration of the ON and OFF periods was distributed exponentially [4]. Data traffic was modeled as a Web source, generating variable size packets at variable interarrival times [18]. The packet size was distributed as a truncated Pareto random variable with the location of 7.3 Kbytes, shape of 1.1, and cutoff of 150 Kbytes. Packet interarrival time was distributed exponentially with the mean equal to 1 sec. VoIP and Web connections had separate buffers, which hold up to 10 Kbytes and 500 Kbytes, respectively, which were large enough to prevent buffer overflow in all the simulated scenarios. The VoIP and Web traffic characterizations are reported in Table 3. The performance was assessed using the following metrics: The transfer delay (or delay for short) is defined as the time interval between the instant when a packet arrives at the MAC layer of the source node (SS/BS) and the time that this packet is completely delivered to the next protocol layer of the destination node (BS/SS). Both the average and the Cumulative Distribution Function (CDF) are estimated. The delay variation is the difference between the 99th percentile of the delay and the packet transmission time, that is, the time that it takes for a packet of minimum length to be transmitted over the air. This metric is of paramount importance for VoIP traffic and should be kept as small as possible so as to satisfy the QoS perceived by the users of VoIP applications. Web traffic, on the other hand, though interactive, has less stringent delay requirements and is thus evaluated by means of the average delay. Last, we measured the number of SSs served in both directions within the same frame, that is, the number of SSs that have at least one downlink and one uplink grants in the downlink and uplink subframes occurring at the same time. The latter helps quantify the impact of the halfduplex constraint on the grant scheduler operation. We set up each replication of the simulation scenario as follows: We provided each SS with a random number of connections. The number of connections was selected according to a geometric distribution with ratio 0.5 truncated at 9. In terms of the workload, we assumed that each connection carries aggregate traffic from a random number of basic sources, either Web or VoIP, depending on the scenario, whose characterization and average rate are reported in Table 3. The number of sources was sampled from a geometric distribution with ratio 0.5 truncated at 9. Furthermore, the MCS of each SS was uniformly distributed in the set {QPSK-3/4, 16-QAM-1/2, 64-QAM-2/3}, which entails encoding 24, 48, and 72 bytes per OFDM symbol, respectively. With regard to SA, each SS was randomly placed into the odd or even set with equal probability. 6.3 Simulation Results In this section, we analyze the results obtained with HDSSs, both HDA and SA, and FD-SSs in simulation scenarios with the following network parameters and workload configuration: 1) different types of traffic (that is, VoIP 6. Uplink and downlink sessions were not correlated.

1394

IEEE TRANSACTIONS ON MOBILE COMPUTING,

VOL. 6, NO. 12,

DECEMBER 2007

TABLE 3 Workload Characterization

and Web), 2) increasing numbers of SSs from 10 to 60, and 3) varied frame durations (that is, 5 ms, 10 ms, and 20 ms). We start with the VoIP traffic with a frame duration equal to 20 ms. Table 4 reports the average number of SSs that were served in both directions within the same frame for 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 characterization, QoS parameters, and frame duration. Additionally, the grant schedulers are subject to the half-duplex constraint, which only holds for HD-SS. Therefore, the difference between the results from the FD case (when only QoS-related requirements are considered by the grant scheduler) and the HDA and SA cases (when the halfduplex constraint is also applied) can be considered as a measure of the impact of the half-duplex constraint on the operation of the grant scheduler. As can be seen, when HDA is employed as a grant allocator, in practice, the halfduplex constraint does not affect the grant scheduler operation; that is, the difference between the HDA and FD results is negligible irrespective of the number of SSs in the network. This metric is always zero in the SA case, where no HD-SS is ever scheduled a downlink grant and an uplink grant in the same frame. We will now analyze the delay variation of uplink and downlink 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 (in uplink, 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 a steep increase in the delay variation which would significantly degrade the quality perceived by the users of VoIP applications. This is clearly due to the uplink and

downlink subframes being saturated by the overall offered load; that is, the system is overloaded. The number of SSs that saturate the subframes with SA is smaller than it is with HDA/FD, which can be explained as follows: Under the 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 the same as the other set. However, this does not mean that the lightly loaded set performs significantly better in terms of the delay variation, as the latter is almost constant with respect to the number of SSs. The performance of the heavily loaded set overly degrades when the overall subframe capacity is exceeded. This is an inherent property of SA, where the half-duplex constraint is worked around by partitioning the SSs into two sets in a static manner since this operation may privilege one set over the other. By using HDA, this unfairness is avoided a priori as each HDSS can be served in any frame. In fact, the HDA and FD curves almost overlap. With regard to the difference between FD and HDA, the delay variation of downlink connections with HDA is slightly greater than with FD. This is because the former incurs the additional overhead of prepending each downlink burst with a physical preamble so as to allow any SS transmitting in the same frame to resynchronize with the transmission from the BS, as described in Section 2. Therefore, even though the half-duplex constraint does not significantly impact the decisions of the BS’s grant scheduler, the net capacity available in the downlink subframe for data transmission with HDA is slightly smaller than with FD. As far as the uplink is concerned, the HDA and FD curves almost overlap because each uplink grant needs to be

TABLE 4 Average Number of SSs Served in Both Directions within the Same Frame

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

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

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.

prepended by a physical preamble, regardless of the halfduplex capabilities of the SS, as described in Section 2. The small difference seen in Fig. 7 is due to the fact that FD-SSs can exploit the full duration of the uplink subframe. This includes the interval when the BS is transmitting the DLMAP and UL-MAP, which is unavailable for HD-SSs. Last, both the uplink and the downlink SA curves lie above the respective HDA/FD curves, where the offset is at least equal to the frame duration, that is, 20 ms. This is because VoIP connections cannot be served at each frame with SA due to the odd/even constraint. In other words, there are cases when the BS’s grant scheduler has a VoIP packet enqueued at a downlink connection (or a pending bandwidth request from an uplink connection), but it cannot schedule a downlink (uplink) grant until the next frame, as the SS of the connection belongs to the “wrong” set. This behavior is investigated further below. It was also verified 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 of downlink and uplink connections with 30 SSs, that is, before the steep increase in delay variation. Let us consider the downlink first. The HDA and FD curves almost overlap, with FD incurring a slightly smaller delay than HDA due to the additional overhead that the latter incurs, as discussed above. The SA curve diverges from the HDA/FD curves as some packets are delayed due to the odd/even eligibility of the destination SS in a given frame, even though there is

1395

Fig. 10. Delay variation of VoIP connections versus the number of SSs (HDA only).

enough capacity to transmit them. This effect is amplified in the uplink case due to the bandwidth request mechanism. Since VoIP applications are served using the rtPS scheduling service, the BS polls all connections at regular intervals equal to the interarrival time of packets, that is, 20 ms. By responding to these polls, the BS becomes aware of the amount of data waiting for transmission at the connection buffers and schedules uplink grants accordingly. With SA, both when polling a connection and when scheduling the uplink grant, the BS is subject to odd/even partitioning. This explains why the tail of the uplink curve is more pronounced than the tail of the downlink curve. In addition, the bandwidth request mechanism justifies the minimum delay of about 30 ms experienced with both HDA/FD and SA. To conclude the analysis of VoIP traffic, we will now investigate how the frame duration impacts on the delay variation of downlink and uplink connections, plotted in Fig. 10. For simplicity’s sake, we only report HDA, since the same conclusions can be drawn from the analysis with FD and SA. As can be seen, the shorter the frame duration, the smaller the delay variation. In downlink, this is because any SDU enqueued at the BS after the DL-MAP has been sent has to wait until the next frame before it can be scheduled for transmission. In uplink, the frame duration has an even stronger impact than in downlink because of the bandwidth request mechanism. In fact, the delay of an SDU includes the latency that the SS experiences for an opportunity to send a bandwidth request to the BS. This becomes greater as the frame duration increases, in addition to the time needed by the BS to schedule an uplink grant to the SS, which is at least the duration of one frame. However, in both directions, the subframe capacity becomes saturated with a smaller number of SSs when the frame duration becomes shorter, which can be explained as follows: In downlink, this is because there is a fixed control overhead per frame due to the transmission of the DL-MAP and UL-MAP messages, including the long physical preamble. This overhead consumes an increasing amount of net capacity available for data transmission when the frame duration is shorter. With regard to the uplink, with shorter frame durations, the BS reacts more promptly to the bandwidth requests sent by the connections. This decreases the delays but increases the number of uplink grants that each connection is scheduled on average in a time unit,

1396

IEEE TRANSACTIONS ON MOBILE COMPUTING,

Fig. 11. Average delay of Web connections versus the number of SSs.

which subsequently increases the overhead due to physical preambles. We will now discuss the results obtained with Web traffic with a frame duration equal to 20 ms. Fig. 11 shows the average delay of downlink and uplink connections. Basically, the same conclusions as those with VoIP traffic can be drawn in this case; that is, the difference between the FD and HDA curves is negligible and increases slightly when the offered load increases, whereas the SA curves lie significantly above the respective FD/HDA curves. Again, this is due to the odd/even constraint on the grant scheduler imposed by SA in terms of the transmission of data and bandwidth requests (uplink only). It is worth noting that, unlike for VoIP, the uplink subframe becomes saturated with a smaller number of SSs than with the uplink subframe. This is because part of the uplink subframe is reserved by the BS for the transmission of bandwidth requests in a contention-based manner. This then reduces the capacity available in the uplink with respect to downlink. We conclude our analysis of Web traffic by analyzing the CDF of the buffer occupancy of downlink and uplink connections before the steep increase in average delays, that is, with 36 and 52 SSs in the uplink and downlink directions, respectively. As shown in Fig. 12, the SA curves always lie below the respective HDA/FD curves. This might become an issue if the IEEE 802.16 devices had limited buffer capacity, in which case, SA would experience a higher drop rate than HDA/FD due to buffer overflow. Moreover, if a transport protocol like Transmission Control Protocol (TCP) is used, then there is a degradation of performance both in terms of delay, since packets need be retransmitted, and throughput due to the congestion control mechanisms.

7

CONCLUSIONS

In this paper, we have proposed a pipeline approach to grant bandwidth at the BS of an IEEE 802.16 FDD network with half-duplex SSs. This approach is based on an allocation algorithm, namely, the HDA algorithm, which is responsible for finalizing the content of DL-MAPs and UL-MAPs, once the size of the grants has been determined by the grant scheduler. We have proved that HDA is optimal in the sense that there is no set of downlink and uplink grants that meet the necessary conditions for the

VOL. 6, NO. 12,

DECEMBER 2007

Fig. 12. CDF of the buffer occupancy of Web connections with 36 (52) SSs in uplink (downlink).

allocation to be feasible and that cannot be allocated by HDA. 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 using an extensive simulation analysis with VoIP and Web traffic under varied load conditions and with different frame durations. The results have shown that the performance of HD-SSs in terms of the most relevant metrics of each traffic type is almost equal to that of FD-SSs. The negligible performance degradation in downlink was due to the additional overhead of HDA, which adds a physical preamble to each downlink grant. The performance degradation in uplink was due to the inability of HD-SSs to transmit while the BS is broadcasting the DL-MAPs and UL-MAPs. Furthermore, we have compared HDA to an alternative approach, namely, SA, where HD-SSs are statically partitioned into two groups served by the grant scheduler alternately in the downlink and uplink subframes. We have shown how the SA approach performs worse than HDA, especially when the SSs are not identical, in terms of offered load and transmission rate.

REFERENCES [1]

[2] [3] [4] [5]

[6]

[7]

D.I. Axiotis, T. Al-Gizawi, K. Peppas, E.N. Protonotarios, F.I. Lazarakis, C. Papadias, and P.I. Philippopoulos, “Services in Interworking 3G and WLAN Environments,” IEEE Wireless Comm., vol. 11, no. 5, pp. 14-20, 2004. B. Bisla, R. Eline, and L.M. Franca-Neto, “RF System and Circuit Challenges for WiMAX,” Intel Technology J., vol. 8, no. 3, pp. 189200, 2004. R.T. Boute, “The Euclidean Definition of the Functions Div and Mod,” ACM Trans. Programming Languages and Systems, vol. 14, no. 2, pp. 127-144, 1992. P.T. Brady, “A Model for Generating On-Off Speech Patterns in Two-Way Conversation,” Bell System Technical J., vol. 48, pp. 24452472, 1969. 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 Evolution Path of 4G Networks: FDD or TDD?” IEEE Comm., vol. 44, no. 12, pp. 42-50, 2006. J. Chen, W. Jiao, and H. Wang, “A Service Flow Management Strategy for IEEE 802.16 Broadband Wireless Access Systems in TDD Mode,” Proc. IEEE Int’l Conf. Comm. (ICC ’05), pp. 3422-3426, May 2005. D.-H. Cho, J.-H. Song, M.-S. Kim, and K.-J. Han, “Performance Analysis of the IEEE 802.16 Wireless Metropolitan Area Network,” Proc. First Int’l Conf. Distributed Frameworks for Multimedia Applications (DFMA ’05), pp. 130-137, Feb. 2005.

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

[8] [9] [10]

[11]

[12] [13] [14] [15]

[16] [17] [18] [19] [20]

[21] [22] [23] [24] [25] [26] [27]

C. Cicconetti, C. Eklund, L. Lenzini, and E. Mingozzi, “Quality of Service Support in IEEE 802.16 Networks,” IEEE Network, vol. 20, no. 2, pp. 50-55, 2006. C. Cicconetti, A. Erta, L. Lenzini, and E. Mingozzi, “Performance Evaluation of the IEEE 802.16 MAC for QoS Support,” IEEE Trans. Mobile Computing, vol. 6, no. 1, pp. 26-38, 2007. C. Eklund, R.B. Marks, K.L. Stanwood, and S. Wang, “IEEE Standard 802.16: A Technical Overview of the WirelessMAN Air Interface for Broadband Wireless Access,” IEEE Comm. Magazine, vol. 40, no. 6, pp. 98-107, 2002. A. Ghosh, D.R. Wolter, J.G. Andrews, and R. Chen, “Broadband Wireless Access with WiMax/802.16: Current Performance Benchmarks and Future Potential,” IEEE Comm., vol. 43, no. 2, pp. 129136, 2005. O. Gusak, N. Oliver, and K. Sohraby, “Performance Evaluation of the 802.16 Medium Access Control Layer,” Lecture Notes on Computer Science, vol. 3280, pp. 228-237, 2004. IEEE 802.16-2004, IEEE Standard for Local and Metropolitan Area Networks—Air Interface for Fixed Broadband Wireless Access Systems (Part 16), IEEE, Oct. 2004. C. Hoymann, “Analysis and Performance Evaluation of the OFDM-Based Metropolitan Area Network IEEE 802.16,” Computer Networks, vol. 49, no. 3, pp. 341-363, 2005. M. Katevenis, S. Sidiropoulos, and C. Courcoubetis, “Weighted Round-Robin Cell Multiplexing in a General-Purpose ATM Switch Chip,” IEEE J. Selected Areas in Comm., vol. 9, no. 8, pp. 1265-1279, 1991. I. Koffman and V. Roman, “Broadband Wireless Access Solutions Based on OFDM Access in IEEE 802.16,” IEEE Comm., vol. 40, no. 4, pp. 96-103, 2002. A.M. Law and W.D. Kelton, Simulation Modeling and Analysis, third ed. McGraw-Hill, 2000. “Evaluation Methods for High Speed Downlink Packet Access (HSDPA),” TSG-R1 document TSGR#14(00)0909, Motorola, 2000. J.F. Mollenauer, J. Klein, and B. Petry, “An Efficient Media Access Control Protocol for Broadband Wireless Access Systems,” IEEE 802.16 Broadband Wireless Access Working Group, Oct. 1999. M. Settembre, M. Puleri, S. Garritano, P. Testa, R. Albanese, M. Mancini, and V. Lo Curto, “Performance Analysis of an Efficient Packet-Based IEEE 802.16 MAC Supporting Adaptive Modulation and Coding,” Proc. Seventh IEEE Int’l Symp. Computer Networks (ISCN ’06), pp. 11-16, June 16-18,2006. M. Shreedhar and G. Varghese, “Efficient Fair Queueing Using Deficit Round Robin,” IEEE/ACM Trans. Networking, vol. 4, no. 3, pp. 375-385, 1996. D. Stiliadis and A. Varma, “Latency-Rate Servers: A General Model for Analysis of Traffic Scheduling Algorithms,” IEEE/ACM Trans. Networking, vol. 6, pp. 675-689, 1998. WiMAX Forum, http://www.wimaxforum.org/, 2007. WiMAX Forum, “Business Case Models for Fixed Broadband Wireless Access Based on WiMAX Technology and the 802.16 Standard,” Oct. 2004. WiMAX Forum, “Initial Certification Profiles and the European Regulatory Framework,” WiMAX Forum Regulatory Working Group, Sept. 2004. K. Wongthavarawat and A. Ganz, “Packet Scheduling for QoS Support in IEEE 802.16 Broadband Wireless Access Systems,” Int’l J. Comm. Systems, vol. 16, no. 1, pp. 81-96, 2003. Y. Yao and J. Sun, “Study of UGS Grant Synchronization for 802.16,” Proc. Ninth IEEE Int’l Symp. Consumer Electronics (ISCE ’05), pp. 105-110, June 2005.

Andrea Bacioccola received the master’s degree (magna cum laude) in computer systems engineering from the University of Pisa, Italy, in December 2005. He is currently a PhD student at the University of Pisa. In 2004, he spent four months at the Nokia Research Center in Helsinki, where he worked on scheduling algorithms for IEEE 802.16 wireless networks. His main research areas are quality of service in wireless multiservice networks, network simulation, and performance evaluation.

1397

Claudio Cicconetti received the bachelor’s degree in computer systems engineering from the University of Pisa, Italy, in October 2003. He is currently pursuing the PhD degree at the same university. His research interests include quality of service in IEEE 802.16 and IEEE 802.11 wireless networks, medium access control protocols for mobile computing, and wireless mesh networks. He is involved in the EuQoS (End-to-end Quality of Service support over heterogeneous networks) project, which participates in the EU Information Society Technologies (IST) Programme. He has served as a member of the organizing committee of the First International Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS 2006). He is a student member of the IEEE. Alessandro Erta received the bachelor’s degree (cum laude) in computer systems engineering from the University of Pisa, Italy, in February 2005. During his master’s thesis, he joined the Nokia Research Center, Helsinki, where he designed and evaluated solutions for the IEEE 802.16/WiMAX standard. He is currently a PhD student at the Institutions, Markets, Technologies (IMT) Lucca Institute for Advanced Studies. He has been involved in the national project NADIR and in projects supported by private companies (Telecom Italia Lab, Nokia). His research interests include quality of service in wireless networks, the design and performance evaluation of medium access control (MAC) protocols, and scheduling algorithms for wireless networks and wireless mesh networks. Luciano Lenzini holds a degree in physics from the University of Pisa, Italy. He joined CNUCE, Italian National Research Council (CNR), in 1970. In 1994, he joined the Department of Information Engineering, University of Pisa, as a full professor. He is currently on the editorial boards of Computer Networks and the Journal of Communications and Networks. He served as chairman for the 1992 IEEE Workshop on Metropolitan Area Networks and for the 2002 European Wireless Conference (EW ’02). He has directed several national and international projects in the area of computer networking. His current research interests include the design and performance evaluation of medium access control (MAC) protocols for wireless networks and the quality-of-service provision in integrated and differentiated services networks. Enzo Mingozzi received the Laurea (cum laude) and PhD degrees in computer systems engineering from the University of Pisa in 1995 and 2000, respectively. He has been an associate professor with the Faculty of Engineering, University of Pisa, Italy, since January 2005. His research activities span several areas, including design and performance evaluation of multiple access protocols for wireless networks, qualityof-service (QoS) provisioning, and service integration in Internet Protocol (IP) networks. He has been involved in several 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 the standardization process of HIPERLAN/2 and HIPERACCESS networks in the framework of the ETSI project Broadband Radio Access Networks (BRAN). He is a member of the IEEE and the IEEE Computer Society.

. For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib.