1500 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 10, …ad57/documents/JLT_SB_FiWi.pdf · 1500...

1500 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO. 10, MAY 15, 2011

QoS Control for Guaranteed Service Bundles OverFiber-Wireless (FiWi) Broadband Access NetworksAhmad R. Dhaini, Student Member, IEEE, Pin-Han Ho, Member, IEEE, and Xiaohong Jiang, Senior Member, IEEE

Abstract—The integration of ethernet passive optical networks(EPONs) and IEEE 802.16 has been lately presented as a promisingcandidate for next-generation broadband access. This paper inves-tigates the performance of the integrated carrier when specific ser-vice bundles (SBs) with bandwidth guarantee and diverse qualityof service requirements are provisioned. We first present a novelframework that fairly distributes the upstream network capacityamong the different SBs. We then propose a novel delay-based ad-mission control scheme to increase the network utilization and en-able an inter-SB statistical multiplexing. To obtain the expecteddelay of each SB stream, a generic analytical model is developed.Based on this model, we further formulate some important perfor-mance measures such as queuing delay, end-to-end (from wirelessuser to the central office of PON) delay, average queue size andoptimal orthogonal frequency division multiplexing frame length.Numerical results validate our analysis and highlight the advan-tages of the proposed solution.

Index Terms—Ethernet passive optical network (EPON), FiWi,optical wireless access, quality-of-service (QoS), service bundle(SB), WiMAX.

I. INTRODUCTION

T HE integration of ethernet passive optical network(EPON) and IEEE 802.16 (WiMAX) has been lately

presented as an attractive solution for realizing fixed mobileconvergence [1], [2]. The integration can take advantage ofthe bandwidth benefit of fiber communications and the mobilenonline-of-sight features of wireless communications to man-ifest a high-speed mobile metro-access network. In addition,the complementary features of both networks have motivateddeploying EPON as backhaul to connect multiple WiMAX basestations (BSs). In specific, EPON and WiMAX perfectly matchin terms of capacity hierarchies. EPON, for instance, supports atotal of 1 Gbps bandwidth in downstream and upstream direc-tions, shared by typically 16–32 remote optical network units(ONUs). On average, each ONU accesses 70 Mbps bandwidth,which matches the total capacity offered by a WiMAX BS overa 20 MHz channel as well [1]–[4].

Manuscript received September 26, 2010; revised January 07, 2011, March06, 2011; accepted March 18, 2011. Date of publication March 28, 2011; date ofcurrent version May 02, 2011. Part of the proposed analytical model appearedin [22] at IEEE Global Telecommunications Conference, Miami, FL, 2010.A. R. Dhaini and P.-H. Ho are with the Department of Electrical and Com-

puter Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada(e-mail: [email protected]; [email protected]).X. Jiang is with the School of Systems Information Science, Future Univer-

sity-Hakodate, Hokkaido, Japan (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/JLT.2011.2132753

Fig. 1. Service bundle provisioning over EPON-WiMAX.

Each registered EPON-WiMAX user may belong to a specificservice bundle (SB) as agreed-upon in the service level agree-ment (SLA). These SBs as illustrated in Fig. 1, allow for the sup-port of premium services and are characterized by their stringentbandwidth needs and diverse quality-of-service (QoS) require-ments. A virtual private network (VPN) is an archetypal SB thatcontains disparate users with different service requirements andauthorities [3], [5]. However, the concept of SB can be general-ized to any scenario with multiple groups of users with diversi-fied applications such as community/campus, home/office, anddata centric networks. A typical SB carries applications span-ning from voice over IP, e-mail, and video calls to audio chan-nels, high-definition television, online gaming, and cloud com-puting. It can be categorized as 1) basic with a typical totalbandwidth requirement of Mbps; 2) intermediate for atotal of Mbps, or 3) advanced for a total of Mbps[6]. The support of these premium SBs in a metropolitan-areawired and wireless integrated infrastructure, entitles the reso-lution of many challenges such as resource management, dy-namic bandwidth allocation (DBA) and admission control (AC).Namely, efficient bandwidthmanagement paradigms are neededin order to ensure guaranteed services for each registered SBuser, which can either be a subscriber station (SS) or a ter-minal connecting to the network through an SS. In the down-stream direction, EPON and WiMAX simply broadcast datapackets over the downstream/downlink media. Conversely inthe upstream direction, packets are launched in the shared up-stream/uplink media, which requires efficient resource manage-ment techniques to enable successful data transmission. There-fore, this work focuses on solutions pertaining to resource man-agement for EPON-WiMAX networks in the upstream/uplinkdirection.

0733-8724/$26.00 © 2011 British Crown Copyright

DHAINI et al.: QOS CONTROL FOR GUARANTEED SERVICE BUNDLES 1501

TABLE IMOST RELEVANT NOTATIONS USED IN THE PAPER

The paper introduces a novel QoS control and managementframework for SB provisioning over the EPON-WiMAX inte-gration. The proposed framework provides statistical bandwidthguarantees for each SB user and offers an efficient bandwidthdistribution approach. In addition, it employs a delay-based ad-mission control (DAC) engine which admits a flow if its ex-pected delay is less than the maximum end-to-end (E2E) delaybound specified in the SLA. The DAC engine measures the ex-pected delay through a generic analytical model that appliesto both WiMAX and EPON networks. By taking advantage ofclassical queuing theory, our analytical model provides a fineestimation of the network behavior with different QoS param-eters. We will show that DAC not only enables inter-SB statis-tical multiplexing, but also achieves high network utilization byadmitting more flows.The proposed framework also helps in setting a number

of salient network parameters such as OFDM (orthogonalfrequency division multiplexing) frame length and buffering

queue size, in order to ensure a statistically guaranteed servicefor each admitted SB flow. The most relevant notations used inthis work are summarized in Table I. The rest of the paper isorganized as follows. Section II presents the proposed QoS con-trol framework and highlights the related design features. Thegeneric analytical model is presented in Section III. Section IVpresents our numerical and simulation results and Section Vconcludes the paper.

II. QOS CONTROL FRAMEWORK FOR GUARANTEED SBS

In this section, the new QoS control framework is presented.The various building blocks and the related design features suchas the SBs’ traffic characteristics are also exhibited.

A. QoS-Provisioning Paradigm

With the proposed QoS provisioning framework as shown inFig. 2, the effective upstream PON cycle , which is thePON cycle time minus the control overhead that is caused by


Fig. 2. Proposed SB QoS-provisioning framework.

Fig. 3. Traffic mapping at ONU-BS.

the polling and requesting signaling, is divided among all theSBs. will be analytically derived in the paper. Letbe the bandwidth reserved for SB (denoted as ) in eachtransmission cycle and the transmission rate of PON inbps. In addition, let each be given a weight to determineits SLA-based paid/committed bandwidth. Therefore, (inbytes, therefore divided by eight) can be computed as follows:

(1)

To avoid starvation, a portion is reserved for the besteffort (BE) traffic, while the real-time flows share the remainingbandwidth, denoted as . The value of is pre-defined in the SLA and reflects the minimum BE throughputrequirement for .

B. Traffic Characteristics and QoS Requirements

In EPON and WiMAX, flows are classified based on theirtype and are mapped to the respective class of service (CoS).

WiMAX mainly supports four CoSs (i.e., unsolicited grantservice (UGS), real-time polling service (rtPS), nonreal-timepolling service (nrtPS) and BE in addition to extended real-timepolling service (ertPS) which is proposed in the IEEE 802.16eversion of the standard [7]. EPON typically supports up to eightCoSs or queues [8]. As illustrated in Fig. 3, in the proposedframework, we assume a simple one-to-one mapping betweenEPON and WiMAX CoSs at the ONU-BS. Hence, a CoSrefers to the same type of flows in both technologies.Constant-bit-rate (CBR) flows (such as UGS) are nonbursty

and can be simply characterized by their mean arrival ratein bits per second. They demand strict delay, jitter, and band-width guarantee requirements. On the other hand, variable-bit-rate (VBR) flows (such as rtPS and nrtPS) are bursty in natureand in addition to , are characterized by the following TrafficSPECifications (TSPEC) parameters:• Peak arrival data rate in bits per second.• Maximum burst size in bits.• Queuing delay bound , which is the maximum amount oftime (in seconds) allowed to transport a traffic stream/flow,


Fig. 4. Dual-token leaky bucket (DTLB).

measured between the arrival of the flow to the MAC layerand the start of transmission in the network.

• MAC service data unit (MSDU) maximum and minimumsizes ( and ). For fixed MSDU size streams ofsize , the mean frame size .

While VBR flows demand strict delay and bandwidth guaranteerequirements, BE traffic is bursty in nature and imposes no spe-cific QoS requirements. Yet with our framework, a minimumSLA-based BE throughput is ensured for each provisioned SB.Therefore, in the following, we focus on achieving statisticalbandwidth guaranteed services for each real-time SB flow.

C. Statistical Guaranteed Service Rate

To attain a statistical guaranteed bandwidth for each real-timeSB stream, a guaranteed rate is computed based on the TSPECparameters of each flow. For a CBR flow (belonging to CoS

, and user ), given a frame error probability per-taining to user and which is a function of the channel condi-tion [i.e., the signal-to-noise-ratio (SNR)] [9], the bandwidth isstatistically guaranteed by defining its guaranteed rate asfollows:

(2)

For VBR traffic, a dual-token leaky bucket (DTLB) is employedat the entrance of the MAC buffer and is associated with eachstream as shown in Fig. 4. The bucket size is calculated asfollows:

(3)

Accordingly, the arrival traffic envelope of the streampassing through the DTLB during , is computed asfollows:

(4)

where . is then constructed from (4) asshown in Fig. 5. With , the guaranteed rate for a VBRflow belonging to CoS , user , and can be easily derivedfrom Fig. 5 using the distance formula [3], [10]

(5)

These rates are then used to perform bandwidth allocation andadmission control in the upstream channel.

Fig. 5. Guaranteed bandwidth derivation graph.

D. Lossless Buffering

Achieving lossless bufferingmeans that the packet drop prob-ability for each CoS queue is equal to zero. For CBR flows, loss-less buffering can always be achieved by allocating the guaran-teed rate as per (2). In contrast, lossless buffering for VBR flowsis DTLB-parameters dependent.Proposition 2.1: To achieve zero packet drop for each VBR

flow, the size of the queue must satisfy the following:

(6)

Proof: According to [11], given a DTLB of mean rate ,peak rate , and bucket size , the dynamic queue sizeshould respect the following bound in order to ensure no packetloss for a stream of guaranteed rate :

(7)

By combining (3), (5), and (7) as well as neglecting , withsome simplifications, the minimum queue size is computed andProposition 2.1 is proved.The value of can be set in the stage of network planning

to achieve lossless buffering in the wireless domain. This is es-sential given that packets transmitted on wireless channels arealready prone to loss [9].

E. Error Control

To ensure reliability of protocol data unit (PDU) transmis-sion, an infinite persistent automatic repeat request-based errorrecovery is used [12]. Assuming an independent error process,the probability that PDUs out of are successfully receivedby the ONU-BS, is obtained as follows:

(8)

F. Delay-Based Admission Control

In the SLA, each CoS of is associated with a max-imum E2E delay bound [i.e., the time taken to transfer datafor an admitted flow from SS to optical line terminal (OLT)].With such information, we design a three-stage DAC enginethat admits a flow if with its inclusion the expected delay mea-surements of all real-time flows are lower than their respective


Fig. 6. Delay-based admission control flowchart.

bounds. As shown in the flowchart in Fig. 6, DAC involves thecollaboration of each SS, every ONU-BS, and the OLT. Sucha decentralized approach reduces the complexity and the “deci-sion time” of the AC engine, as opposed to installing it at oneend (e.g., the OLT). Namely if the latter is adopted, the OLTwill have to store and process information for every wirelessand optical user in the network; whereas with DAC, ONU-BS,and SS collectively handle the wireless domain and leave theoptical domain handling to the OLT.1) At the SS: The first stage of DAC is performed at the SS

where the admission control unit (ACU) extracts the parametersfor an incoming flow . The flow is directly admitted if it isa BE flow, and it shares the reserved BE bandwidth with otheradmitted BE flows. Conversely if is a real-time flow, its guar-anteed rate is computed and then reported to the ONU-BS.2) At the ONU-BS: Upon receiving the flow request from the

SS, the ONU-BS computes the expected delay in the wirelessdomain and forwards it to the OLT along with ’s guaranteedrate for the final stage of AC.3) At the OLT: Since the OLT has all the information about

all the connected nodes and users (e.g., number of SBs andnumber of ONU-BSs) as well as the SLA-based QoS require-ments and the admitted guaranteed rates, it can make the finaldecision on whether or not to admit the incoming flow bycomputing the expected E2E flow delay . Morespecifically, the OLT admits a flow if :

(9)

(E2E) is computed in the next section. In order tocommit the minimum per-SB bandwidth that is computed in(1), bandwidth can be shared among SBs only if all the SBs canbe accommodated. More specifically, a flow with guaranteedrate is admitted, if the following conditions are satisfied:

(10a)

and ,

(10b)

With such an admission rule, if an admitted flow in doesnot “leave” the network before the arrival of a new flow ofthe same class, inter-SB bandwidth sharing could be enabledbetween the involved SBs. With this regards, the upstreambandwidth acts as a pool of resources for all users of differentSBs; thereby achieving an inter-SB statistical multiplexingrather than the fixed bandwidth reservation proposed in [3].This obviously leads to increased network utilization and thushigher throughput while meeting the QoS requirements of alladmitted SB flows.Note that the communication between the OLT/ONU-BS and

theONU-BSs/SSs is polling-based. That is, each SS/ONU-BS ispolled in one polling interval (PI) and is assigned a transmissionslot in the next PI. The flows’ requests and grants are embeddedas additional fields in the control messages (i.e., BW_Request,UL_MAP, REPORT, and GATE) [3]. The values of these fieldsare filled with the proper information whenever a flow request/grant takes place, otherwise they are either left empty or givena negative value. Since the default EPON cycle length is 2 ms[13], and the maximumOFDM frame size is 20 ms [7], the max-imum flow admission decision time will also be 20 ms, whichis considered tolerable [3], [10].

G. Dynamic Bandwidth Allocation

Each admitted flow requires an uplink bandwidth portionequivalent to its calculated guaranteed rate to be allocated ineach PI or cycle/frame. Similar to the previous art [3], theDBA in the proposed framework divides each upstream/uplinkcycle/frame into two subcycles, where the first subcycle is usedto allocate guaranteed bandwidth for admitted real-time traffic,whereas the second subcycle is used to allocate BE bandwidthper SB. At the ONU-BS, the DBA takes into account the phys-ical (PHY) profile of each SS. An SS with lower transmission


rate is allocated more transmission time proportional to otherSSs on a per-frame basis, such that a statistical bandwidthguarantee is achieved.Remark 2.1: While the DBA ensures that the committed

guaranteed rate for each admitted flow is allocated, its “reserva-tion” process might cause more flows to be dropped (as detailedin [3]), and hence the network may exhibit lower throughput.Therefore, an advanced DBA may be designed jointly withDAC to achieve higher network throughput. Since our workdoes not focus on DBA design, we adopted such a DBA tocomplement the proposed framework in order to demonstrateits performance and to highlight the advantages of DAC overother related AC schemes.

III. ANALYTICAL MODEL

In this section, we develop a generic analytical model tomeasure the expected delay of each admitted SB flow. Wefirst overview the related work and show how the proposedanalytical model is different from the previous art.In addition to the expected delay required to perform DAC,

our model presents other important performance metrics suchas average queuing delay and average queue size for each mea-sured CoS. In addition, it computes the optimal OFDM framelength that can maximize the network utilization while ensuringthe committed bandwidth.

A. Related Work

To the best of our knowledge, only the work in [14] pre-sented an analytical model to measure the packet delay inEPON-WiMAX. Nonetheless, it only focused on ingressand egress queues at ONU-BSs, with an undefined accessmechanism and bandwidth allocation scheme. Therefore, it isnecessary to develop a new model that can better serve ourframework.In WiMAX, many previously reported studies have proposed

analytical models to measure the packet delay. Notably in [12],the authors proposed an analytical model to measure the perfor-mance of polling and nonpolling services based on the grant-per-subscriber-station (GPSS) allocation scheme1 [7]. Hence,no per-flow analysis was presented. The authors of [15] pro-posed an analytical model to measure the performance of uni-cast polling services with only one packet transmission in eachframe. Furthermore, a bandwidth allocation mechanism was ab-sent and the various QoS requirements were not taken into ac-count. Similarly in [16], an analytical model was presented witha hybrid unicast-multicast polling system model. The modelonly focused on the impact of the number of polls on the overallnetwork performance without a DBA scheme that can achievemulticlass service support.In EPON, very fewworks were presented to analytically mea-

sure the packet delay except for [17], [18]. Nonetheless, bothstudies focused on a single queuing system and did not con-sider any QoS requirements/measurements under a multiclassand multiservice scenario.For all these aforementioned reasons, we design a new

generic analytical model that applies to both WiMAX andEPON networks, as well as to their integration. Our model

1In GPSS, the BS allocates bandwidth per-SS, which in turn is responsiblefor distributing the allocated bandwidth among the CoSs.

clearly differs from the previous work by providing a per-flowQoS performance analysis that can facilitate the design of MACprotocols as well as the optimization of network parameters tooffer an efficiently traffic-engineered FiWi network.

B. Preliminaries

In our model, we refer to a polling node as server and a polledstation as client. Thus, the OLT is considered a server wherepolling the ONU-BS (i.e., client) in the optical domain; whereasan ONU-BS acts as a server where polling an SS (i.e., client) inthe wireless domain. Therefore, client indicates an SS if themodel is applied in the wireless domain and an ONU-BS if themodel is applied in the optical domain.The EPON-WiMAX network consists of multiple clients,

with each client having multiple queues, accessing the trans-mission medium in a time-division multiple access (TDMA)fashion in the optical domain and OFDM-TDMA in the wire-less domain. The server allocates bandwidth such that theguaranteed rate is ensured; thus the number of packets thatare transmitted in each frame/cycle is equal to the guaranteedrate of each service. Therefore, we model each client as aweighted round robin (WRR) scheduler with only one roundof scheduling, such that the client transmits all the bandwidthallocated for each CoS in this round. Nonetheless due to theTDMA channel access, each scheduler will be exposed to a“vacation time” before accessing its portion of channel (or timeslot). More specifically, this vacation time represents the timewhere no data packets are being transmitted.In order to facilitate the analysis and with the similarity be-

tween polling-based WiMAX and EPON networks, we graphi-cally illustrate in Fig. 7 the temporal events that occur in a singlePI (wireless or optical). Here, the clients are polled/scheduledsequentially with client 0 as the first polled/scheduled client,henceforth until client . The vacation time is dividedinto three folds: server vacation, best-effort vacation, and clientvacation.1) Server Vacation: A server vacation, denoted , is the

idle period displayed in the system between two consecutive up-link/upstream data transmissions. That is in each PI, the serverwaits until all the request messages (i.e., BW Request messagesin WiMAX [7] and REPORT messages in EPON [19]) are re-ceived from its connected clients before performing bandwidthallocation. The respective waiting time converges to only thepropagation time of the last message sent from client , be-cause the transmission time of all request messages is assumedto be of much shorter length than data transmission windows.Hence, all the requests sent from client 0 until client willarrive at the server’s side while client is still transmittingdata packets in the uplink direction. At the beginning of a newPI, the server spends an amount of time to process theincoming messages and to compute the DBA algorithm.Consequently, the server broadcasts grants (i.e., GATE in EPONand UL_MAP in WiMAX) for each client. Without loss of gen-erality, the analytical model assumes a uniform client-server dis-tance (i.e., equal message propagation time), where the grantmessage destined to client 0 is transmitted first on the downlinkchannel.2) Best-Effort Vacation: The main target of our model is to

derive the expected E2E delay for real-time queues (i.e., for


Fig. 7. Illustration of temporal events in each PI.

), where class is for BE traffic. How-ever, to measure the performance of real-time SB streams withthe existence of heavy-load BE traffic (i.e., is fully uti-lized), we assume that the total BE (of all SBs) reserved band-width portion is represented as a vacation time, denoted , forreal-time queues of each client. More specifically, we claim theexistence of at least one user per , and this user may fully ac-cess ’s reserved BE portion.3) Client Vacation: A client vacation, denoted , is the idle

period exhibited between any two contiguous transmission timeslots. As shown in Fig. 7, in addition to the best-effort vaca-tion, consists of the time used for transmitting a request mes-sage plus the guard time that separates the transmission of twoadjacent clients (e.g., clients 0 and 1) in the uplink/upstreamdirection.

C. Assumptions and Analysis

To make the modeling process tractable, we assume that theguaranteed rates of all clients are Poisson-distributed, identicaland independently distributed, with per-client guaranteed rate

. As a result, we model each client as a com-bination of WRR with one round of scheduling, and multiser-vice queue with vacations [18], [20]. Note that the pur-pose the model is to capture the long-term estimated averagebehavior of each admitted flow to perform DAC. While theassumption of Poisson-distributed traffic is valid for unshapednonbursty traffic, it is a compromise between the precision andtractability of themodel by using Poisson distribution to approx-imate the shaped arrival processes. To support this assumption,we have conducted a simulation study on the traffic that is beingshaped using the DTLB (i.e., ). Here, we have applied threeincoming traffic profiles 1) a real video trace2; 2) self-similarPareto-distributed traffic; and 3) Poisson-distributed traffic. Asshown in Fig. 8, all traffics (of mean rate 750 Kbps) after passingthrough the DTLB, exhibit similar behavior regardless of theirincoming traffic profiles. More importantly, the results clearlyindicate how the unshaped Poisson-distributed traffic can nicely

2Available at http://trace.eas.asu.edu/preencoded/index.html.

capture the behavior of the shaped bursty traffic and hence, aswe assumed, can be used to estimate . Note that it is possibleto claim that the shaped traffic can be seen as constant. However,such assumption is very aggressive as it does not consider anyobserved traffic fluctuation; whereas the claim of a Poisson-dis-tributed is regarded as a more conservative and valid as-sumption. Our numerical results will also verify the statisticaladequacy of this approximation. We further apply the followingrelevant assumptions.1) The wireless channel quality of each connection remainsconstant on a per-frame basis.

2) Perfect channel state information for each SS is available atthe ONU-BS receiver. Thus, the SNR reports are correctlyreceived by the ONU-BS through the BW_Requests overan error-free feedback channel.

3) There exist enough OFDM subchannels to accommodateall admitted users.

4) The buffer size of each queue is computed according to (6),where no packet dropping is possible.

5) A traffic of any class is the same for all SBs. That is,and

.Since we assume that all traffic of the same class for different

SBs are equal, we omit the usage of in our notations in thefollowing context. In addition, we use to denote the numberof clients connected to one server in a particular domain (Fior Wi). The average arrival rate at class of a wireless serveris the sum of all arrival rates of class of all wireless clientsconnecting to the same server. Hence, the total arrival ratewill then be calculated in the following manner:

(11)


Fig. 8. Comparison between different traffic profiles.

TABLE IIADAPTIVE MODULATION AND CODING MODES

The first and second moments of the transmission times fora class and client packet, can be expressed as

and , respectively, with de-noting the service time. The respective utilization factor is hencegiven by .We also assume that a steady state always exists. That is,

(12)

Note that the steady state is enforced by allowing DAC to re-ject incoming flows when (12) is violated. In the Fi domain,all clients have equal transmission rates and are assumed to beequally loaded. Conversely in the Wi domain, each client mayhave a different transmission rate , corresponding to anadaptive modulation and coding (AMC) mode as per Table II,and reflecting the channel condition of the client. Nonethelessas mentioned, the adopted DBA deals with this issue by allo-cating more “time” (translated to capacity) for users with lowertransmission rates, to achieve per-SB statistical bandwidth guar-antees for each CoS. Using (1), we can estimate the best-effortvacation time in the following way:

(13)

Fig. 9. TDD WiMAX frame structure.

where is defined as the average transmission rate in one wire-less domain (i.e., at one server) and is computed as follows:

The vacation intervals and are computed based on thedomain the client belongs to (i.e., Fi or Wi). The client vacationis uniform in both domains and is given by

(14)

While is uniform, the server vacation varies due the timedivision duplexing (TDD) frame nature in WiMAX (illustratedin Fig. 9). Hence, we compute as follows:

(15)

In the wireless domain, OFDM frames have fixed lengths (5, 10,or 20 ms) [7]. Thus, in the case where the OFDM uplink sub-frame is not fully utilized, each client will exhibit an additionalvacation/idle time proportional to the frame size (see Fig. 9).This time is derived based on the uplink subframe utilizationas follows:

(16)

is extracted from the traffic transmitted in the uplink channelas follows:

(17)

where is the average data cycle length and is approximatedas follows [21]:

(18)


Combining (16) and (18), will then be given by

(19)

We also define as the access interval (vacation plus data)for a client in interval , and where is the vacation periodappearing just before ’s data interval. As shown in Fig. 7,depends on ’s position in each PI and is estimated as follows:

(20)

The polling control overhead in each PI can then be estimatedas the sum of all vacations. As a result, in (1) will thenbe computed as follows:

(21)

D. E2E Packet Delay

Each packet may arrive to any client during the whole PIand can belong to any SB of class . In each domain, will besubject to a delay , such that

(22)

where and are ’s average queuing delay andtransmission time, respectively. In the steady state, as ,the expected value of the total delay is then given as

(23)

where is given by and. Therefore, in order to compute

(also denoted as ), we need to derive an expression for. Once computed, the E2E packet delay will then be

equal to the following:

(24)

where and are the average packet delay inthe optical and wireless domains, respectively.

E. Queuing Delay Analysis

The queuing delay of arriving at client is expressed by

(25)

where is the mean service time of packet . We note that. Similarly,, and .

In the wireless domain, the queuing delay also includes theadditional delay that is caused by the DTLB shaping (as de-scribed in Section II.C).We start by computing the queuing delay for classes 1 and

2, and then provide a generalized expression for class , where

. If belongs to class 1, its expected queuingdelay will then be equal to the following:

(26)

where is client ’s proportional to all clients’ s:

(27)

In steady state, will see the same average number of packetsqueued, at both its enqueuing and dequeuing times. The ex-pected number of arriving packets to class 1, at those times, isequivalent to . As a result,

(28)

Hence, the expected queuing delay of the priority queue 1 isthen computed as follows:

(29)

According to the aforementioned client ’s WRR (with oneround) scheduling mechanism, the expected delay of a packetarriving at the second queue shall wait for all the packets in thehigher priority queue and the packets that arrived earlier to thesame priority queue, in addition to and . Thus,

(30)

Similarly, a general expression of the expected queuing delayfor class , where , can then be given by

(31)

To find the value of , we use the concept of the meanresidual service time [18], [20], with a graphical argument. Asshown in Fig. 10, (the residual time at time ) exhibitsvacation times depending on the position of client in each PI.Therefore, the time average of in is

(32)

where is the number of vacations appeared in , anddenotes a class serviced packet, both during . By


Fig. 10. Derivation of the mean residual time during .

assuming equally loaded clients, the number of vacations incan be evaluated as just , with

(the total number of vacations occurred during ). This is dueto the fact that the vacations in repeat once in everyconsecutive vacations. Hence, we can rewrite (32) as follows:

where is computed from (20), and denotes the second mo-ment of client ’s service time averaged over all classes. Morespecifically,

We note that

Let . As a result for CoS

where is the average duration of one vaca-tion period. When , the mean residual time will then begiven as

(33)

The value of in (27), is basically equivalent to the com-putation of the probability that packet arrives duringwhen , denoted as . By assuming equal data intervallengths for all clients, at steady state can belong to client withprobability . As a result will arrive during client ’s datainterval with probability , and to its vacation interval withprobability . Consequently, is computedas follows:

(34)

To determine , we first denote

where

%

denotes the probability of the operand. As noticed, thecomputation of is dependent on the location of %(see Fig. 7). In other words, if % , this meansthat will be requested in the next PI and transmitted in theone after. This is due to the fact that a packet cannot be trans-mitted in a PI by a client unless it is first reported to the serverin the pervious PI. Hence, will have to wait for a full PI be-fore transmission, as well as the remaining PI before being re-quested. As a result, the total amount of gaps or vacations ex-hibited in such scenario is equal to (for the current PI)plus (the average vacation time in one PI). Similarly,if % , then will be reported in the cur-rent PI, and transmitted in the one after. Consequently, the totalvacation time exhibited in this scenario will be equal to (forthe current PI) plus . Note that in case arrives during

, then the total exhibited vacation time will also fall under


this category (i.e., % ). Accordingly,we can evaluate as follows:

%% .

Since each client has a total mean rate of , hence each ar-riving packet can belong to any client with probability .This implies that the conditional probability that arrives atclient % during is also . Thus, with

[defined in (34)], is computed in(35), shown at the bottom of the page. As a result, and withsome simplifications, we obtain the value of as follows:

.

(36)

Finally, by gathering the values of , and from (33),(34), and (36), respectively, we can obtain the expected queuingdelay for each class . Usingin both domains, we also get and .

F. Per-Class Average Queue Size

Using Little’s theorem [20], the class average queue size ofclient , denoted , is given by

(37)

G. Optimal Frame Length

It has long been a challenging problem in wireless networksto determine the frame length that can achieve the best com-promise between high loss/retransmission rate due to lengthyframes and the larger overhead in case the frame length is setsmall. The issue is addressed in this subsection.Proposition 3.1: Given a number of wireless users and

CoS traffic parameters and , to achieve the best uti-lization of uplink subframe while ensuring guaranteed QoS, theOFDM frame length should be set as follows:

(38)

Proof: An optimal frame length means that the idle time iskept theminimal.With the assumption that all users are identical

and by solving (19) for will then be computed asfollows:

(39)

By replacing (39) in (Table I), Proposition 3.1is proved.From the computed value of , we can select the closest

OFDM frame length to either 5, 10, or 20 ms, thereby mini-mizing the idle frame length and maximizing the network uti-lization while achieving a guaranteed service for each user.

IV. NUMERICAL AND SIMULATION RESULTS

To validate the effectiveness of the proposed analyticalmodel versus the simulated proposed framework, we haveimplemented a simulator using OMNET . The relevant sim-ulation parameters are shown in Table III. The AMC of eachSS is randomly selected from the adopted modes in Table II.Each SS has four flows (UGS, rtPS, nrtPS, and BE). EveryUGS flow is generated with a mean/guaranteed rate of 64 Kbps[19]. Each rtPS flow is generated at a guaranteed rate of 5 Mbps(which is the average bit rate of a DVD-quality video [19]) andeach nrtPS flow is generated at a guaranteed rate of 500 Kbps[3]. Each self-similar Parato-shaped BE flow is generated at amean rate of 2 Mbps [3]. Packet sizes are uniformly distributedbetween 64 and 1518 bytes. The 90% confidence interval ofthe simulation results are shown in the figures. The first 10% ofthe simulation time is considered as the transient period, and isthus discarded.We first plot in Fig. 11 the relation between the utilization

factor in the optical domain (i.e., at the OLT) and the utilizationfactor in the wireless domain (i.e., at one ONU-BS). Since allSSs and ONU-BSs are assumed to be equally loaded, the loadon one ONU-BS can be generalized to all ONU-BSs and hencecan give the load in the optical domain. As a result and as an al-ternative to a 3-D graph, this relation will simplify the represen-tation of the subsequent figures to make them easily readable. Inthose figures, the results are drawn versus the optical utilizationfactor.Fig. 12 depicts the E2E average packet delay, obtained by the-

oretical and simulation experiments, for three CoSs of taggedclients and . Note that in our simulationmodel and unlike the assumption made in the analytical model,BE traffic load builds up gradually with time. This fact results

(35)


TABLE IIISIMULATION PARAMETERS

Fig. 11. Relationship between wireless and optical utilization factors.

in a very slight increase of the E2E packet delay in the analyt-ical part versus the simulation one, at moderately lower networkloads . Nonetheless, both results in general matchwith a fine degree at all loads and a very small difference of 2ms (especially at high loads), even when the BE reserved por-tion is fully utilized. Moreover, although our simulation modelhas been implemented without the assumptions made in the an-alytical model (e.g., guaranteed rate is Poisson-distributed), theresults show that these assumptions are statistically requisite.Fig. 13 shows the average queue size of each CoS in the op-

tical domain, where each optical client (at the same time a wire-less server) acts as a multiplexer of all traffic arriving from thewireless clients connected to it. As shown, both the analyticaland simulation results show a fine match of almost 95% for allclasses; which again shows the effectiveness of our analysis.Note that we do not plot the wireless client’s average queue sizebecause a similar behavior was observed.

Fig. 12. Average end-to-end packet delay: (E2E). (a) .(b) . (c) .

To study the selection of the OFDM frame length underthe proposed framework, we show in Fig. 14 the frame lengthversus the number of wireless users. As noticed, for an OFDMframe length of 5 ms, the maximum number of users that canbe accommodated while achieving a guaranteed rate service,is almost six. Similarly, eight users can be best accommodated


Fig. 13. Average queue size in the (Fi) domain.

Fig. 14. Optimal wireless frame length.

Fig. 15. Admitted real-time traffic throughput.

for a 10 ms OFDM frame length; and almost ten users for a20 ms frame length. With these values, we could configure ournetwork such that the resource wastage is minimized whileguaranteeing the bandwidth for each admitted flow/user.Finally, to show the advantage of our proposed DAC scheme

over other AC mechanisms that also achieve guaranteedbandwidth, we plot in Fig. 15 the admitted real-time traffic

throughput under all of DAC, VPN-AC [3], and with theapplication of no admission control (i.e., NO-AC). VPN-ACis a measurement-based AC scheme that admits a flow if itsguaranteed rate can be supported in its reserved VPN (i.e., SB)bandwidth share. As elaborated in the figure, enabling inter-SBstatistical multiplexing allows DAC to admit more real-timeflows in the network, which in turn increases the resourceutilization and throughput. We note here that since our analysisassumes a steady-state network, all incoming flows are rejectedonce the network saturation is reached (same as with VPN-AC).

V. CONCLUSION AND FUTURE WORK

In this paper, a new framework was introduced to provisionguaranteed SBs with strict and diverse QoS requirements, overFiWi networks. The new framework presents a new QoS-pro-visioning module and a DAC engine to better exploit the avail-able resources and enable inter-SB statistical multiplexing. Theexpected delay used by DAC is measured via a new analyticalmodel. The proposed model is designed to be generic and isused to study the performance of EPON, WiMAX, and possiblyany other polling-based FiWi network. Numerical results vali-dated our analysis and showed the advantages of the proposedframework in achieving higher network utilization over existingsolutions while satisfying the QoS demands of all SBs.As future work, an advanced DBA can be designed to enable

a more aggressive admission policy that can admit more flowswhile meeting the QoS requirements of all SBs. Furthermore,a dynamic bandwidth distribution (i.e., dynamic ) can be de-signed to better exploit the available resources and adaptivelydistribute the bandwidth among all SBs.

ACKNOWLEDGMENT

The authors would like to thank Prof. A. Shami from UWOand the anonymous reviewers for their constructive commentsthat helped improving this work.

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Ahmad R. Dhaini (S’05) received the B.Sc. degree in computer science fromthe American University of Beirut, Beirut, Lebanon, in 2004, and theM.App.Sc.degree in electrical and computer engineering from Concordia University, Mon-treal, QC, Canada, with a best thesis award nomination in 2006. He is currentlyworking toward the Ph.D. degree in electrical and computer engineering fromthe University of Waterloo, ON, Canada, where he currently holds the OntarioGraduate Scholarship in Science and Technology.During 2006–2007, he was a Software Consultant at TEKSystems, Montreal;

and during 2007–2008, a Software Designer at Ericsson, Montreal. He has au-thored a book and published several papers in major journals and conferencesrelated to his area of expertise. His research interests focus on access networks;more specifically on optical/wireless broadband access networks.Mr. Dhaini has been assigned as a Technical Program Committee Member,

Technical Reviewer, and Editorial Board Member in major conferences andjournals.

Pin-Han Ho (M’02) received the B.Sc. and M.Sc. degrees at the ElectricalEngineering Department, National Taiwan University, in 1993 and 1995, re-spectively, and the Ph.D. degree from Queen’s University, Kingston, Canada,in 2002.He is currently an Associate Professor in the Department of Electrical and

Computer Engineering, University of Waterloo, Waterloo, ON, Canada. He isthe author/coauthor of more than 150 refereed technical papers, several bookchapters, and the coauthor of a book on optical networking and survivability.His current research interests cover a wide range of topics in broadband wiredand wireless communication networks, including survivable network design,wireless metropolitan area networks such as the IEEE 802.16 networks, fiber-wireless network integration, and network security.Dr. Ho is the recipient of the Distinguished Research Excellent Award in the

Electrical and Computer Engineering Department of University of Waterloo,Early Researcher Award (Premier Research Excellence Award) in 2005, theBest Paper Award in International Symposium on Performance Evaluation ofComputer and Telecommunication Systems in 2002, International Conferenceon Communication Optical Networking Symposium in 2005, and InternationalConference on Communication Security andWireless Communications sympo-sium in 2007, and the Outstanding Paper Award in International Conference onHigh Performance Switching and Routing in 2002.

Xiaohong Jiang (SM’07) received the B.S., M.S., and Ph.D. degrees from Xi-dian University, Xi’an, China, in 1989, 1992, and 1999, respectively.He is currently a Full Professor of Future University-Hakodate, Hokkaido,

Japan. Before joining Future University, he was an Associate Professor at To-hokuUniversity, from February 2005 toMarch 2010. FromOctober 2001 to Jan-uary 2005, he was an Assistant Professor in the Graduate School of InformationScience, Japan Advanced Institute of Science and Technology (JAIST). FromOctober 1999 to October 2001, he was a JSPS (Japan Society for the Promotionof Science) Postdoctoral Research Fellow at JAIST. From March 1999 to Oc-tober 1999, he was a Research Associate in the Department of Electronics andElectrical Engineering, University of Edinburgh. His research interests includeoptical switching networks, routers, network coding, wavelength division mul-tiplexing networks, VoIP, interconnection networks, IC yield modeling, timinganalysis of digital circuits, clock distribution, and fault-tolerant technologies forvery large scale integration/wafer-scale integration. He has published more than150 referred technical papers in these areas.

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