a novel bandwidth allocation algorithm for ieee 802.16 tdd mode wireless access networks

8/13/2019 A Novel Bandwidth Allocation Algorithm for IEEE 802.16 TDD Mode Wireless Access Networks

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Wireless Pers Commun (2012) 67:665688DOI 10.1007/s11277-011-0403-7

A Novel Bandwidth Allocation Algorithm for IEEE

802.16 TDD Mode Wireless Access Networks

Chia-Chuan Liang Jung-Shyr Wu

Published online: 13 October 2011 Springer Science+Business Media, LLC. 2011

Abstract In this paper, we propose a novel bandwidth allocation algorithm for a two-tier

hierarchy in IEEE 802.16 time division duplex mode wireless access networks under sym-

metric and/or asymmetric uplink and downlink traffic input. We demonstrate the performance

of the new bandwidth allocation algorithm in terms of accumulated throughput (cumulative

bandwidth) and fairness in both infinite and finite buffer cases compared with others by

simulations. The simulation results show that the proposed algorithm not only can provide

much better fairness and maintain satisfactory QoS support and high cumulative bandwidthbut also in the case of finite buffer depth is less buffer-consuming than the others, meaning

that the hardware cost can be reduced by employing the proposed algorithm.

Keywords Bandwidth allocation algorithm BWA Fairness IEEE 802.16 WiMAX

1 Introduction

Undoubtedly, the technologies specified in IEEE 802.16 standards[1,2] have been the most

promising solutions in the broadband wireless access (BWA) networks. Among these stan-

dards, the well-known worldwide interoperability for microwave access (WiMAX) networks

has selected the technology of the point to multipoint (PMP) architecture as the common

specification. In the PMP mode, the network at least consists of one base station (BS) and a

number of subscriber stations (SSs) playing the role of last-mile access to the internet [3,4].

C.-C. Liang

Department of Electrical Engineering, National Central University, No. 300, Jhongda Rd.,Jhongli City 32001, Taoyuan County, Taiwan, ROC

e-mail: [email protected]

J.-S. Wu (B)

Department of Communication Engineering, National Central University, No. 300, Jhongda Rd.,

Jhongli City 32001, Taoyuan County, Taiwan, ROC

e-mail: [email protected]

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666 C.-C. Liang, J.-S. Wu

Having defined four types of service[1], IEEE 802.16 standard still left the implemen-

tation of resource allocation supporting the four different qualities of service (QoS) classes

as an open issue. Several studies have devoted themselves in this area [514]. In [5], Chen

proposed a scheduling algorithm called deficit fair priority queue (DFPQ) to obtain both the

high accumulated throughput and better fairness under the asymmetric uplink and downlinktraffic. By utilizing the nature of unbalanced traffic as the dynamic bandwidth allocation

mechanism, DFPQ could obtain better performance than strict priority queue (PQ) algo-

rithm [6]. In these studies, some of them focus primarily on the QoS support [ 610] and

others specifically concentrate on the bandwidth allocation [11,12]. While in[13,14], the

authors propose a bandwidth allocation algorithm employing the queue state information and

utilizing utility functions to distinguish the level of user satisfaction.

As illustrated in [5], the time division duplex (TDD) mode can offer larger benefits than

the frequency division duplex (FDD) mode in respect of dynamic and flexible resource allo-

cation; besides, the two-tier scheduler can both control more efficiently all service flows

and provide more organized QoS than one-tier one can[15]; hence, the authors investigate

the bandwidth allocation problem specifically in IEEE 802.16 TDD mode wireless access

networks. In this paper, we follow the same issue and propose a dynamic bandwidth allo-

cation algorithm with a two-tier hierarchy that could obtain better performance in terms of

cumulative bandwidth and fairness in both infinite and finite buffer cases than the DFPQ

algorithm for IEEE 802.16 TDD mode wireless access networks under the symmetric and/or

asymmetric uplink and downlink traffic input. This paper is a revision and expansion of the

earlier research [16]; however, the major differences between the previous literature and the

current one may be considered under the following heads: (1) the proposed algorithm has

been revised to obtain the faster rate of converging to the steady state and the better fairness;(2) the performance evaluation in the finite buffer depth case has been included and the results

show that the revised algorithm could save the buffer size in hardware at the expense of a more

complicated resource and buffer control processing. Moreover, in regard to the second tier of

the two-tier hierarchy, the proposed algorithm possessing long-term average throughput con-

trol and short-term non-urgent bandwidth fine-tuning for each connection contrasts starkly

with DFPQ with a variable DeficitCounterdetermined according to 1.2 times the value of

the specified request for rtPS and nrtPS, 0.8 times the value of the specified request for BE

and the size of the packets to maintain the maximum allowable bandwidth for each service

class.

The rest of the paper is organized as follows. In Sect. 2, we briefly introduce the QoSframework of IEEE 802.16 TDD mode wireless access networks. We elaborate the proposed

bandwidth allocation algorithm by illustrating its flowchart and expound it in detail by an

example in Sect.3.In Sect.4,we demonstrate the performance of the proposed algorithm

by simulations. Finally, we conclude the paper in Sect. 5.

2 The QoS Framework of IEEE 802.16 TDD Mode Wireless Access Networks

The IEEE 802.16 standard[1] defines a connection-oriented MAC protocol, and a mecha-

nism of QoS differentiation for four different types of services. In IEEE 802.16 TDD BWA

networks, the QoS management mechanism located at BS consists of a module of admission

control, a connection classifier, a bandwidth allocation scheduler, and a MAP generator, as

depicted in Fig.1. The module of admission control is used to confine the number of flows

entering the network to avoid overflow and starvation of the services. Among them, real-

time constant bit rate (CBR) applications such as VoIP without silence suppression and time

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A Novel Bandwidth Allocation Algorithm 667

Fig. 1 The QoS framework of BS and SS

division multiplexing (TDM) services are classified into UGS types; services of real-time

variable bit rate such as MPEG streams or VoIP with silence suppression are categorized

into rtPS types; non-real-time applications such as file transferring are grouped under nrtPStypes; services not subject to any QoS support such as those using HTTP are sorted out to

BE types. Correspondingly, the specified arrival rates (such as users to apply for the bit rate)

of the aforementioned types are denoted asUGS, rtPS, nrtPS, andBE, respectively.

As shown in Fig.1,these service flows can be created, changed, or deleted through the

messages, Dynamic Service Addition (DSA), Dynamic Service Change (DSC), and Dynamic

Service Deletion (DSD)[1,2]. Each of the above actions can be initiated by either SS and/or

BS. For example, a new service flow initiated by SS is built as follows: When SS detects

the occurrence of a new service request, it will calculate the available resources to determine

whether a DSA request will be sent or not. Upon the reception of the DSA request, BS ver-

ifies if this request can be supported, and then sends a DSA response back to SS. Finally,according to the DSA response, the SS sends a DSA acknowledgement to BS and enables

the new service flow.

Because the IEEE 802.16 MAC protocol is designed to provide connection-oriented ser-

vices, the SSs must first establish the connection with the BS to request the associated

service flows (UGS, rtPS, nrtPS, and/or BE). Connections between SS and BS are identified

by assigning a unique connection identifier (CID) to each uplink (from SS to BS) and/or

downlink (from BS to SS) transmission.

Once a connection is created, the connection classifier will look up its request and classify

it into one of the UGS,

rtPS,

nrtPS, and BE service flows. Thereafter, the SSs will send thebandwidth request (BW-REQ) message to the BS. Each packet from the traffic is tagged

with its own CID and service flow ID (SFID), and is classified by the connection classifier

according to its CID and SFID, and then is forwarded to the corresponding scheduling list

waiting to be served. The bandwidth allocation scheduler then retrieves the requests from

the scheduling lists and the MAP generator generates a UL-MAP and/or DL-MAP message

following the bandwidth allocation results accordingly.

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Fig. 2 Proposed two-tier scheduler structure

3 Proposed Bandwidth Allocation Algorithm

3.1 Two-Tier Bandwidth Allocation Hierarchy

The proposed bandwidth allocation algorithm adopts a two-tier hierarchy to manipulate the

dynamic bandwidth allocation, as illustrated in Fig.2.In order to handle the dynamic bandwidth allocation under the balanced and unbalanced

traffic input, the transmission of uplink and downlink direction is considered simultaneously.

The notation of the service types with prefix of UL represents the service flows in the uplink

direction. The notation of the service types with prefix of DL represents the service flows in

the downlink direction. Following[5], the BW-REQ of the connection served in the wait-

ing scheduling list represents the number of requested packets in the uplink direction. After

classified by the connection classifier, all packets are forwarded to the first tier schedul-

ers composed of the schedulers of service flows UGS (including DL_UGS and UL_UGS),

rtPS (including DL_rtPS and UL_rtPS), nrtPS (including DL_nrtPS and UL_nrtPS), and BE(including DL_BE and UL_BE) accordingly, as depicted in Fig. 2.In the first tier sched-

ulers, the packet of each service flow is scheduled by the corresponding packet scheduling

algorithms. Since the UGS service flow has a fixed bandwidth in transmission, it is allocated

directly in each output frame without scheduling. Following the similar philosophy proposed

in[5,6], the rtPS service flow is handled by means of the Earlier Deadline First (EDF) algo-

rithm[17], i.e., the packets with the earliest deadline will be scheduled first. The deadline

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of the rtPS packet is calculated by its arrival time plus the maximum delay constraint of

connection. The nrtPS service flow is scheduled according to the Weighted Fair Queuing

(WFQ) algorithm [18] and the BE service flow is served following the Round Robin (RR)

algorithm [19].

On the other hand, the bandwidth allocation scheduler of the second tier is a kind of inter-class scheduling mechanism allocating bandwidth to each packet from the different service

flows. Different from the ones investigated in [5,6], all the packets of connections coming

from the first tier schedulers are re-scheduled into a temporary scheduling list according

to their assigned priority by the proposed algorithm, Later Deadline First (LDF), until the

transmission bandwidth of each frame is fully occupied. Eventually, the output traffic of the

temporary scheduling list is combined with that of UGS to form the final re-ordered output

frame. The priority of the different service flows managed by the proposed algorithm is

assigned first according to its service type and then by its transmission direction. For various

service flows, the priority is given as follows. Differentiated by the service type, the priority

of rtPS service flow is greater than that of nrtPS service flow and the priority of nrtPS ser-

vice flow is greater than that of BE service flow. In respect of transmission directions, the

priority of the downlink direction is greater than that of uplink direction, with the exception

of the rtPS service flow whose priority is further sorted out by its deadline regardless of the

transmission direction.

3.2 The Later Deadline First Algorithm

As mentioned in the above section, we propose a novel bandwidth allocation algorithm called

Later Deadline First, LDF, as the second tier scheduler to handle the different service flows

and demands in IEEE 802.16 TDD wireless access networks. The name of LDF comes after

the fact that the non-urgent rtPS packets with the latest deadline existing in the temporary

scheduling list could be fine-tuned first by non-real-time packets (such as nrtPS or BE)

according to the rules explained below.

In order to obtain the benefits of LDF, we first categorize real-time packets (such as UGS

or rtPS) into urgent ones and non-urgent ones according to their deadline constraints. The

urgent real-time packets are real-time packets that must be served before the frame ends;

otherwise, they will be dropped due to exceeding the deadline constraints. Therefore, the

urgent rtPS packets own the highest priority than the other packets. A real-time packet issued

at the j th frame is called an urgent real-time packet if its deadline constraint satisfies thefollowing criterion,

0< ai,j + di t f, (1)

where ai,j is the arrival time of the packet of the i th connection issued at the j th frame;direpresents the specified maximum delay constraint of thei th connection,tmeans the current

time, and f is equal to the time duration of one frame. The other rtPS packets not meeting

the above criterion are categorized into the non-urgent rtPS packets. Before the operation of

LDF is formally introduced, we first define several items that are going to be used in the LDF

operation as follows:

ThNi : the accumulated throughput (cumulative bandwidth) of the connection

C I Di over N frames[5]:

ThNi =

N

j=0

ma pi,j , (2)

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where ma pi,j is the bandwidth of the served packet of the connection

C I Di at the j th frame.

L f r am e: the total bandwidth of a frame.

L total : the remaining bandwidth of a frame subtracting UGS fromL f r am e.

La : the current available bandwidth of the frame.Counter[rtPS]: a counter recording the allocated bandwidth of rtPS connections in the

current frame.

Counter[BE]: a counter recording the allocated bandwidth of BE connections in the

current frame.

Counter[mapi]: a counter recording the accumulated bandwidth of the served packet of

the connectionC I Di . The value stored in Counter[mapi]over N frames

is equal toThNi .

When LDF is initiated, all counters defined above are set to zero. Assume that the current

frame is the Nth frame and there are totally k C I Ds with indices 1, . . . , n for UGS serviceflow,n + 1, . . . , mfor rtPS service flow,m + 1, . . . , lfor nrtPS service flow, and l + 1, . . . , k

for BE service flow. We then illustrate the flowchart depicting LDF operation in Fig.3.

According to Fig. 3, the operation principle of LDF can be explained in detail in the

following steps:

Step 1: At the beginning of each frame, all counters are initialized to zero except

Counter[mapi] which is continuously accumulated at each frame, and L a =

L f r a me UGSCounter[rtPS]Counter[BE] = L f r a me UGS00= L total .

Step 2: Schedule the order of packets of DL_rtPS and UL_rtPS connections coming from

the EDF algorithm of the first tier schedulers in a ascending way according totheir deadline. In this manner, the order of DL_rtPS and UL_rtPS packets may be

changed at the beginning of every frame since the deadline of the packet of later

arrivals may be earlier than that of the packet of previous ones. If the deadlines of

two packets are the same, schedule the two packets following First-Come-First-

Served (FCFS) service discipline. After that, schedule the ordered packets into

a temporary scheduling list and record the allocated bandwidth in the counter

Counter[rtPS]. Designate packets of connections that meet(1) as urgent real-time

packets and label the others as non-urgent real-time packets.

Step 3: Serve the packet waiting in the scheduling list and then record the bandwidth of theserved packet of the connection C I Di into the counter Counter[mapi]. Calculate

the new value ofLa by computing L a = L total Counter[rtPS] Counter[BE].

IfLa =0, go toStep 4. Otherwise, go toStep 5.

Step 4: Check if there are other packets waiting to be served in the lower priority sched-

uling lists. If there are, the first scheduling round has not ended yet. Under this

condition, if the next packet to be served is in other lower priority scheduling lists,

go toStep 4.1. Otherwise, go toStep 4.2. On the other hand, if the first scheduling

round has ended, then go toStep 10.

Step 4.1: Switch to the lower priority scheduling lists and then go to

Step 4.2.Step 4.2: Check if the current serving packet is a non-real-time packet; if it is

not, go back to Step 3; otherwise, check if the average throughput,

ThN1i /N, of the connectionC I Di in the scheduling list indexed with

i is less than its specified arrival rate i (specified arrival rate equals

average data rate requirement based on traffic contract of the connec-

tion), i.e., check ifThN1i /N =N1

j =0 ma pi,j /N, i {m + 1, m +

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N-1

N

N N

N

N

N

N

N

Fig. 3 The flowchart of the LDF scheduling algorithm

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2, . . . , k} < i , whereN1

j=0 mapi,j is the current stored value of

Counter[mapi]. If this average throughput of the connection is less

than its specified arrival rate, go back to Step 3; otherwise, go back to

Step 4.

Step 5: If the bandwidth of the frame in the temporary scheduling list is fully allocated

to the rtPS packets, calculate the average throughput of the DL_nrtPS connection

with the highest priority in the DL_nrtPS scheduling list by computing ThNi /N =Nj =0m api,j /N, i {m +1, m +2, . . . , l}, where

Nj =0mapi,j is the current

updated value stored in Counter[mapi], and then go to Step 7. Otherwise, go to

Step 6.

Step 6: Check if the current serving non-real-time packet is fragmented (i.e., the allocated

bandwidth of the current frame is full while the current non-real-time packet is

served). If it is fragmented, calculate its average throughput, ThNi /N, of the connec-

tion with the fragmented packet in the scheduling list indexed withi by computingThNi /N =

Nj=0mapi,j /N, i {m + 1, m + 2, . . . , k}, where

Nj =0mapi,j is

the current updated value (the stored value + the newly served fragmented part)

stored in Counter[mapi], and then go to Step 7. Otherwise, calculate the average

throughput of the connection of the next packet in the scheduling list indexed with

r by computing ThNr /N =N

j=0mapr,j /N, r {i +1, i +2, . . . , k}, whereNj =0m apr,j is the current updated value (the stored value + the newly served

one) stored in Counter[mapr], and then go toStep 7.

Step 7: Check if the average throughput of the connection computed in the previous step is

less than its specified arrival rate. If it is less, go toStep 8. Otherwise, go toStep 9.Step 8: Calculate the average throughput of the connection of each packet tagged as non-

urgent rtPS packets by computing ThNi /N, i {n + 1, n + 2, . . . , m}, where

ThNi equals the value updated in the counter Counter[mapi]. Check if the average

throughput of each non-urgent rtPS packet is greater than its specified arrival rate.

If there is no such packet existing, go to Step 13. If there is more than one such

packet, these packets are non-urgent rtPS packets that could be fine-tuned by non-

real-time packets. The fine-tuning bandwidth, Fi , from non-urgent rtPS packets of

the connectioni is calculated as follows:

Fi =ThNi,nu i,nuN, i {n +1, n +2, . . . , m}, (3)

whereThNi,nu is accumulated throughput of each non-urgent rtPS packet accommo-

dated in the temporary scheduling list, that meets the condition of fine-tuning and

i,nu is its specified arrival rate. Consequently, the total fine-tuning bandwidth can

be calculated as

i

Fi =

i

(ThNi,nu i,nuN). (4)

The available bandwidth,L

a , now becomes

i F

i . Re-update the value stored inCounter[mapi] by subtracting the amount of fine-tuned bandwidth from the cur-

rent value for each connection of non-urgent rtPS packets. Check if the average

throughput of each non-urgent rtPS packet is equal to its specified arrival rate or

the total fine-tuning bandwidth has been exhausted after the fine-tuning process.

Note that the fine-tuning process will not cease until one of the above conditions

is satisfied. If the fine-tuning process stops, go toStep 13. Otherwise, go toStep 9.

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Step 9: Check if there is no more packet from other lower priority scheduling lists. If it is

so, go toStep 13. Otherwise, go toStep 9.1.

Step 9.1: Check if the next packet is from other lower priority scheduling lists.

If it is, switch to the lower priority scheduling lists and then calculate

the average throughput,ThNi /N, of the connection of the packet in the

lower priority scheduling list indexed withi by computingThNi /N =Nj =0mapi,j /N, i {m + 1, m +2, . . . , k}, and then go back to

Step 7. Otherwise, calculate the average throughput of the connection

of the next packet in the scheduling list indexed with rby computing

ThNr /N =N

j =0mapr,j /N, r {i +1, i +2, . . . , k}, and then go

back toStep 7.

Step 10: Check if all scheduling lists are empty. If it is true, go toStep 13. Otherwise, go to

Step 11.

Step 11: Begin the second scheduling round. Serve packets in the non-empty scheduling

lists by the Weighted Round Robin (WRR) algorithm[20]. Determine the number

of the packet, L i = f i x(L a Wi ), waiting to be served, where Wi is the weight

(the ratio of the specified arrival rate of the connection coming from the non-empty

scheduling list to sum of specified arrival rates of these connections waiting to be

served from the non-empty scheduling lists),i is the index of the connection, and

the function f i x(A)rounds the elements of A toward zero. Thereafter, check the

new value ofLa . IfLa =0, go toStep 13. Otherwise, go toStep 12.

Step 12: Begin the third scheduling round. The remaining bandwidth is allocated to the cor-

responding packets from the scheduling lists according to the given priority andthen go toStep 13.

Step 13: The generator sends theMAP message of the current frame and then the algorithm

goes back toStep 1to process the next frame.

For the highlighting of the key features of the LDF operation, the major steps of the LDF

operation by a much further account of the rationale can be explicated below:

InStep 2, the major purpose of DL_rtPS and UL_rtPS packets rearranged according to

their deadline and FCFS service discipline is to serve urgent rtPS packets and to fine-tune

the bandwidth of non-urgent rtPS packets.

Steps 34.2make it plain that LDF schedules in turn rtPS packets rearranged accordingtoStep 2and non-real-time packets determined according to the average throughput of

their connection being less than its specified arrival rate into a temporary scheduling

list until the bandwidth of the current frame is fully allocated. In Step 4.2, the average

throughput of the connection is less than its specified arrival rate equaling average data

rate requirement based on traffic contract of the connection, meaning that the bandwidth

of the connection has not yet been sufficed. The physical meaning for this is that LDF

calculates average throughput of the connection before non-real-time packets are sched-

uled into a temporary scheduling list. This aim is to maintain average throughput of the

connection. The average throughput of the connection is equal to its specified arrival rate,indicating that the bandwidth of the connection has been sufficed and that its specified

requirements are met; the average throughput of the connection is greater to its specified

arrival rate, implying that the bandwidth of the connection has been excessively sufficed.

In Step 5, the main goal of calculating the average throughput of the DL_nrtPS connection

with the highest priority in the DL_nrtPS scheduling list is to fine-tune the bandwidth of

non-urgent rtPS packets.

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Similarly, calculating average throughput of the connection of non-real-time packets in

Step 6andStep 9.1is primarily concerned with fine-tuning the bandwidth of non-urgent

rtPS packets.

Step 8explains that non-real-time packets could fine-tune the total fine-tuning bandwidth

calculated from the average throughput of the connection of non-urgent rtPS packetsbeing greater than its specified arrival rate when the average throughput of their connec-

tion is less than its specified arrival rate.

To fairly allocate the bandwidth unallocated in first scheduling round to each connection,

the unallocated bandwidth left after first scheduling round end can be served by means

of the WRR algorithm presented particularly inStep 11.

InStep 12, Utilizing the function f i x(A)in the second scheduling round could lead to

remaining some bandwidth in third scheduling round; as a result, the remaining band-

width left after the second scheduling round end is allocated to the corresponding packets

from the scheduling lists according to the given priority.

Having expounded the LDF operation principle, we subsequently turn to the LDF test

case by an example in the next subsection.

3.3 The Example Test-Case of the LDF Algorithm

In order to clarify the LDF operation principle clearly, we demonstrate the LDF operation

by an elaborate example in Fig.4. In this example, we first assume

The total transmission capacity of the link,Ctotal

, equals 0.3 Mbps.

The duration of one frame, f, is 10 ms; therefore, L f r a me=3,000 bits.

The UGS service flow is set to 500 bits/frame; hence,L total =2,500 bits.

There are only two types of service, rtPS and BE.

There are 4 connections of rtPS service flow denoted as C I D1, C I D2, C I D3, and C I D4each with the specified arrival rate 1 = 600 bits/frame, 2 = 250 bits/frame, 3 = 300

bits/frame, and 4 = 150 bits/frame, respectively. The maximum delay constraint for

each CID isd1 =10 ms,d2 =30 ms,d3 =40 ms, andd4 =50 ms, respectively.

There are 3 connections of BE service flow denoted asC I D5, C I D6, andC I D7 each

with the specified arrival rate5 = 400 bits/frame,6 =400 bits/frame, and7 =400

bits/frame, respectively.

Secondly, because of the fine-tuning process, some of the packets of the rtPS connection

issued in the previous frame may be reserved to be served at the current frame. For the sake

of easiness of understanding the fine-tuning process, we introduce two notations, pkti,j and

di,j , for the example, in which pkti,j is the packet of the i th connection issued at the j th

frame and di,j = ai,j +di is the deadline of pk ti,j . Again, the accumulated throughput,

ThNi =N

j =0mapi,j , is equal to the accumulated bandwidth of the served packet of the

connectionC I Di storing in Counter[mapi]over Nframes. Hereafter, the calculation of the

average throughput will recall the value from Counter[map

i]

directly.AsshowninFig. 4a,atthebeginningofFrame1,currenttimet= 0sec,N= 1,pkt1,1 = 600

bits, pkt2,1 = 300 bits, pkt3,1 = 400 bits, pkt4,1 = 200 bits, pk t5,1 = 800 bits, pkt6,1 = 450

bits, andpkt7,1 = 100 bits. The arrival time of these packets issued at Frame 1, a1,1, . . . , a7,1,

is equal to 0 sec. The deadline of each rtPS packet, pk t1,1,pkt2,1,pkt3,1, and pkt4,1,

is d1,1 = a1,1 + d1 = 10 ms, d2,1 = a2,1 + d2 = 30 ms, d3,1 = a3,1 + d3 = 40 ms, and

d4,1 = a4,1 + d4 = 50 ms, respectively. Initially, in accordance with Step 1, all counters are

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(a)

(b)

Fig. 4 An example demonstrating the LDF algorithm:athe fine-tuning process of the first scheduling round;

bthe weighted bandwidth allocation in the second scheduling round

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reset to 0, andL a = L f r am e U G S Counter[rtPS] Counter[BE] = 3, 000 500 0

0 = 2, 500 =L total . Since the rtPS service flow own the higher priority, its packet is allocated

first.

At the service point 1-1, the scheduled order of these packets is pkt1,1,pkt2,1,pkt3,1,

and finally pk t4,1 by the EDF algorithm. Following the operation principle in Step 2, sincethere is no reserved packet left due to the fine-tuning in the previous frame, the original

scheduled order is preserved in the temporary scheduling list. Among these packets, since

0 < a1,1 + d1 t f,pkt1,1 meets (1). Therefore, pkt1,1 is tagged as a urgent real-time

packet. The rest of the rtPS packets, pkt2,1,pkt3,1, and pkt4,1, are labeled as non-urgent

real-time packets. Next, by Step 3, serve pk t1,1 600 bits in the rtPS scheduling list first.

At this moment, the bandwidth of rtPS connections recorded in Counter[rtPS] is equal to

600 and the bandwidth of the served packet recorded in Counter[map1]is also equal to 600

resulting inL a = L total Counter[rtPS] Counter[BE] =2, 500 600 0= 1,900. Since

L a =0, identify if the first scheduling round has ended or not following the criteria depicted

in Step 4. As the next packet waiting to be served in the rtPS scheduling list ispkt2,1, the first

scheduling round has not ended yet. Also, because pk t2,1 is not in the other lower priority

scheduling list, the algorithm jumps toStep 4.2to examine whether the packet is a non-real-

time packet or not. Since pkt2,1 is not a non-real-time packet, the algorithm goes back to

Step 3and schedules pkt2,1into the temporary scheduling list. Now, Counter[rtPS] becomes

pk t1,1+ pk t2,1 =600 + 300= 900 and Counter[map2] equals pkt2,1 =300, which leads

to La = L total Counter[rtPS] Counter[BE]= 2,500900 0=1,600. The remaining

packets in rtPS scheduling list are served following the same operation principle until the

rtPS scheduling list is empty completely. At this moment, the scheduled order of rtPS packets

into the temporary scheduling list is pkt1,1,pkt2,1,pkt3,1, and finally pkt4,1, as depictedin Fig.4a. Now, Counter[rtPS] becomes pkt1,1 + pkt2,1 + pk t3,1 + pkt4,1 =600 + 300 +

400 + 200= 1500, Counter[map3] = pkt3,1 = 400, Counter[map4] = pk t4,1 = 200, and

L a = L total Counter[rtPS] Counter[BE] = 2,5001500 0 = 1,000, meaning that there

are still 1,000 bits bandwidth available to serve BE packets. Because L a =0, the algorithm

moves to evaluate the condition ofStep 4 thereon. The next packet waiting to be served is

pk t5,1listed in the BE scheduling list with lower priority; therefore, the algorithm moves to

Step 4.1to examine the current serving packet from the lower priority BE scheduling list.

At the service point 1-2, sincepkt5,1is a non-real-time packet coming out of the BE sched-

uling list, the condition ofStep 4.2is sufficed. Beforepkt5,1is scheduled into the temporary

scheduling list, the current average throughput ofC I D5 is Counter[map5]/1=0/1 =0 4, Counter[map3]/1 = 400/1 = 400 > 3, and

Counter[map2]/1 = 300/1 = 300> 2, respectively. Consequently, the bandwidth allocated

to pk t4,1 can be fine-tuned by (3), which is equal to F4 = Th14 4N= Counter[map4]

(1501) = 200150 = 50. Similarly, the bandwidthallocated topkt3,1 andpkt2,1 also meets

the fine-tuning criteria. The fine-tuned bandwidth ofpk t3,1and pkt2,1is F3 = Th13 3N=

Counter[map3] (300 1) = 400 300 = 100 and F2 = Th12 2N= Counter[map2]

(250 1) = 300 250 = 50, respectively. The fine-tuning process results in the reduction of

the bandwidth allocation of pk t4,1,pkt3,1, and pkt2,1in the temporary scheduling list. The

final bandwidth allocated to pkt4,1,pkt3,1, and pkt2,1 now reduces to pkt4,1 F4 = 150

bits, pk t3,1 F3 = 300 bits, and pkt2,1 F2 = 250 bits, respectively. The algorithm then

updates the final allocated bandwidth to Counter[map4], Counter[map3], and Counter[map2]

respectively. Accordingly, following (4), La now equals

i Fi = F4+ F3+ F2 = 200.At the service point 14, due to the fine-tuning process, the current available bandwidth

L a is allocated to the fragmented part ofC I D6. After fine-tuning, there ar still 50 bits of

pk t6,1 and 100 bits of pk t7,1 in the waiting scheduling list of BE waiting to be served. The

algorithm then updates Counter[map6] to pk t6,1 + pk t6,1 = 200+200 = 400. At this

instant, the total fine-tuning bandwidth is exhausted; hence, followingStep 13, the algorithm

triggers theMAP generator to send out theMAP message of Frame 1 and then goes back to

Step 1to process Frame 2.

As depicted in Fig. 4b, at the beginning of Frame 2, the current time t= 10 ms,

N= 2, there are still 50 bits of pk t2,1 with the deadline d2,1 = a2,1 + d2 = 30 ms,

100 bits of pk t3,1 with the deadline d3,1 = a3,1 + d3 = 40 msec, 50 bits of pkt4,1with the deadline d4,1 = a4,1 + d4 = 50 ms, 50 bits of pk t6,1, and 100 bits of pk t7,1left in corresponding waiting scheduling lists, while new packets, pkt1,2 = 700 bits,

pk t2,2 = 250 bits, pkt3,2 = 350 bits, pk t4,2 = 150 bits, pk t5,2 = 600 bits, pkt6,2 = 300 bits,

and pk t7,2 = 350 bits, each with arrival time 10 ms (i.e., a1,2 = a2,2 = . . . = a7,2 = 10 ms)

arrive. The deadline of each new rtPS packet is d1,2 = a1,2 + d1 = 20 ms, d2,2 = a2,2 +

d2 = 40 ms, d3,2 = a3,2 + d3 = 50 ms, and d4,2 = a4,2 + d4 = 60 ms. At this instant,

Counter[map1] = 600, Counter[map2] = 250, Counter[map3] = 300, Counter[map4] = 150,

Counter[map5] = 800, Counter[map6] = 400, and Counter[map7] = 0 while Counter[rtPS]

and Counter[BE] are initialized to 0.At the service point 21, following Step 2, sort out the new scheduled order for the old

and the new rtPS packets according to its deadline and FCFS service discipline in a sequence

of pkt1,2 = 700 bits with the deadline 20 ms, pk t2,1 = 50 bits with the deadline 30 ms,

pk t3,1 = 100 bits with the deadline 40 ms, pk t2,2 = 250 bits with the deadline 40 ms,

pk t4,1 = 50 bits with the deadline 50 ms, pk t3,2 = 350 bits with the deadline 50 ms, and

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pk t4,2 =150 bits with the deadline 60 ms. Among these packets, onlypk t1,2meets (1) since

0< a1,2 +d1 10=10 10. Therefore,pkt1,2is tagged as an urgent real-time packet. Since

the service discipline of BE connections is always FCFS and RR, the scheduled order of the

BE packets is in a sequence ofpkt6,1,pkt7,1,pkt5,2, pkt6,2, and pkt7,2. The algorithm then

goes to Step 3 and then schedules the 700 bits ofpkt1,2into the temporary scheduling list. Atthis moment, Counter[rtPS] is set to 700, and Counter[map1] is updated to 600+700=1,300,

makingL a =2,5007000= 1,800. Theother packets listed in the rtPS waiting scheduling

list will be processed following the similar steps depicted in service point 1-1 repeatedly until

the whole rtPS scheduling list is empty. Consequently, the order of the rest of the rtPS packets

into the temporary scheduling list ispkt2,1,pkt3,1,pkt2,2,pkt4,1,pkt3,2, and finallypkt4,2.

Now, Counter[rtPS] is set to 700+50+100+250+50+350+150= 1,650, Counter[map3]

is updated to 300 + 100 + 350=750, Counter[map4] is updated to 150 + 50 + 150=350

resulting inL a =2,500 1,650 0=850, which indicates that there are 850 bits available

to serve BE packets. Seeing that L a =0 and the first scheduling round has not ended since

pk t6,1 is in the lower priority BE scheduling list, the service point moves to serve pk t6,1 in

the lower priority BE scheduling list.

At the service point 22, the packets listed in the BE waiting scheduling list are served

adhering to the steps illustrated in service point 12 until the BE scheduling list is empty

except 600 bits of pk t5,2 since only its average throughput ofC I D5 has reached the spec-

ified arrival rate 5. Then 600 bits of pkt5,1 are held back in the BE waiting scheduling

list. Accordingly, the order of BE packets scheduled into the temporary scheduling list is

pk t6,1,pkt7,1,pkt6,2, and finally pkt7,2making Counter[BE] =50 + 100 + 300 + 350=

800, Counter[map6] =400 + 50 + 300=750, Counter[map7] =0 + 100 + 350= 450, and

L a = L total Counter[rtPS] Counter[BE] =2,500 1,650 800= 50. Since La =0,the algorithm goes to Step 4again, and finds out that there is no more other service request

waiting to be served; hence, the algorithm identifies the first round is completed. Thereafter,

the algorithm moves to Step 10to check if all scheduling lists are empty. Since the BE waiting

scheduling list is not empty and there is still bandwidth available to be allocated in the current

output frame, the algorithm goes to Step 11to proceed the second scheduling round.

At the service point 23, since pkt5,2 is still listed in the BE waiting scheduling list, the

algorithm then determines the weightW5by computingW5 = 5/(1 5+0 6+0 7)=

5/5 =1. It then calculates L i byL i = f i x(La W5)= f i x(50 1)= 50. This means

that only 50 bits of pk t5,2 is allowed to be served, leaving 600 50 =550 bits listed in the

BE waiting scheduling list. Next, the algorithm updates Counter[BE] to 800 + 50= 850 andCounter[map5] to 800+ 50 = 850 leading to L a = 2,500 1,650850 = 0. Now, since

L a = 0, the algorithm goes to Step 13; the generator sends the MAP message of Frame 2.

The algorithm then goes back toStep 1to process Frame 3.

From the elaboration of the operation principle of the proposed algorithm, it is easy to

observe that the proposed bandwidth allocation algorithm, LDF, possesses two important

characteristics, long-term average throughput control and short-term non-urgent bandwidth

fine-tuning. Intuitively, we infer that LDF can not only guarantee the QoS requirements but

also provide better fairness in both the infinite and the finite buffer case. We validate this

inference by simulations in the next section.

4 Performance Analysis: Simulation Results

The simulation assumptions are sixfold: (1) the total capacity of the link, Ctotal , is equal to

10 Mbps and the duration of one frame, f, equals 10 ms; therefore,L f r a me =100 Kbits. (2)

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Table 1 Simulation parametersCID Type Maximum delay

constraint (ms)

1 DL_rtPS 10 60

2 DL_rtPS 10 40

3 DL_rtPS 10 20

4 UL_rtPS 7 70

5 UL_rtPS 7 50

6 UL_rtPS 6 30

7 DL_nrtPS 6

8 DL_nrtPS 6

9 DL_nrtPS 6

10 UL_nrtPS 4

11 UL_nrtPS 4

12 UL_nrtPS 4

13 DL_BE 2

14 DL_BE 2

15 DL_BE 2

16 UL_BE 2

17 UL_BE 1

18 UL_BE 1

The total bandwidth of the UGS service flow in each frame is 10 Kbits. (3) Each service flow

has three connections; for easiness, the connections of the UGS service flow are not given

anyC I D, and hence the total number ofC I Ds is 18. (4) The packets are assumed to arrive

at the beginning of each frame following the Poisson distribution with the specified arrival

rate,i , i {1, 2, . . . , 18}, for each connection. (5) The traffic ratio between the downlink

and the uplink direction is set to 3 : 2 to reflect the impact of the asymmetric uplink and

downlink traffic input. (6) The corresponding QoS parameters (both the specified arrival rate

which equals average data rate requirement and the maximum delay constraint form traffic

contract of the connection for rtPS; and further, the specified arrival rate for nrtPS and BE)

specified for each service connection are given in Table1.The simulation output following

the Arrival-Service curve concept [6]: (1) the (generated) arrival curve describing the arrival

pattern of the traffic input; (2) the service curve presenting the service pattern provided by

the bandwidth allocation scheduler. For notational convenience, letGenNi denote cumulative

bandwidth of the generated arrival of the connection C I Di over Nframes. The cumulative

bandwidth of the generated arrival can be calculated by:

GenNi =

N

j =0

poi ssr nd(i,j ), (5)

where poissrnd(i,j ) is the generated arrival of the connection C I Di following Poisson dis-

tribution with specified arrival rate i at the j th frame. We then investigate the performance

of the LDF algorithm in the cases of the infinite and finite buffer depth, respectively.

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4.1 Infinite Buffer Depth Case

To gain insight into the advantage of the LDF algorithm in serving packets, the notation,

X, is introduced to represent the deviation of the cumulative bandwidth from the specified

requirements for both the simulated (generated) arrival and the accumulated throughput. Xof the cumulative bandwidth is defined as follows:

X =(ThNi or GenNi ) iN, i =1, 2, . . . , 18, (6)

where the accumulated throughput ThNi and cumulative bandwidth of the generated arrival

GenNi of the connection C I Di follow(2) and(5), respectively, i is its specified arrival

rate, Nis the total number of scheduled frames currently, and iNis the cumulative band-

width of the specified arrival. Obviously, X = 0 means that the cumulative bandwidth

of the generated arrival or the accumulated throughput is equal to that of the specified one;

X >0 indicates that the cumulative bandwidth of the generated arrival or the accumulated

throughput is greater than that of the specified one. Figure5depictsXof each connection

at N = 1 108. From Fig. 5, it is observed that the generated cumulative bandwidth of

the connectionsC I D2, C I D7, C I D8, C I D10, C I D14, C I D16, andC I D17 is greater than

the specified one while the generated cumulative bandwidth of the other connections is

less than or equal to the specified one. The generated cumulative bandwidth of the connec-

tionsC I D1, . . . , C I D9, C I D11, . . . , C I D13, andC I D15 is all served by LDF and DFPQ,

whether the generated arrival are greater than the specified one or not. The uplink nrtPS

connections and the QoS requirements, specified arrival rate and maximum delay constraints

given in Table1, of all the rtPS connections are sufficed by deploying LDF and DFPQ. Thegenerated cumulative bandwidth of the uplink nrtPS connection, C I D10, and the downlink

BE connection, C I D14, could be all served by using DFPQ and could not be all served

by employing LDF. However, it is also observed that the cumulative bandwidth ofC I D10employing LDF is already greater than the specified one and the cumulative bandwidth of

C I D14 is exactly equal to the specified one. This means that the less bandwidth has been

allocated to these connections by using LDF since these connections have already obtained

enough bandwidth, i.e., the specified cumulative bandwidth requirements of these connec-

tions are already sufficed. The sufficed bandwidth that is allocated to the connections C I D10and C I D14 by using DFPQ is used to serve the uplink BE connections C I D16, C I D17,

andC I D18 when adopting LDF making the accumulated throughput ofC I D16and C I D17equals its specified cumulative bandwidth and letting the accumulated throughput ofC I D18equals its generated cumulative bandwidth. Therefore, LDF achieves significantly better per-

formance than DFPQ. Consequently, the service curve of the uplink BE connections is greatly

improved and its specified requirements are met. In addition, the reason that the accumu-

lated throughput of the connections, C I D7, C I D8, andC I D10, is greater than its specified

cumulative bandwidth is that all the generated cumulative bandwidth of these connections

is served except the one of C I D10 and that its accumulated throughput has sufficed the

specified requirements. Therefore, the remaining capacity of the link could be allocated to

the connections with accumulated throughput equaling their specified requirements by thegiven priorities. In Fig.5, since the QoS requirements of all the rtPS connections are sufficed

and served completely, the three nrtPS connections,C I D7, C I D8, andC I D10, have higher

priority than the rest of the connections, and the extra bandwidth could be allocated to them

resulting in the cumulative bandwidth being greater than the specified one.

Figures6,7, and8illustrate the comparisons of the arrival and service curves in terms of

the cumulative bandwidth following (2) and(5)between LDF and DFPQ at N = 1 108

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Fig. 5 The comparison of

deviation of the cumulative

bandwidth of the generated

arrival and the accumulated

throughput from the specified

requirements of each connection

between LDF and DFPQ at

N =1 108

with infinite buffer depth for rtPS, nrtPS, and BE service flows, respectively; additionally,

the result of each figure is composed of three connections presented in Table 1 for each

service flow. For a more detailed understanding of this relationship of Figs. 5,6,7, and8,

the close look at the downlink rtPS connections (C I D1, C I D2, and C I D3), uplink rtPS

connections (C I D4, C I D5, and C I D6), downlink nrtPS connections (C I D7, C I D8, and

C I D9), uplink nrtPS connections (C I D10, C I D11, andC I D12), downlink BE connections

(C I D13, C I D14, andC I D15), and uplink BE connections (C I D16, C I D17, andC I D18) of

Fig.5is reflected in Figs.6,7, and8,respectively. As Fig.5indicates, the generated cumu-

lative bandwidth of the connectionsC I D1, . . . , C I D9is all served well by LDF and DFPQ,whether the generated cumulative bandwidth is greater than the specified one or not. These

results combined their own three connections are reflected in Figs. 6a, b, and 7a, respectively;

it is apparent that these service curves adapt and follow these arrival curves. The reason why

rtPS can be served very well by LDF is that the order of the rtPS packets is arranged in order

of its deadline and the urgent real-time packets must be served before the frame ends. By

contrast, the reason that rtPS can be served very well by DFPQ is that DFPQ allows serving

the amount of bandwidth determined according to both the size of the packets and 1.2 times

the value of the specified request for rtPS and nrtPS to maintain the maximum allowable

bandwidth. For these reasons given above, there is no packet discarded in rtPS using LDF

and DFPQ. As a result, it is quite obvious that both the LDF and DFPQ algorithm can assurethe QoS requirements of the rtPS service flow. Likewise, in Fig. 5,it is easy to perceive that

since not only the cumulative bandwidth ofC I D10andC I D14utilizing LDF is slightly less

than its generated one but also the cumulative bandwidth ofC I D11, C I D12, C I D13, and

C I D15 is equal to generated one, the service curves of both uplink nrtPS and downlink BE

exploiting LDF are slightly less than its generated cumulative bandwidth revealed in Figs.7b

and8a, respectively; besides, these service curves employing LDF are slightly worse than

those using DFPQ. Nevertheless, this is actually an advantage rather than a shortage, since

these service flows have already met their specified cumulative bandwidth requirements, i.e.,

the circle in Fig.5designates the accumulated throughput equaling the specified cumulativebandwidth whenX =0. Therefore, it is not necessary to allocate more bandwidth to these

connections. Similarly, Figs. 5and8b appear to be highly related in the sense that as the

cumulative bandwidth of both C I D16 and C I D17 applying LDF is equal to its specified

one and the cumulative bandwidth ofC I D18 using LDF is equal to the generated one, the

service curve of the uplink BE service flow is also significantly enhanced. The main reason

is that the bandwidth unallocated to the connectionsC I D10andC I D14can be used to serve

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Fig. 6 The arrival and service

curves of the rtPS service flow at

N =1 108 with infinite buffer

depth:adownlink;buplink

9.999 9.9992 9.9994 9.9996 9.9998 10

x 108

2,999,700,000

2,999,750,000

2,999,800,000

2,999,850,000

2,999,900,000

2,999,950,000

3,000,000,000

Time (msec)

(a)

(b)

CumulativeBandwidth(kbits)

GeneratedArrival

Service-LDF

Service-DFPQ

9.999 9.9992 9.9994 9.9996 9.9998 10

x 108

1,999,760,000

1,999,800,000

1,999,840,000

1,999,880,000

1,999,920,000

1,999,960,000

Time (msec)


GeneratedArrivalService-LDF

Service-DFPQ

more uplink BE requests; consequently, the service curve of the uplink BE service flow not

only is greatly improved and can conform to the specified requirements but also reveals the

superiority of LDF over DFPQ.

Following the same scenario, we then investigate the performance of fairness by means

of the coefficient of variation. The coefficient of variation (CV) is defined as

C V =Standard Deviation

Mean=

1n1

nk=1(xk )

2

, (7)

where kis the index of the connection, nis the number of connections, the mean, , ofxkcan

be expressed as 1n

nk=1xk, andxkis the ratio of the kth connection accumulated throughput

to its optimal one. Thekth connection optimal accumulated throughput is equal to the cumu-

lative bandwidth of its specified arrival. From the definition of the coefficient of variation, it

is obvious that the closer thexk, k =1, 2, . . . , n, is to each other, the closer the coefficient of

variation is to 0, denoting better fairness in bandwidth allocation. Stated another way, lowervalues (down to zero) of this metric imply greater fairness. Figure 9 illustrates the fairness

comparison in the coefficient of variation between LDF and DFPQ, where the unit of time is

in ms and is equal to the number of frames Ntimes one frame duration 10 ms. From Fig.9,

it is easy to observe that as time goes by the coefficient of variation becomes closer and

closer to 0 and finally achieves its steady state. From Fig.9,it is clear that LDF converges

to its steady state in a monotonic way with a faster speed than DFPQ. This indicates that

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curves of the nrtPS service flow at



9.999 9.9992 9.9994 9.9996 9.9998 10

x 108

1,799,860,000

1,799,900,000

1,799,940,000

1,799,980,000

1,800,020,000

Time (msec)

(a)

(b)


GeneratedArrival

Service-LDF

Service-DFPQ

9.999 9.9992 9.9994 9.9996 9.9998 10

x 108

1,199,880,000

1,199,900,000

1,199,920,000

1,199,940,000

1,199,960,000

1,199,980,000

1,200,000,000

Time (msec)



Service-DFPQ

LDF could indeed provide better fairness in bandwidth allocation regardless of the bursty

characteristics of traffic in time. From the above results, we can validate our inference that

LDF can not only guarantee the QoS requirements but also provide better fairness due to

possessing characteristics of long-term average throughput control and short-term non-urgent

bandwidth fine-tuning.

4.2 Finite Buffer Depth Case

In the case of infinite buffer depth, only the real-time rtPS packets will be dropped due to

over the maximum delay constraints. In the case of finite buffer depth, not only the real-time

packets but also the non-real-time ones will be dropped due to over the finite buffer depth. In

order to investigate the effectiveness of LDF running over finite buffer condition, the packets

drop ratio ( P D R) is introduced to evaluate the performance. P D R is defined as follows:

P D R =Cumulative Dropped packets

Cumulative Generated packets

, (8)

where Cumulative Dropped packets represents the total number of dropped packets and

Cumulative Generated packetsdenotes the total number of generated packets.

Figure10depicts the comparison between LDF and DFPQ in P D Ragainst buffer length

of downlink and uplink rtPS, nrtPS, and BE service flows at N = 1 108. It is observed

that both LDF and DFPQ can ensure the QoS requirements since there is no packet dropped

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curves of the BE service flow at



9.999 9.9991 9.9992 9.9993 9.9994 9.9995 9.9996 9.9997 9.99989.9999 10

x 108

599,920,000

599,940,000

599,960,000

599,980,000

600,000,000

Time (msec)

(a)

(b)


GeneratedArrival

Service-LDF

Service-DFPQ

9.999 9.9991 9.9992 9.9993 9.9994 9.9995 9.9996 9.9997 9.99989.9999 10

x 108

399,920,000

399,940,000

399,960,000

399,980,000

Time (msec)



Service-DFPQ

Fig. 9 The fairness comparison

in the coefficient of variation

between LDF and DFPQ

1 2 3 4 5 6 7 8 9 10

x 108

0.5

1

1.5

2

2.5

3

3.5

4x 10

-4

Time (msec)

CoefficientofV

ariation

LDF

DFPQ

in the rtPS, uplink nrtPS and downlink BE service flows. However, in Fig.10a, the packets

of connections of the downlink nrtPS service flow adopting LDF begins to be dropped when

the buffer length is less than 3.3 104 kbits while there is still no packet dropped for the

same service flow employing DFPQ. The reason is that some excessive packets arrive while

LDF sustains the specified value of the request by its long-term average throughput control,

1 3


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(a) (b)

Fig. 10 The comparison between LDF and DFPQ in P D R against buffer length of rtPS, nrtPS, and BE

service flows at N =1 108:adownlink;buplink

and hence some packets are dropped. DFPQ, on the other hand, allows serving 1.2 times

the value of the specified request for the rtPS and nrtPS service flows; therefore, there is

no packet dropped. In other words, since DFPQ serves too many packets of connections of

the rtPS and nrtPS service flows, it results in a lot of uplink BE packets being dropped as

illustrated in Fig.10b.

In order to understand the comparison of the overall performance between LDF and DFPQ

when the buffer depth is finite, we first compute the cumulative dropped packets in kbits in

Fig.11when the buffer length is 3.1 104

kbits. It is easy to find out that the total numberof dropped packets using LDF is far less than that of using DFPQ. Therefore, it is obvious

that even LDF leads to downlink nrtPS packets being dropped at the buffer length equaling

3.1 104 kbits and the fairness of LDF could still be better than that of DFPQ. Moreover,

with a practically large enough buffer length, e.g., 3.3 104 kbits for each scheduling list,

LDF is able to handle all packets without dropping them and provides excellent fairness

performance.

Accordingly, we then compare the cumulative bandwidth of the arrival and service curves

for the uplink BE service flow when the buffer length is equal to 3.3 104 kbits in Fig.12.

The reason that only the uplink BE service flow is investigated in Fig. 12is that the other

service flows exhibit the similar performance as illustrated in Figs. 6,7, and8a. By com-paring Figs.8b and12,it is obvious that how much LDF could improve when the buffer

length is finite and limited. This reflects that LDF could not only provide much better fair-

ness and maintain satisfactory QoS requirements but also save the buffer size in hardware at

the expense of a more complicated resource and buffer control processing.

On the contrary, Fig.13illustrates the fairness comparisons between LDF and DFPQ at

two buffer length cases, i.e., the case of buffer length equaling to 3.1 104 kbits and the

case of buffer length equaling to 3.3 104 kbits, respectively. By comparing the results in

Fig.9with the ones in Fig. 13,it is quite evident that the fairness of DFPQ degrades in the

case of finite buffer length due to the excessive loss of uplink BE packets. On the other hand,LDF is almost not changed, indicating that the fairness of LDF is indeed more stable and

less sensitive to the variation of the buffer behaviors in traffic and system characteristics; fur-

thermore, as expected, LDF possessing the characteristics of long-term average throughput

control and short-term non-urgent bandwidth fine-tuning indeed obtains better fairness and

maintains satisfactory QoS requirements and saves buffer sizes in hardware at the expense

of a more complicated resource and buffer control processing.

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Fig. 11 Comparison of the

cumulative dropped packets when

the buffer length is 3.1 104

kbits for each scheduling list


curves of uplink BE service flow

at the buffer length equaling

3.3 104 kbits for each

scheduling list

9.999 9.9991 9.9992 9.9993 9.9994 9.9995 9.9996 9.9997 9.99989.9999 10

x 108

399,880,000

399,900,000

399,920,000

399,940,000

399,960,000

399,980,000

400,000,000

Time (msec)


GeneratedArrival

Service-LDF

Service-DFPQ

Fig. 13 The comparison

between LDF and DFPQ in the

coefficient of variation when thebuffer length equals 3.1 104

kbits and 3.3 104 kbits,

respectively

1 2 3 4 5 6 7 8 9 10

x 108

0.5

1

1.5

2

2.5

3

3.5

4 x 10

-4

Time (msec)

CoefficientofVariation

LDF- Buffer Length 3.1x104kbits

LDF- Buffer Length 3.3x104

kbitsDFPQ- Buffer Length 3.1x10

4kbits

DFPQ- Buffer Length 3.3x104kbits

1 3


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5 Conclusions

In this paper, a novel bandwidth allocation algorithm of a two-tier hierarchy for IEEE 802.16

TDD mode wireless access networks under symmetric and/or asymmetric uplink and down-

link traffic input is proposed. We introduce and expound the newly proposed algorithm, LDF,in detail by the step-by-step operation principles and an elaborated example. From the elabo-

ration of the LDF algorithm and the simulation results, it is obvious that LDF possessing two

important characteristics, long-term average throughput control and short-term non-urgent

bandwidth fine-tuning, can provide better fairness and maintain satisfactory QoS require-

ments and save buffer sizes in hardware at the expense of a more complicated resource and

buffer control processing.

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Author Biographies

Chia-Chuan Liang received the B.S. and M.S. degree from National

Yunlin University of Science and Technology, Yunlin, Taiwan, in 1996

and 1998, respectively. Currently, he is working towards the Ph.D.

degree in Electrical Engineering at National Central University. Hisresearch interests include mobile communication and radio resource

management of wireless networks.

Jung-Shyr Wu received the B.S. and M.S. degrees in electrical engi-

neering from National Chiao Tung University, Hsinchu, Taiwan, in

1979 and 1981, respectively, and Ph.D. degrees in electrical engineer-

ing University of Calgary, Calgary, Canada, in 1988. Currently, He

is a Professor in the Communication Engineering at National Central

University, Jhung-Li, Taiwan. His research interests include computer

communication, queue model, and mobile communication.

a novel bandwidth allocation algorithm for ieee 802.16 tdd mode wireless access networks

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