exploiting platform diversity for gos improvement for users with different high altitude platform...

196 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 1, JANUARY 2009

Exploiting Platform Diversity forGoS Improvement for Users with

Different High Altitude Platform AvailabilityYiming Liu, David Grace, Member, IEEE, and Paul D. Mitchell, Member, IEEE

Abstract—This paper investigates the ways of improving theGrade-of-Service (GoS) in a coexistence scenario with differentuser types in a multiple High Altitude Platforms (HAPs) systemwith shared coverage area and radio spectrum. It is achievedthrough the exploitation of HAP diversity. An analytical modelbased on a two-dimensional state-transition-rate diagram isdeveloped to describe system behaviour of a coexistence scenariocontaining two user groups, which have full and limited HAPavailability. On the basis of the analytical model, a novel restric-tion mechanism is implemented in order to achieve a fair balanceof GoS to the two user groups using connection admission control(CAC). The mechanism restricts access to the channel resourcefor users with full HAP choice in order to give more chanceof access to users with a more limited HAP selection. Differenttypes of restriction function are analysed and the paper showsthat a Step Restriction function is the most suitable mechanismto provide a balanced low blocking probability performance toboth user groups simultaneously. Furthermore, the mechanismcan potentially provide a certain level of GoS guarantee for theusers if adequate flexibility is available within the whole system.

Index Terms—Wireless communication, High Altitude Plat-forms (HAPs), grade of service, connection admission control,stratospheric platforms.

I. INTRODUCTION

H IGH Altitude Platform (HAP) technology is draw-ing more and more attention from both industry and

academia [1-5]. A HAP is an airship or aircraft operating atan altitude of 17-22 km in the stratosphere [6]. It can providelarge area coverage communications with relatively short delayusing the mm-wave bands. In order to use the mm-wave bands,Line-of-Sight (LOS) connections are required [5].

Employing more than one HAP to serve a common coveragearea can significantly increase the capacity of the system, i.e.number of supportable users, by exploiting the directional userantennas, which effectively improves the spectrum efficiency[7]. Such a scenario is shown in Figure 1. It has beenshown that the capacity per channel can increase almost pro-rata with number of HAPs, if a shared frequency band isused over a common coverage area [7]. Such configurationsallow for incremental deployment of HAPs, delivering extracapacity when it is needed [7]. It can also provide a way

Manuscript received June 20, 2007; revised November 15, 2007 and March11, 2008; accepted April 14, 2008. The associate editor coordinating thereview of this paper and approving it for publication was Y. B. Lin.

The authors are with the Communications Research Group, Depart-ment of Electronics, University of York, York, UK (e-mail: yl127, dg,[email protected]).

Digital Object Identifier 10.1109/T-WC.2009.070676

HAP1 HAP2 HAP3

User1 User2 User3

BroadbandService

Provider

Using the same mm-waveband resource on the

downlink

stratosphere

ground

Fig. 1. A multiple HAPs scenario.

of allowing multiple operators to have access to a commoncoverage area and spectrum [8]. When reusing the spectrumresource, interference must be carefully controlled to maintainthe required channel quality for users [9]. A narrow beamwidthdirectional user antenna and a large spacing radius of theHAPs in the constellation can reduce the likelihood of sig-nificant interference [10].

A multiple HAP system can potentially provide bothQuality-of-Service (QoS) improvement for individual users ona connection-to-connection basis, and Grade-of-Service (GoS)improvement for collective users as a group, by exploitingHAP diversity. Regarding QoS improvement, authors of [11]have studied the platform diversity gain over individual con-nections in a fading environment. Considering GoS perfor-mance, the design of a multiple HAP system should also takeinto account the probability that the system cannot establisha connection, i.e. the probability that no channel is availableto users. With full availability, the capability of a system tosupport users with a particular blocking probability require-ment can be calculated using the Erlang loss function [12].However, a range of factors including various obstacles, signalattenuation and user terminal limitations, e.g. use of fixedrather than steerable antennas [7], will decrease the availabilityof the HAPs to some of the users. In these circumstances, usersof the system will face a limited availability environment. In[13], a scenario is considered where users are all equippedwith fixed antennas, which leads to a limited HAP choice forall users.

A heterogeneous scenario is likely to happen, where userswith a limited HAP choice and users with a full HAP choicecoexist in the same system. This is because different users

1536-1276/09$25.00 c© 2009 IEEE

LIU et al.: EXPLOITING PLATFORM DIVERSITY FOR GOS IMPROVEMENT FOR USERS WITH DIFFERENT HIGH ALTITUDE PLATFORM AVAILABILITY 197

often have different geographical locations, elevation angles,and/or antenna equipment choices, etc. With both types ofusers coexisting in the same coverage area sharing a commonresource pool, the resource utilization level of the two groupswill influence each other. This interaction between differenttypes of users can actually degrade the performance of someusers and make the appropriate management of spectrum moredifficult. In this case, a mechanism is required for connectionadmission control (CAC) to provide an appropriate GoS forboth types of users.

Previously, a restriction mechanism has been applied to acellular single HAP scenario in order to achieve fair GoSperformance across different overlapping cellular regions, withparameters derived from simulation [14]. Previous multipleHAP research, has concentrated on determining worst casecapacity for homogeneous users, both in a static scenario[7,10] and in a dynamic scenario [9]. The potential of usingrestriction for fairness control in a multi-HAP system hasbeen indicated in [8], but it has not been extensively exploredor analytical supported. In this paper, using newly developedanalysis, a novel restriction mechanism is developed for ourparticular multiple HAP coexistence scenario that aims toachieve fair and controlled allocation of resources and overallcapacity improvement to disparate user types in the commoncoverage area.

The rest of this paper is organized as follows. In section II,the coexistence scenario is presented. Section III provides ananalytical model, which incorporates a restriction mechanismto describe the system behaviour of the coexistence scenario.The usage and impact of restriction mechanisms are shownin section IV. The restriction mechanisms are used to balancethe performance of different groups while maintaining highoverall capacity, and impact of variation in the proportion ofthe different group users is shown as well. Finally, conclusionsare given in section V.

II. COEXISTENCE SCENARIO

In this paper, we analyze a coexistence scenario with twoHAPs for the sake of simplicity. Figure 2 shows a scenariowhere users having full HAP availability (Group F) and usershaving limited HAP availability (Group L) coexist in a com-mon coverage area of the two HAPs (HAP1 and HAP2), usingshared radio spectrum. The Group F users can potentiallyaccess both HAP1 and HAP2, while the Group L users canonly access one of the HAPs. In realistic applications, Group Fusers here refer to the users equipped with steerable antennasor even smart antennas that allow them to select from bothHAPs, and there are no obstacles to block the users fromconnecting to both HAPs. On the other hand, Group L usersrepresent users equipped with a simple fixed antenna such thatthey can only connect to one HAP, or alternatively they can beconsidered as users suffering from radio link outage, caused byterrestrial obstacles or significant signal attenuation [15]. Thuscontrolling the GoS of Group L users while maintaining highoverall system capacity is more difficult than the opposite case.In practical situations it is important that either user group hasaccess to controlled GoS. In this paper through the restrictionmechanism discussed later we describe how the GoS can becontrolled for the Group L users. To GoS control on a practicalbasis will require that each HAP has knowledge of the HAP

HAP1 HAP2

Group F user Group L user

Fig. 2. A coexistence scenario with different types of users.

0,0 0,1 0,m-10,2 0,m

1,0 1,1 1,2 1,m-1 1,m

2,22,12,0 2,m2,m-1

m-1,2

m,mm,m-1

m-1,m-1 m-1,mm-1,0

m,0 m,1

m-1,1

m,2

L2+ F2

L1+ F1+ F2L1+ F1

L1+ F1

L2+ F2+ F1

2

m

2 m

2 m

2

m

L2+ F2 L2+ F2

L1+ F1+ F2

L1+ F1+ F2

L2+ F2+ F1 L2+ F2+ F1

L1+ F1

Fig. 3. State-transition-rate diagram for a coexistence scenario.

connection possibilities for each user. This can be achievedby each user communicating this information to the HAP(s)via the uplink control channels. The HAP(s) then apply theappropriate access constraints depending on whether the useris a member of Group L or Group F.

III. ANALYTICAL MODEL

In this section, the system behaviour of the coexistencescenario is analysed. Considering individual users accessingthe system, poisson arrival and departure processes of bothGroup F and Group L are assumed in the scenario due to itsuser initiated nature [16]. Figure 3 shows a state-transition-rate diagram to denote the behaviour of an m-channel 2-HAPsystem. Each node in the diagram represents a state. The firstdigit in the node denotes the number of occupied channels onHAP1, the second digit in the node denotes the number ofsimultaneously occupied channels on HAP2.

Notations in use are explained as follows:

λF1 Arrival rate of Group F users to access HAP1.λL1 Arrival rate of Group L users to access HAP1.λF2 Arrival rate of Group F users to access HAP2.λL2 Arrival rate of Group L users to access HAP2.m Number of channels on each HAP.


HAP1

HAP2 Group LGroup F

(a)

1 2 3 99 100

Probability of Access to Channel Pool

(%)0

Group L

RestrictionGroup L

HAP1

HAP2

Group F

(b)

Group F

Group L1 2 3 99 100

Probability of Access to Channel Pool

(%)0

......

......

Fig. 4. Restriction mechanism used to compensate for the inferior GoSperformance of Group L.

μ Departure rate per channel. It is assumed that thedeparture rate per channel is constant and the servicetime (1/μ) is exponentially distributed unless other-wise stated. We also assume a normalized departurerate per channel of 1 with respect to the arrival rate.

The channel allocation process shown in Figure 3 is a birth-death process [17]. Transitions in vertical direction representthe arrival and departure process on HAP1, while transitionsin the horizontal direction represent the arrival and departureprocess on HAP2. In the vertical direction, the arrival rate onHAP1 equals λF1+λL1, when channels in HAP2 are not fullyoccupied (j2 < m). When channels on HAP2 are all occupied,i.e. j2 = m, the arrival rate in the vertical direction becomesλF1+λL1+λF2. This is because when Group F users initiallyarriving at HAP2 cannot find any channels available on HAP2,they will access HAP1 instead in search of free channels,which contribute as λF2 in λF1+λL1+λF2. The departure rateon HAP1 in the vertical direction equals kμ, where k is thenumber of busy channels in the state with greater numberof occupied channels. In the horizontal direction, a similarbehaviour can be found for arrival and departure processes onHAP2.

In order to improve the potentially inferior GoS of GroupL due to relatively poorer HAP availability, it is important tocontrol and balance the resource distribution to achieve a fairallocation pattern in the coexistence scenario by exploitingHAP diversity in the system. As shown in Figure 4 (a), theflexibility is limited to only one HAP for Group L, whileGroup F has freedom to choose between both HAPs. Inorder to eliminate the performance disparity, we could simplyconstrain Group F users to one HAP. In other words, we couldchange the Group F users into Group L users by restrictingtheir choices so that there are only limited access users inthe system. However, this also means we totally sacrificethe superior flexibility of Group F and also the resultingcapacity gain arising from this flexibility. Alternatively, we canimpose a restriction to Group F as shown in Figure 4(b). Thiseffectively constrains the availability of channels for GroupF rather than the number of available HAPs. In this way, wecan exploit the superior HAP availability to the Group F users,and also share some of this flexibility with Group L users.

On the basis of the channel availability restriction, we can

Fig. 5. State-transition-rate diagram with restriction mechanism applied.

further apply a restriction function to the previously describedMarkov model. The restriction mechanism is designed toequalize the blocking probability of Group F and Group L. Ina controlled and flexible way, it blocks some Group F usersto reserve more channels for Group L users which have themore limited HAP flexibility. It is this compensation effect thatallows the system to achieve a balanced blocking probability.The modified model with restriction factor is shown in Figure5. We can see the restriction function r(j) is subject to j, thenumber of occupied channels prior to the user’s arrival on thechosen HAP, assuming there is spare capacity on a HAP whena Group F user arrives at one HAP. The restriction function isdefined in terms of the probability of access to channel whenin a particular state. Thus r(j) = p, means that a user hasaccess to the channel with probability p when in state j. If agroup F user is denied access to the chosen HAP as a result ofthe restriction mechanism, it will not be considered for accessto the other HAP. If a group F user is inhibited from accessingthe chosen HAP because all the channels are occupied, the newGroup F user will access the other HAP subject to a restrictionfunction based on the number of occupied channels on theother HAP (unless the other HAP is also fully occupied). Ingeneral, the restriction function is only determined by thenumber of occupied channels on the HAP which is aboutto make the channel admission decision, and requires noinformation from the other HAP. This means the restrictionmechanism can be implemented in a distributed fashion, whichcan effectively reduce the coordination overhead of the system.

A. Equilibrium Analysis

In statistical equilibrium the transition rate into state (j1, j2)equals the transition rate out of state (j1, j2). The systemwill be in state (j1, j2) with a state probability p(j1, j2), i.e.the probability of observing the system in state (j1, j2) at arandom point in time. The nodes in Figure 5 can be splitinto four components in the corners, four components on theedge and one component in the centre with nine differentequilibrium equation formats respectively. Providing that wecannot have a negative number of occupied channels in our


system, we can use the condition p(-1,j2) = p(j1,-1)=0,0≤ j1, j2 ≤ m, to simplify the equilibrium expression. Inthis way, the number of equation formats can be reduced tofour, which are presented as follows

For state (j1, j2), 0 ≤ j1, j2 < m, we have

(λF1 · r(j1) + λL1 + λF2 · r(j2) + λL2 + j1μ + j2μ)· p(j1, j2) = (λF1 · r(j1 − 1) + λL1) · p(j1 − 1, j2)+ (λF2 · r(j2 − 1) + λL2) · p(j1, j2 − 1) + (j1 + 1)μ· p(j1 + 1, j2) + (j2 + 1)μ · p(j1, j2 + 1)[p(−1, j2) = p(j1,−1) = 0]

(1)

For state (j1, m), 0 ≤ j1 < m,

(j1μ + mμ + (λF1 + λF2) · r(j1) + λL1) · p(j1, m)= ((λF1 + λF2) · r(j1 − 1) + λL1) · p(j1 − 1, m)+ (j1 + 1)μ · p(j1 + 1, m) + (λF2 · r(m − 1)+ λL2) · p(j1, m − 1)[p(−1, m) = 0]

(2)

For state (m, j2), 0 ≤ j2 < m,

(j2μ + mμ + (λF2 + λF1) · r(j2) + λL2) · p(m, j2)= ((λF2 + λF1) · r(j2 − 1) + λL2) · p(m, j2 − 1)+ (j2 + 1)μ · p(m, j2 + 1) + (λF1 · r(m − 1)+ λL1) · p(m − 1, j2)[p(m,−1) = 0]

(3)

For state (m, m),

(mμ + mμ) · p(m, m) = ((λF1 + λF2) · r(m − 1)+ λL1) · p(m − 1, m) + (λF2 + λF1) · r(m − 1)+ λL2) · p(m, m − 1)

(4)

In the (m+1)2 equations above, one of them is redundant,which means it can be derived from other (m+1)2-1 equations.As the system always will be in a state, the state probabilitiesmust also satisfy the normalization equation

m∑j1=0

m∑j2=0

p(j1, j2) = 1 (5)

The (m+1)2 equations including the (m+1)2-1 equilibriumequations and the normalization equation can be expressed ina matrix format

AP = B (6)

where A is the (m+1)2×(m+1)2 coefficient matrix, P is the(m+1)2×1 state probability vector, and B is the (m+1)2×1constant vector.

By solving the matrix equation, we can obtain the stateprobability vector P and effectively all the (m+1)2 stateprobabilities p(j1, j2), 0≤ j1,j2 ≤ m.

P = A−1B (7)

An expression of p(j1, j2) for a unrestricted scenario withunlimited resource has been derived in a product solution form[18], but for the more complex restriction case presented inthis paper, it is too complex to show it in a closed form. Weinstead use numerically derived results in subsequent sectionsfrom the above equations.

B. Blocking Probability

We can calculate the state probabilities p(j1, j2), 0≤j1,j2 ≤ m incorporating the restriction function. The blockingprobability of Group L (Pb L) is equivalent to the sum of thestate probabilities on the bottom or right edge

Pb L1 =m∑

j1=0

p(j1, m) (8)

Pb L2 =m∑

j2=0

p(m, j2) (9)

Pb L = Pb L1 = Pb L2 (10)

The blocking probability of Group F (Pb F ) should take intoaccount not only the state probability p(m, m) but also theblocking probability caused by the restriction mechanism. Forthe Group F users on HAP1, the blocking probability (Pb F1)can be expressed as

Pb F1 = p(m, m) +m−1∑j1=0

m∑j2=0

p(j1, j2) · (1 − r(j1))

+m−1∑j2=0

p(m, j2) · (1 − r(j2))

(11)

Similarly, the blocking probability of the Group F users onHAP2 (Pb F2) can be expressed as

Pb F2 = p(m, m) +m−1∑j2=0

m∑j1=0

p(j1, j2) · (1 − r(j2))

+m−1∑j1=0

p(j1, m) · (1 − r(j1))

(12)

Again, if we assume λF1=λL1 and λF2=λL2, then due to thesymmetry of the diagram we have

Pb F = Pb F1 = Pb F2. (13)

C. Analytical and Simulation Results Comparison

In Figure 6, we compare the analytical and Monte Carlosimulation results of the considered scenario for 28 channels(m=28) assuming no restriction effect (r(·) = 1) and identicalarrival rates per channel for both Group F and Group L onboth HAP1 and HAP2 (λF1=λL1=λF2=λL2). As suggestedin [19], a more general distribution is desirable to model theservice time of wireless systems that exercise flat rate billing,while the exponential service time assumption is justifiedfor existing cellular systems, where wireless connections arecharged based on the length of the service holding time.Consequently, not only an exponentially distributed servicetime, but also a more generalized Erlang-k distribution forservice time is considered for the simulations. It shows that theresults generated from the analytical model are consistent withthe simulation results for a wide range of traffic load levels forboth exponential and Erlang-k (k=10, as an example) servicetime distribution. The slight discrepancy between analytical


0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42

0.01

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Blocking Probability Comparison

Traffic Load/Channel (Erlang)

Prob

abili

ty

Group L AnalyticalGroup F AnalyticalGroup L Simulation (exponential)Group F Simulation (exponential)Group L Simulation (erlang−10)Group F Simulation (erlang−10)

Fig. 6. Comparison of analytical and simulation results of blockingprobability performance. Simulations with both exponential and Erlang-k(k=10) service time distribution are considered, assuming identical meanservice time.

results and simulation results assuming Erlang-k service timedistribution is due to the decreased traffic burstness comparedto the analytical scenario where exponential distribution isassumed. Overall, it indicates that the analytical model isa good representation of the system. As we expected, theseresults also show the inherent unfairness in this system whenthese two types of users coexist. The less flexible Group Lusers have a much poorer blocking probability performancecompared with Group F, since they are unable to select fromthe wider resource pool.

It is important to note that for most practical systems it isthe GoS that each group receives that is crucially important,and not for instance, some other criterion like the average GoSof both Group L and Group F. In other words, we face a min-max problem [20]. In our particular case, the poor GoS ofGroup L is the bottleneck of the system design. As a result,the objective is to improve the GoS performance of GroupL at the lowest cost in terms of the overall system capacityand complexity. Hence, the restriction mechanism is used toachieve this objective.

IV. RESTRICTION MECHANISM

A. Restriction Function Selection

As we intend to use restriction mechanism to improveGoS performance, the restriction function should be carefullychosen. We look at a number of ways of restricting GroupF availability to the HAPs through a series of restrictionfunctions. The most basic one is the constant restriction, whichapplies an equal probability of restriction to the Group F usersindependent of the occupancy level of the system. We thenlook at ways of placing greater emphasis on the restrictiontowards the higher channel occupancy levels of each HAP,using linear, quadratic and step restriction functions. Theseare specified as follows

Constant Restriction function:

r(j) = cc, 0 < cc < 1 (14)

Linear Restriction function:

r(j) = 1 − clj, 0 < cl <1

m − 1(15)

Quadratic Restriction function:

r(j) = 1 − cqj2, 0 < cq <

1(m − 1)2

(16)

Step Restriction function:

r(j) =

⎧⎨⎩

cs, j = m − s1, j ∈ {0, 1, ..., m− s − 1} & s < m0, j ∈ {m − s + 1, m − s + 2, ...m − 1} & s > 1

0 < cs < 1, s ∈ {1, 2, ..., m} (17)

cc, cl, cq and [cs, s] are the coefficients of each restrictionfunctions. Note that for Step Restriction, values of cs and sare determined together.

By using the restriction functions we can obtain a certaindegree of controllability of GoS performance. For example,if we want to equalize the blocking probabilities of the twogroups, i.e. a completely fair system, the coefficients can becalculated by solving the following equation on the basis ofequations (8,9,10) and equation (13)

Pb F = Pb L (18)

The coefficients are calculated using a standard numericalroot-finding method, since a closed form expression is notavailable. Note that for the Step Restriction function, s iscalculated first and cs is calculated afterwards, both in anumerical way. If we want to provide a target blockingprobability performance (Pb tar), i.e. a level of GoS guarantee(for a situation where users perhaps operate under differentialpricing schemes, e.g. Group F—best effort, Group L—GoSguarantee), for Group L, then the coefficients can be calculatedby solving the equation as follows

Pb L = Pb tar (19)

This general analytical approach and controlling mechanismproposed here could have wider applicability to other systemswith two user types with different access constraints to acommon system, but that is beyond the scope of this paper.

Figure 7 shows the performance comparison of the differentrestriction functions aiming to equalize the blocking proba-bility performance, again assuming identical arrival rates perchannel for both Group F and Group L on both HAP1 andHAP2 (λF1=λL1=λF2=λL2). The results can represent eitherthe performance of Group F or the performance of Group L,since Pb F = Pb L. The results are based on the proposedanalytical model with restriction mechanism and generatedby solving equation (18). The Constant Restriction functionhas the poorest overall blocking probability. It performs evenworse than the case with only Group L users, i.e. where theflexibility of Group F users is constrained to the same levelas Group L users. The Linear Restriction function performsslightly better since it restricts Group F users more whenthe channel occupancy level is high. In the same way, theQuadratic Restriction function has a better performance thanthe Linear Restriction function. In the extreme case, theStep Restriction function has a much lower overall balanced


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Probability vs Traffic Load

Traffic Load/Channel (Erlang)

Prob

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Constant RestrictionLinear RestrictionQuadratic RestrictionStep RestrictionOnly Group L users

Fig. 7. Blocking probability performance comparison of either Group F orGroup L users (Pb F = Pb L) for different restriction functions.

TABLE IVALUE OF THE COEFFICIENTS OF THE DIFFERENT RESTRICTION

FUNCTIONS

blocking probability performance. For example, with a trafficload of 0.42 Erlang/channel/user type, the balanced blockingprobability can be reduced from 6% to 5% compared with thecase with only Group L users, from 5.9% to 5%. This alsomeans that the highest traffic load can be supported with theStep Restriction function for the same blocking probabilityrequirement applied to all the users within the system. Thismeans it is beneficial to postpone the restriction effect untilhigher occupancy levels are achieved because restriction atlow occupancy level is likely to cause unnecessary blocking.Notice that restriction is aimed at ensuring free resources forGroup L especially in times of high occupancy. Clearly, thedistributed restriction mechanism with the Step Restrictionfunction can provide the lowest blocking probability perfor-mance with fairness achieved between different types of users.The values of the coefficients for a range of traffic load levelsare presented in Table 1. Note in Table 1 that Step Restrictionin this case needs only to be applied to the last channel.

B. Impact of the Variation in the Proportion of the Two UserGroups

In the previous sections, we have assumed identical trafficloads for the different groups (λF =λL). In this section, welook at the performance of the restriction mechanism withvarious traffic loads for the different groups. In order to showthe impact of relative traffic variation, we assume a constanttotal traffic load for the system and the proportion of the loadattributable to each group is changed.

0 0.2 0.4 0.6 0.8 1

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GoS performance with various traffic proportion (total: 0.8erlang/channel)

Proportion of Group L

Prob

abili

ty

Group LGroup FGroup L simulationGroup F simulationGroup L(NoRestriction)Group F(NoRestriction)Integral(NoRestriction)

Fig. 8. Blocking probability performance comparison of different restrictionfunctions.

Figure 8 shows the restriction mechanism is able to equalizethe blocking probability performance of two groups. The re-sults are again generated by solving equation (18) numerically.The total traffic load remains 0.8 Erlang/channel, and therelative proportion of each group changes. In general, theblocking probability of Group L and Group F users witha Step Restriction increases when there are more Group Lusers. This is sensible because more Group L users mean lessflexibility in general, which leads to a poorer performance.Moreover, the simulation and analytical results match for therestriction scenario in general. As a result, we can use the an-alytical model to predict the restriction coefficients accordingto the current traffic load level, so that a balanced optimumblocking probability performance, i.e. GoS performance, canbe achieved.

Also, we can see the blocking probability performance ofeach group without the control of the restriction mechanism.The performance of both Group L and Group F decreaseswhen there are more Group L users. However, the combinedperformance, which represents the scaled average blockingprobability for all the users in the system, increases withincreasing proportion of Group L. This means collectivelyless flexibility does cause higher (poorer) blocking probabilityperformance. The combined performance without restriction isbetter than the equalized performance with Step Restriction.This is because the equalizing effect comes at the expense ofrestraining the original flexibility of the system.

Figure 8 also shows the performance of Group L withrestriction is better than the performance without restriction.This implies the GoS performance of a group with limitedHAP availability can be improved by using restriction ingeneral for any proportion of Group L users in the system.If there are two groups of users in the system, like in ourscenario, and both of them are equally important, then we needto satisfy their GoS requirement respectively. As a result, itis the group with poorer GoS that we should take care of. Inour scenario, it is Group L. It shows the GoS of Group L canbe reduced from 6% to 3% when there are very few Group Lusers, from 5% to 3.5% when half of the traffic is from GroupL, and there is obviously no improvement when all the users


0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1 0

0. 00 5

0. 01

0. 01 5

0. 02

0. 02 5

0. 03

0. 03 5

0. 04

0. 04 5

0. 05

St


Restriction probability with different traffic proportions

Pro

babi

lity

ep Re ct ri ct io n Co ns ta nt Re st ri ct io n

Fig. 9. Restriction probability of Group F users with different trafficproportions for Step Restriction and Constant Restriction.

are in Group L. In general, it shows a continuous trade-offbetween GoS improvement and population of beneficiaries inthe system.

Figure 9 shows the restriction probability values that need tobe used for various proportions of traffic levels of Group L forthe Step and Constant Restrictions. The restriction probability(PR) is defined as the percentage of resource constrained forGroup F use relative to the total resource. For the ConstantRestriction, it can be calculated as:

PR = 1 − cc (20)

For the Step Restriction, it can be calculated as:

PR =s + (1 − cs)

m(21)

Figure 9 shows the restriction probability using ConstantRestriction is much higher than the performance using StepRestriction. Note that both restriction functions achieve thesame effect of equalizing blocking probabilities for two dif-ferent groups. The Step Restriction is optimised to reduce theflexibility of the system the least, and thus it actually providesthe best performance, i.e. it serves a lower bound of blockingprobability performance using the restriction mechanism.

Rather than equalizing the GoS performance, the restrictionmechanism can also provide a certain level of GoS guaranteefor a group of users. Figure 10 shows the blocking probabilityperformance with GoS guarantee for Group L when the steprestriction function is used. The results are generated bysolving equation (2) numerically. It shows in Figure 10(a)that the blocking probability performance of Group L can bemaintained at different target GoS levels, until there is no moreflexibility to utilize from Group F. For example, when the GoStarget is 1%, and 83% of the traffic comes from Group L,there is no more flexibility from the Group F users availableas shown in Figure 10(b). At that point, the GoS target cannotbe achieved if the proportion of Group L is increased, becauseall Group F users are blocked in order to sustain the Group Lusers. Actually, the blocking probability of Group L equals theblocking probability with only Group L traffic, which servesas a lower bound. The previous conclusion about constant and

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

Blocking probability with different traffic proportion(a) Group L performance


Prob

abili

ty

No Group F trafficGoS=0.01GoS=0.02GoS=0.04

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1(b) Group F performance


Prob

abili

ty

GoS=0.01GoS=0.02GoS=0.04

Fig. 10. Blocking probability performance with GoS guarantee (Pb tar) forGroup L.

0 0.2 0.4 0.6 0.8 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Restriction probability with different traffic proportion


Prob

abili

ty

GoS=0.01GoS=0.02GoS=0.04

Fig. 11. Restriction probability performance of Group F users with differentGoS target (Pb tar) for Group L.

step restriction is still true even when the proportion of GroupL users is changed.

The restriction probability performance with GoS guaranteeis shown in Figure 11. When GoS target is set high, therestriction probability is then relatively low. This is becauseblocking probability requirement is easier to satisfy if thevalue is greater, consequently less flexibility of Group F needsto be sacrificed. Note that the discrepancy between Figure 11and Figure 10(b) is the state probability p(m, m) in equation(11), which represents the blocking caused by unavailabilityof channels rather than the restriction mechanism.

V. CONCLUSION

In this paper a technique has been developed to control theGoS for two different types of user that access a multipleHAP system. An analytical model has been developed tounderstand the way in which different types of users, i.e.groups with full/limited HAP availability, affect each other’sGoS performance. It incorporates a distributed restrictionmechanism to control the relative GoS performance among


different groups. Simulation results are provided to show theeffectiveness of the proposed model. It is shown how byapplying a restriction mechanism that progressively constrainsaccess to channels at high occupancy level, the balancedblocking probability performance is progressively improved.The restriction mechanism with a Step Restriction function canprovide a fair allocation pattern with different proportions ofthe user groups and significantly decreases the overall blockingprobability compared with other functions. It is also capableof providing a certain degree of GoS guarantee for the usergroup with limited HAP availability by trading off some of theextra flexibility present with the user group that has access toall HAPs. Results show that it is possible to improve GoS ofusers with limited HAP availability by sharing the flexibilityof users with greater HAP availability. The analytical approachand controlling mechanism proposed in this paper are not onlysuitable for a multiple HAP system but are also potentiallyapplicable to general communication systems.

ACKNOWLEDGMENT

This work has been partly funded by the CAPANINAProject (FP6-IST-2003-506745), which receives funding fromthe 6th Framework Programme of the European Commission.

REFERENCES

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Yiming Liu received his B.Sc. degree in InformationEngineering degree from the Southeast University,Nanjing, China in 2003, and Ph.D. in Electronicsfrom the University of York, York, UK in 2007. HisPh.D. thesis dealt with ‘Radio Resource Manage-ment for a High Altitude Platform System’. He wasa Research Assistant since 2005 in the Communi-cations Research Group at York, where he is now aResearch Associate. His research interests includeradio resource management, cognitive networkingand dynamic pricing.

David Grace (S’95-A’99-M’00) received his MEngdegree in Electronic Systems Engineering D.Phildegree from the University of York, UK in 1993and 1999 respectively. His D. Phil thesis dealt with‘Distributed Dynamic Channel Assignment for theWireless Environment’. Since 1994 he has been amember of the Communications Research Group atYork, where he is now a Senior Research Fellow. Hehas worked on a variety of research contracts includ-ing several from the former Defence Evaluation andResearch Agency. Current research interests include

cognitive radio and dynamic spectrum management, particularly for high-altitude platform and terrestrial ad hoc networks. Until January 2007 he wasPrincipal Scientific Officer for CAPANINA a major European Frameworksix project that developed broadband communications from high-altitudeplatforms. He is an author of over 130 conference and journal papers,many relating to HAP communications. He has been an invited to speakon HAP communications systems at a number of conferences and industriallocations worldwide. He chairs WG1 ‘Radio Communications’ of COST 297- HAPCOS, and is a Director of SkyLARC Technologies Ltd, a York basedcompany, specialising in broadband communications from aerial platforms.He is a member of the IEEE Technical Committee on Cognitive Networksand IEEE Satellite and Space Technical Committee.

Paul Mitchell received his MEng and PhD degreesfrom the University of York, York, U.K., in 1999and 2003, respectively. He is Lecturer in the Com-munications Research Group at the University ofYork. Doctoral research on medium access controlfor satellite systems was supported by BT, with otherindustrial experience gained at QinetiQ. Dr Mitchellis an author and reviewer of refereed journal papers,has served on international conference programmecommittees, and has been an invited speaker at theIET and the University of Bradford. He is an execu-

tive committee member of the IET Knowledge Network on Satellite Systemsand Applications. His research expertise and interests include medium accesscontrol, sensor networks, queuing theory, traffic modelling and system levelsimulation in which he has over eight years experience.

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