the geometric dynamic channel allocation as a practical strategy

8/6/2019 The Geometric Dynamic Channel Allocation as a Practical Strategy

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14 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 44, NO. I , FEBRUARY 1995

The Geometric Dynamic ChannelAllocation as a Practical Strategy in MobileNetworks with Bursty User MobilityAndrea Baiocchi, Francesco Delli Priscoli, Francesco Grilli, and Fabrizio Sestini

Abstract-In this paper we refer to a specific c lass of DynamicChannel Allocation (DCA) strategies, namely the inferference-free, timid, not-conditioned class. The main concern of this workis to verify if and to what extent strategies belonging to thisclass can offer better performance th an Fixed Chann el Allocation(FCA). Th e interest in this kind of strategies is motivated by theirfeasibility with current TDM technologies, the limited am ount ofinformation required to carry ou t channel assignments and theirintrinsic stability. In this framew ork we present a simple, but veryattractive DC A strategy, the so-called Geometric DCA (GDCA).A performance evaluation is carried out to compare somerepresentative DC A strategies of the considered class, by usinga user mobility model that accounts for the large fluctuationsof the number of users in a cell coverage area expected in amicrocellular e nvironm ent. The effect of the non-null propagationtime required by the information exchange in the DC A strategiesis also taken into account.It emerges that the proposed GDCA allows better perfor-mance tha n more sophisticated strategies already proposed, atthe expense of a frequency planning carried out only at networkconfiguration. T his is due to the ability of GDCA to exploit the apriori information to maintain a tight geometric packing of usedcarriers. The reported results also show that DC A strategies in theconsidered class cope with large and sudden traffic fluctuationsremarkably better than the FC A scheme does and that theadvantage becomes more evident as the burstiness of the usermobility process (hence of the offered traffic) increases.

I. INTRODUCTIONSOLUTION TO the increasing spectrum efficiency de-A mand in Personal Comm unication Networks (P CN s) isthe implementation of a Dynamic Channel Allocation (DCA)strategy with distributed control [ 11-[8]. The DCA strategyforesees that the assignment of radio resources to the variouscells is dynamically rearranged on a real time basis, to meetthe rapidly changing demand for communication channels.The distributed control entails that decisions are made by theMobile Stations (MSs) and/or by the Base Stations (BSs)rather than by a centralized network control station. Thisreduces control information exchanges and increases systemrobustness.

Manuscript received Novem ber 30, 1993; revised March 9 , 1994. This workwas supported by the Italian National Research Council in the framework ofthe Telecomm unicat ion Project.A . Baiocchi, F. Grilli, and F. Sestini are with the Dip. INFOCOM,University of Roma La Sapienza, 00184 Ro ma, Italy.F. D. Priscolli is with the Dip. di Informatica e Sistemistica, University ofRoma L a Sapienza, 00184 Roma, Italy.IEEE Log Number 9403789.

In the literature, various DCA strategies are described(e.g., see [2]-[4]) having very different characteristics. In thispaper we refer to a specific class ;I) of traffic adaptive DCAstrategies, namely the interference-free, timid, not-conditionedclass.By interference-free we mean that no interference is allowedat any time beyond a given threshold, Le., channel reuseis subject to the constraint that the probability of the eventC / I > [C/I],,i, at any point in the coverage area of acell be greater than 1 - E . The values of [C/I],,irl an d Eare determined by the desired signal reception quality andthe target percentage of over-threshold coverage area in acell, respectively. Such a constraint leads to a conservativeestimate of potential interference received by a user in agiven cell: in fact, the channel reuse distance must be chosenso as to meet the prescribed requirement even in the worstinterference scenario. Therefore, we do not take advantageof the actual user perceived C / I , e.g., considering its actualdistance from its BS and/or the actual number of interferersand their distances from the interfered BS . On the counterpart,much less information is needed to dynamically assign radiochannels and still maintain acceptable values of the C/I.As for the timid characteristic, channels can be seized byBSs and/or MSs according to two basic strategies: either onerefrains from using a new channel in case that should causeunacceptable interference to anyone else or such a cautionis overlooked. The first case refers to the so called timidstrategies, while the other is known as aggressive strategy[3]. It can be argued [3], [8] that better performance can beobtained by means of this last approach. However, instabilitycan arise owing to consecutive channel reassignments in aneffort to keep interference below a proper threshold. On thecontrary, no instability is introduced by a timid strategy.

By not-conditioned we mean that a congested BS alwaysacquires a new chan nel, provided one is available that does notcause intolerable interference to any other channel currently inuse. Conversely, by conditioned we mean that a congestedBS can refrain from acquiring new channels, even thoughthere exist available channels that do not yield interferenceproblems. So, the occurrence of some call blocking and/ordropping in the relevant cell is accepted to prevent heavierblocking and/or dropping phenomena in the medium/longterm. The key problem of the conditioned DCA strategies isthe assessment of such mediumbong term effects and hencethe identification of the situations where it is convenient to

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refrain from assigning a new channel. The not-conditionedDCA's and the FCA can be considered as two limit strategiesinto the conditioned strategy class.The main concem of this work is to verify if and to whatextent strategies belonging to this class can offer better perfor-mance than FCA does. The interest in this kind of strategies ismotivated by their feasibility with current TDM technologies,the limited amount of information required to carry out channelassignments, and their intrinsic stability. In particular, we

describe DCA strategies where carrier acquisition is performedaccording to a priority scheme. The simplest strategy of thiskind is referred to as Priority List DCA (PLDCA) in thefollowing. A more sophisticated priority scheme based on aprior^' information has been defined, namely the GeometricDCA (GDCA) strategy.

We consider both call and mobility processes. The adopteduser mobility model accounts for the large fluctuations ofthe number of users in a cell coverage area expected in amicrocellular environment; in this model offered traffic ismodulated by a highly bursty migration process [ I l l .Also, a distinctive feature of this study is to consider theeffect of the non-null time needed to propagate the informationthe DCA strategy is based on. It is shown how some traffichandling mechanism can be set up to overcome that problem.The main results are that: (i) in the considered networkscenarios, the GDCA provides better performance than all theother considered strategies, including FCA; (ii) performancein terms of call blocking and dropping (due to unsuccessfulhand-offs) w orsens as the mobility process ge ts more and morebursty, but worsening is much larger for FCA than for theconsidered DCA strategies; (iii) increasing the burstiness ofthe user mobility process and/or increasing the overall meanoffered load leads to smaller differences of the DCA strategieswith respect to one another: and (iv) the negative effects offinite propagation delays in the information exchange can beovercome by introducing a carrier acquisition protocol andproperly tuning a few traffic handling parameters.As for the paper organization, Section I1 is devoted tothe description of the reference network scenario. Section 111outlines the adopted traffic and mobility mode ls. In Section IV ,four representative DCA strategies belonging to class D ar eoutlined. A performance comparison among the FCA and theconsidered D CA strategies is carried out in Section V . SectionV I deals with issues conceming the implementation of DCAstrategies in the presence of non-negligible propagation delays.Finally, conclusions are drawn in Section VII.

11. R E F E R E N C EETWORK S C E N A R I OA cellular mobile radio network based on a mixed frequencyand time division access technique is considered. This access

technique is used for example by the GSM pan-Europeanmobile radio network [12]. The radio resource consists of aset of carriers, which can be assigned to cells independentlyof one another. Each carrier is organized in frames includinga number of time slots. Each time slot can support a call.In the following we assume that all time slots belongingto a carrier are assigned to the same cell, Le., the minimum

Cell belonging o theinterferenceneighborhoodof the refer ence cell

0 ther cells whosecarrier utilizationmust be known bythe reference cellin the CFDCA strategy

Fig. I .mation exchange.Interference neighborhood of a cell and cells involved in the infor-

assignable bandwidth p ortion is that corresponding to a carrier.In a FCA strategy carriers are semipermanently assigned tocells. Instead, in a DCA strategy carriers can be acquired(or released) by the various cells in real time according totheir present traffic load. We assume that the acquisition andrelease decisions are up to the BS's. Moreover, a one-to-onecorrespondence between BS's and cells is assumed for thesake of simplicity, Le., a cell (1 is served by the BS a.Following [2], we define the interf ewir e neighbor-hood of acell a as the set of cells which cannot reuse a carrier assignedto cell (1. because of potentially unacceptable interference: inthe following this set is indicated as ,kr(o).We note explicitlythat ,vi(.) does not depend on time t , since chann el reusabilityis no t assessed on a real time basis, but instead establishedonce for all considering the w orst case interference conditionsresulting from cell layout, power control scheme, e.m. fieldpropagation characteristics, etc.

If the cellular network is regarded as a regular grid ofhexagonal cells, then all the interference neighborhoods havethe same shape and include the same number of cells: more-over, it is possible to define a unique reuse distance. LetR be the cell radius and D be the reuse distance measuredwith reference to the cell centers. Since each cell has sixnearest interferers in case of hexagonal cells, i t is easy toverify that the worst case C / I ratio in the up-link is given by[C/I],l,i,,= [ ( D / R ) ]'/G, if a fourth-power law attenuationis assumed. For example, in Fig. 1 the reuse distance D isequal to 3&R, so that [C/I], , , , , , 17 dB. The interferenceneighborhood relevant to the black cell is depicted in darkgray. In general, in a real cellular network the interferenceneighborhoods can have different shapes and can includedifferent number of cells. because of the irregular cell layout.Further, a carrier which is neither assigned to cell ( I no rto any cell belonging to ,LT(a) at time t , is defined to be anai*ai/ablecar-r-ier.at t with respect to cell (1 . Le t us definethe set A(u. ) including all available carriers at time f withrespect to cell (1,.Finally, we define the set S(a. ) including the carriersassigned to cell n at time t . Obviously in the FCA strategythis set is independent of time. if we neglect long-term systemmanagement operations that can alter the carrier assi,Onment.


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A DCA strategy belongs to class V if and only if BS nseizes a carrier belonging to d ( u , t ) , whenever it needs toincrease its capacity at time t. While the set A(n, ) s uniquelydefined, there are many ways of choosing a carrier out of thosebelonging to d ( u , ) if any). Defining a DCA strategy in class2) orresponds to defining that way.

111. MOBILITY N D TRAFFICMODELSThe negative exponential probability density is widely usedas a simple way to describe user cell crossing times, but it fails

to account for highly variable user densities. In fact, suddenaggregations of users can be encountered within a cell area,especially in a microcellular environment, where cell sizesare such that we cannot rely on a significant spatial average.Then the cell crossing time statistics has to account for thatvariability, while keeping analytically tractable.A good compromise seems to be a two-state Markov Mod-ulated Poisson Process (MMPP), where one state (N state)corresponds to a normal cell, characterized by quite highaverage values of the user speed and hence low cell crossingtimes; on the contrary, the other state (H state) correspondsto a hot cell, Le., a cell where some user congestion hasoccurred and/or stationary users prevail, so that average userspeed is low and cell crossing takes a relatively long time. Eachcell can dwell in either state for an exponentially distributedtime, independently of one another.In the end our mobility model is described by means of fourparameters: the mean cell crossing time in the N state, SN;the mean cell crossing time in the H state, S H ; the rate ofchange from the N to the H state, a ; he rate of changefrom the H to the N state, [j.The cells composing the service area are assumed to be in-distinguishable of one another. Therefore, the mobility modelapplies to all cells with the same values of the four parametersb . ~ ,H, x an d [j. The state of each cell is independent of allothers.As for the offered traffic, we assume that each user behavesas a Markovian source of call attempts. Therefore, as longas a user is not engaged in a call, time intervals betweensuccessive call attempts are independent of one another andof the system state and exponentially distributed with mean1/X. A call attempt fails if and only if it cannot get throughwithin a specified time-out 7, hat corresponds to the maximumtolerable value of the pre-selection delay. Once a user isengaged, he holds the call for an exponentially distributed timewith mean 1/p, unless the call has to be tom-down.Further, we assume a handover takes place as soon asa MS with a call in progress crosses a cell boundary: thisguarantees that C / I > [C/I]Il,in,f only the deterministicattenuation with distance is accounted for. The value ofthe maximum tolerable delay for handovers to be carriedout is assumed to be negligible with respect to 7. Hence,an handover can be successfully performed if and only ifsufficient radio resources are immediately found in the newcell. An unsuccessful handover causes the call to be dropped;in this model we neglect call droppings due to imperfectelectromagnetic coverage of the cell area.

Fig. 2. Cell-to-label assignment example with 11 = 9Finally, mobility and traffic behaviors are supposed to beindependent of each other.

Iv . DESCRIPTIONF TH E GDC A A NDOTHER REFERENCETRATEGIES IN CLASS vThe GDCA [I31 is described in Section IV-A. For per-formance comparison purposes other representative strategiesbelonging to class D are introduced: (i) the Anarchic DCA(ADCA), which is widely used as a simple reference DCAstrategy (Section IV-B); (ii) the PLDCA, which is a trivialmodification of the ADCA and can also be viewed as a

simplified version of the GDCA (Section IV-C); (iii) the CostFunction DCA (CFDCA) [ 2 ] , by far the most sophisticatedamong the considered strategies (Section IV-D).For each DCA strategy we outline the way carriers areselected, whenever a carrier acquisition or release has to beperformed. The conditions leading to a carrier acquisitionattempt or carrier release are detailed in Sections V and VI.Note that a carrier release is initiated only if the BS hasenough unused slots so that it can give up to one or morecarriers. Before any carriers are actually released, it couldbe necessary to reallocate some on-going calls by means ofintracell handovers.A. Geometric DCA

The G DCA strategy is based on the label an d pool of car-rier-Cell Labeling; Each cell in the mobile network is assigned1) a cell cannot be assigned any of the labels already givento cells belonging to its interference neighborhood;2 ) the number of different labels in the whole cellularnetwork must be kept to the minimum compatible withrule 1.Hereinafter, the labels will be indicated with capital letters(i.e., A: B , . ). Moreover, the number of different labels willbe denoted by v.As a matter of example, in Fig. 2 the cellularnetwork is depicted as a regular grid of hexagonal cells andthe reuse distance is 3 d R : n this case 11 = 9 labels (A-I)

are sufficient for the whole cellular network.In a real cellular network the cell-to-label assignment isno more immediate as in Fig. 2 ; nevertheless, it can be stillperformed with the same complexity as that required forthe carrier-to-cell assignment in case of FCA. In particular,whenever a cell is added/removed to/from the network, acell-to-label rearrangement could be necessary. Again, the

concepts.a label according to the following two rules:


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2n dchoice41)

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3rd 4t h 5th 6th 7th 8t hchoice choice choice choice choice choiceW T3) f i 4 ) 95 ) 4 6 ) 97)

problem is equivalent to that of rearranging the carrier-to-cellassignment in case of FCA [9], [ lo ] .Pools of Carriers: The GDCA strategy foresees the split-ting of the set of carriers in v pools of car-riers and thedefinition of a one-to-one association between labels and pools.In the following the i-th pool of carriers is indicated as

P ( i ) . = 0. . . .v - 1. For instance, in the case of Fig. 2, theset of carriers is split into nine pools. Moreover, the carriersbelonging to each pool are assigned a prioriry, thus formingan ordered list of carriers fo r each pool.In a microcellular environment, it is likely that each poolcontains the same number of carriers, since the high trafficvariability prevents reliable traffic forecasts in single cells.The GDCA strategy is based on preference lists for carrieracquisition and release. Such preference lists are diffeer-entfo rBSs with diffei-ent labels, while the same lists are attributed toBSs with the same label. Let C d s be the carrier acquisitionpreference list associated to the label X , the first carrierappearing in the list being the highest priority one. Each listCAs consists of an ordered sequence of pools of carriers,the first one being that associated to the label X. In thefollowing we associate a different integer number to each labelas follows: A tf 0, B f 1 , C H . . Then, if I; denotes theinteger associated to the label S, e let:LA-\- = { P ( i ) . P ( [ i I] i i l d v ) . P ( [ i 21 1110~1 v) . . .

P(i + / - 11 iiiod v) } ( 1 )where I I iiiotl 7ri denotes the remainder of the division of nby 7 n . The carrier release preference list is just the re\erse(carrier by carrier) of C d s .We can now state the carrier acquisition and release rules.We consider a BS (L, with label X, attempting a carrieracquisition or performing a carrier release at time t . Then:

Carrier Acquisition Algorithm: Th e BS (i acquires the car-rier with highest priority (according to LA.\-) n the set A(a. ) ,if any.Cui-i-ierRelease Algorithm: The BS ii releases the carrierwith lowest priority (according to LA-\-) n the set S(n . ) .As long as carriers are chosen among those belonging tothe first pool of the preference list yirst choice cw riers) , theGDCA strategy behaves just the same as the FCA scheme.However, carriers other than those belonging to the first choice

pool (second choice carriers) can be dynamically seized by aBS.The preference lists ensure that the system has an intrinsictendency to maintain a tight carrier spatial reuse (dense geo-metric packing) . thanks to the a priori network planning thatis built in those lists. To this end, the qualifying element of theGDCA is the association of diffeimtfir.st choice pools to a BSa and to the BSs belonging to N(a). s for the second choicecarriers, the definition adopted i n ( 1 ) for the GDCA aimsat maintaining a possibly geometrically regular assignmentof carriers even for second choice ones. The sensitivity ofthe obtained performance to the specific carrier acquisitionpreference list is currently under study: the preliminary resultsindicate that the ordering of second choice carriers hardlyaffects traffic performance, provided the first choice carriersare assigned according to the GDCA criteria.

TABLE IC A R R I E RCQUISITIONR E F E R E V E I S T \ C;\SEOF N I \ E L A B E L SI

93 )45)

The carrier acquisition preference lists are shown in TableI fo r v = 9. Let us assume that there be 45 carriers and letf ; denote the ith carrier, 1 5 i 5 45; we define the functionp( ) by means of the correspondence =1 - , B - . . . . .I tf 8; we let P ( i ) = { f j ; + , . . f j , + 2 . f i r + 3 . . f > ; + 4 . . f i r + j } .i = O . . . . . 8. As a matter of example, the carrier ac-quisition preference list of a BS, say one with label B ,is CAB = { f ~ .; .. . . . ~ ~ .4:. f l . ? . f ~ .4. f > } ; the car-rier release preference list is just the reverse. i.e., CRB ={f j . f 4 . f : ~ . f ? . f l . f 4 j . . f 44 . - . . . . f ; . . . f c } .B . Anar-chic DCA

Carrier Acquisition: Th e BS (1 attempting a carrier acqui-sition at time t , chooses a carrier in the set d(u. ) at random;obviously, the acquisition fails if this set is empty.Carrier Release: The BS (I, releasing a carrier at time t .identifies the least busy carrier in the set S(u . ) . say .f*: then,the on-going calls of the BS (1 are packed on all other carriersby means of intracell handovers and the carrier f * is released.

C . Priority List DCAEach carrier is permanently assigned a priority. Le.. a uniquecarrier ordering C is defined. This strategy works essentiallyas the ADCA does, except that the carrier choice is driven bya predefined static priority rather than by chance.Car rier Acquisitiori: The BS (1 attempting a carrier acqui-sition at time t seizes the carrier in the set d(i1. ) with highestpriority, according to the ordering C; bviously, the acquisitionfails if the set d(a. ) is empty.Carrier Release: The BS (1 releasing a carrier at time freleases the carrier in the set S((1.t)with lowest priorityaccording to the ordering C.

D. Cost Function DCAThis DCA strategy has been proposed by S. Nanda and D.J. Goodman [2]. It is based on the definition of a cost function

C ( ( L . J .) fo r a certain carrier ,J in a certain cell ii at time t .Le t us consider the set I ( a . J . ) of the cells belonging to theinterference neighborhood of a cell (1 that at time t are alreadyinterfered on the frequency of carrier , j. Formally:I ( ( / , . . J . f ) {( E . & ( ( I ) I 3b : [ E .t,(h)nd ,j E S(b. ) } .

( 2 )


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Then C ( a . . t ) = IN (u ) I - I ( a . j . t ) l , where the vertical barsindicate the set cardinality.Carrier Acquisition: The BS a attempting a carrier acqui-sition at time t chooses the carrier in the set A(u, ) having theminimum cost (in case of ties, the carrier with highest priorityis chosen according to a unique predefined priority list L);obviously, the acquisition fails if the set d(a , ) s empty.Carrier Release: The BS a releasing a carrier at time tidentifies the carrier in the set S ( a , t ) having the maximumcost, disengages it by means of a number of intracell handoversequal to the number of time slots currently in use and, lastly,releases it (in case of ties, the carrier with lowest priority ischosen according to the list C) .

Rate of change from the "N" o the "H" stateRate of chan ge from the "H" to the "N" stateMea n call interarrival time of a single userMean call holding timeReuse distance 3RNumber of lab els in the GDCANumber of carriers 15Number of slots per carrier

11 1 620 S-l1/180 -l78 min120 s34

E . Information Required by the Considered DCA StrategiesIn the ADCA, the PLDCA and the GDCA, the BS a isrequired to know which carriers belong to A(a, ) at any timet ; this is equivalent to knowing which carriers are overallassigned in h f ( a ) . n the example shown in Fig. 1 the ADCA,the PLDCA and the GDCA strategies require that the BS ofthe black cell knows which carriers are assigned in the darkgray area. However, besides this real time information, theGDCA requires that each BS is provided with the non-realtime information con cem ing the carrier acquisition and releasepreference lists. Such lists must be updated, whenever a ne wcell is added to the cellular network or an already existing cellis removed.The CFDCA strategy requires knowledge of whichcarriers are currently assigned to each BS b such that,V(a) n ,V(b)# 0, to compute the costs C ( u . j . t ) . EA ( u . ) , or a BS a. Note that for all the other considered D CAstrategies it does not matter to which BS a carrier is assignedwithin ,u(a) . In the example in Fig. 1 the CFDCA strategyrequires the BS of the black cell to know which carriersare assigned to the BS's in the dark and light gray areas.Therefore, the real time information exchange is more complex

and slower than in the other considered DCA strategies.v. PERFORMANCE EV AL UA TIO NF TH E FC A

A ND OF TH E CONSIDERED DCASWe assume that cell sizes, shapes and e.m. field propagationare such that a constant reuse distance D ca n be defined. Thecells are supposed to be hexagonal, with a radius R. To makesimulations feasible, we choose a reuse distance D = 3R,although that corresponds to a rather low quality transmissionchannel ([C/I],;,, sz 4.2 dB in the up-link). By performingthe cell-to-label assignment according to the rules describedin Section IV-A, we get 11= 3. In the FCA case, the clustersize equals just v.Table I1summarizes the meaning and thevalues of the traffic and system parameters. Note that 20

voice channels would be assigned to each cell in case of FCAstrategy with an uniform resource partition.In the performance evaluation of this section, we let T = 0,Le., no pre-selection delay is allowed. Also, the carrier as-signment information required by a given DCA algorithm issupposed to be instantaneously updated by each BS as soonas any carrier acquisition or release is successfully performed.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 44, NO. I , FEBRUARY 1Y95

TABLE I1ASSUMED A L U E S FOR PERFORMANCE EVALUATION

This hypothesis is relaxed in the next section, where finitepropagation delays are accounted for.Finally, we assume that a carrier acquisition is attemptedwhenever a new call or a handed-off call requires a slot to aBS that has no available slots; conversely, a carrier release isperformed, whenev er the number of unused slots assigned to aBS grows up to S. Note that before a carrier release is carriedout, it could be necessary to pack the on-going calls on theremaining carriers by means of intracell handovers.I I b blocking probability, Le., the probability that a call attemptis blocked;IId dropping probability, i.e., the probability that an estab-lished call has to be dropped before its natural end;IIp failure probability, Le., the probability that a call is eitherblocked, or, once it has been set up, it incurs in a forcedtear-down (call dropping): I I p = I I b + (1 -Ih average rate of intracell handovers in each cell.

The aim of the presented p erformance evaluation is to assessthe relative merits of the considered DCA strategies versusone another and versus FCA as a function of the mean offeredtraffic and of the user mobility burstiness. The quantity IIFgives an overall, not weighted characterization of the userperceived grade of service; therefore, such a parameter is usedfo r a fair comparison between the considered scenarios andstrategies.All performance results have been obtained via simulation:the 95% confidence intervals are less than 10% of the esti-mated values, so that they have not been plotted for the sakeof neatness.The reported graphs plot either I I b or I I p as a function ofthe average number of users per cell N , or the FCA and theconsidered DCA strategies. Note that, on the average, onlyabout NA/p = N / 40 users per cell are engaged in calls atany given time. Fig. 3 plots I I b in case of fixed users (i.e.,

6~ = b~ = 00). Obviously, in such a case I I d = 0 and henceIIp = I I b . Figs. 4 and 5 plot I I b an d IIF respectively, whenuser mobility is considered, but there are no hot cells (Le.,6~ = 6~ = 6 0 s) . Figs. 6 and 7 plot & an d n p espectively,when both user mobility and hot cells are considered (Le.,

Three main conclusions can be drawn from the results inFigs. 3-7.First, the overall performance advantage of DCA strategiesbelonging to class ;I) over the FCA increases as the offeredtraffic peakedness (variance to mean ratio of the offered

We introduce the following performance measures:

6~ = 6 0 S, 6~ = 600 s ) .


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16.6 13.5 20.2 15.916.2 13.3 19.2 15.215.2 12 5 19 9 1.5 7

TABLE 111AVERAGEUMBERF INTRACELLHANDOVERSER M I N U T EPER CELLN TH E DCA STRATEGIESH C = H O TELLS)I N=400 I N=500 1

DC A strategy I I,, (no HC ) I /h (with HC ) I h (no HC ) 1 /,,(with HC )ADCA I 12.1 I 9.8 I 13.5 I 10.9

network implementation. During transient phases the carrierpattern achieved according to such strategies can be quite farfrom their optimal working point, so that the occurrence ofcall blocking and dropping in a given time interval is heavierthan in the stationary behavior.Finally, Table 111 reports the average rate of intracell han-dovers I h (intracell handovers/min per cell) for two valuesof N and for the considered DCA strategies. The parameterI h is a significant measure of the control information burdencaused by the various DCA strategies with respect to FCA.From Table 111 it can be seen that the PLDCA, the CFDCAand the GDCA require on the average similar numbers ofintracell handovers, whereas the lower values of I,, for theADCA result from the carrier release rule given in SectionIV-B for that strategy.VI. PRACTICA L IMPLEMENTATION OF THE DC A STRATEGIES

It is often assumed that every BS could instantaneouslyknow the carrier utilization in neighboring BSs [ 2 ] , [3],so BSs synchronization in carrier acquisition would not benecessary. Here, we account for the finite propagation delaysin the information exchange among the BSs.In Section VI-A we present a simple distributed controlsolution to avoid colliding decisions in carrier acquisition,namely the Synchronous Carrier Acquisition (SCA) algorithm.Section VI-B is devoted to the introduction of traffic handlingparameters that can improve performance in the presence ofimpairments due to the finite propagation times. In SectionsVI-C and VI-D we apply these considerations to the GDCAstrategy: first the dimensioning of the traffic handling pa-rameters is dealt with (Section VI-C), second the obtainedperformance results are presented (Section VI-D).A. Synchronous Carrier Acquisition Algorithm

All DCA strategies here described require that the BSsbe able to exchange information about carrier utilization. TheBSs can get this knowledge in different ways: through a fixedsignaling network connecting the BSs and/or the relevantswitching centers, or simply listening to the carriers emittedby the neighboring BSs. In the latter case, BSs may simplymake measurements of received carrier powers, or exchangeradio signaling messages, following an appropriate protocol.Whatever method is used, it takes a time T b l , ~or a BSto update its carrier utilization map. TMIN ill range fromless than a few ms (e.g., in the case of a MAN connectingthe BSs) to a few seconds (e.g., in the case of radio C / Imeasurements).

Fig. 8.acquisition algorithm: decision tim e slot definition.Organization of the time axis according to the synchronous carrier

In case of a not controlled (random) carrier acquisition, ifat time t o the BS a acquires the carrier c, in the time intervalbetween t o and to + T ~ ~ I Nnother BS belonging to N(a)could decide to utilize the same carrier c , eventually causingintolerable interference in the cell of the BS (I (collision).Collisions imply the release of carrier c in both colliding BSs,and a subsequent retry for another unused carrier. This canresult in a performance worsening. In fact, the unpredictabledelay in a random ca rrier acquisition due to collisions can giverise to call blocking or dropping.Let the time axis be divided in time intervals of equal dura-tion A, called Decision Time Slots (DTSs), with A > Tk41;u .Let us consider the cell-to-label assignment described inSection IV-A for the GDCA strategy: we associate each DTSto a label in a cyclic fashion, as shown in Fig. 8 in case ofv = 9. The SCA algorithm requires the cells associated to agiven label X to decide which carrier to acquire only at theend of the DTS associated to the label X . Carrier releasesmay be done regardless of the current DTS, as they cannotgenerate any collision.Due to the rule (1) of cell-to-label assignment (see SectionIV-A), all BSs associated with the same label may use thesame carriers without collision, since they are not nearer thanthe reuse distance. As for B Ss nearer than the reuse distance,they are labeled differently; therefore carrier acquisition colli-sions cannot occur, since these BSs decide in different DTSs.Le t T = V A e the interval between two consecutivedecision opportunities for a given BS. Clearly, it resultsT > v T ~ ~ I N ,here v is constrained to be as low as possi-ble by the rules of the cell-to-label assignment. It is worthnoting that the acquisition delay 0 of an asynchronous carrieracquisition algorithm, where conflicting decisions may occur,is a random variable, whose mean could even be less thanthe delay T implied by the SCA algorithm. However, this lastdelay is constant and can be counterbalanced by introducingappropriate traffic handling parameters (s ee Section VI-B); onthe contrary, the random delay 0 is hardly predictable andtherefore cannot be adequately compensated for.The implementation of the SCA requires a slight additionalcomplexity, beside the label assignment described in SectionIV-A. As the frequency of DTSs associated with the samelabel is quite low, BSs synchronization requirements are notcritical: as an example, if T L ~ I N1 s and the uncertainty onthe beginning of each DTS cannot exceed k % , 1 slip/day isobtained with a clock precision of about lop6, which is thatof a good quartz clock.B . Traffic Handling Parameters

We introduce two param eters that are useful to im prove callblocking and dropping performance, when used together withthe SCA algorithm:


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BAlOCCHl c f u/ GEOMETRIC DYNAMIC CHANNEL ALLOCATION

- T = 25s - T = 0 5 s - T = l s- T = 2 5 s - T = 5 s - - - - - - C - T = l O s

811.OE4 4

0 1 2 3"Ha

Fig. 9.for different values of T . with T = 0 . 5 s, o = 3 an d -1- 1 0 0 .nr, (solid lines) and n,,dashed l ines) versus I / I ~ O in the GDCA.

(T minimum number of slots to be left available in each cellto allocate new calls and incoming handovers;7 ! H o number of slots in each cell which can be used only toallocate incoming handovers.

Le t n ( t ) denote the overall number of time slots assigned toa given BS at time t an d b ( t ) be the number of active calls inthe considered BS at time t . Let also w ( t ) denote the numberof call attempts that are waiting to be assigned a channel andwhose time-out has not yet expired at time t.The parameter (T is used to maintain a supply of availableslots, to accommodate call attempts offered in between twosuccessive carrier acquisition opportunities (see Section VI-A). Such a supply is the more useful, the greater T is. Infact, resource acquisition can only take place once every Tseconds and i t might be T > T . T being the maximum allowedpre-selection delay. Formally, let i l k = u( tO+ k T ) , bl; =b ( t o + k?") an d w k = rrl(to+ AT) be the number of assignedslots, active calls and waiting call attempts respectively at thek-th resource acquisition opportunity for the considered BS .At that opportunity, if IT 2 ( i l k - bl; - l l ; ) , the BS attemptsto get x new slots with x = 0 - n k - k - w k ) ; conversely,if IT < ( ? / , k- k - ilk), he BS releases ,y = nl;- )k - UII ;- Tslots. To this end, in the former case K, = [x/Sl carriersare acquired, while in the latter case K, = L x / S ] carriers arereleased, where [ . I* ] ( L : I : ] ) denotes the least integer not less than.I ' (the largest integer not greater than .c). If less than ti carriersare available, all of them are taken by the BS. In any case theBS tends to restore a supply of at least IT available slots.As to n H ( ) , i t is the number of slots that are reserved forincoming h andove rs, i.e., only iiiax{O . , n ( t )- ( t )- 1 ~ 3 0 ) lotsare available to new calls, while up to ~ ( t ) ( t ) slots can beused to allocate incoming handovers. The handover reservedslots are useful, since we assume that calls that are handed offhave to be immediately allocated (no waiting is permitted).otherwise they are dropped.

We note that i i ~ ond (T are independent of each other.However, if IT 5 T ~ H O ,t may happen that rieM' calls waiting

1OE+Q

1 1.OE-1fPI

21

1 OE-341 2 3 4 5 6 7 8 9 1 0 1 1 1 2

UFig. IO .I I H O = 2 an d .1-= 3 0 0 .IIr, versus CT in the GDCA. for different values of 7 .with r = U . i s.

to be established are blocked, in spite of a successful carrieracquisition that restores a supply of IT available slot. This sug-gests that better performance should correspond to choosing

C . Parameter Selectiori for- the G eometric DCAIn this Section the parameters IT an d n H 3 0 are dimensionedwith reference to the GDC A by assuming T = 0.5 s, h.- = 60 san d b~ = 600 s (bursty user mobility); the values of all otherparameters are reported in Table 11.Fig. 9 plots & an d IId as a function of 71HO fo r 0 = 3(the sensitivity of these plots with respect to variations of (Tis very low), ;li 300 and various values of T . A s one couldexpect, an increase in 7LHO yields a reduction of & and anincrease in &.For the performance evaluation carried out in the nextsection we have selected 7lHO = 2, which is the minimumvalue guaranteeing that, at least for T 2 .5 s, the ratio I I b / n , lis not lower than 10.A s to IT, Figs. I O an d 1 1 plot I I b an d IId respectively, asa function of (T for various values of T , assuming i i H o = 2slots an d N = 300 userkell .Fig. I O shows that, by reducing the SCA cycle time T, I I breduces as well, since tracking of the traffic fluctuations istighter. Due to the slots reserved for the incoming handovers,these considerations do not apply to n,,se e Fig. 1 1 ) . Moreover, in case T > T , the curves in Fig. 10 have aminimum at IT = IT,,,'.s a matter of fact, decreasing (Tfrom mOp t , I I b increases since the supply of available slotscannot cope with the new call attempts offered in betweentwo carrier acquisition opportunities. For increasing values of(T from uopt,I&, increases due to the inefficiency caused bythe over-dimensioned supply of available slots. For T 5 T ,there is no use in maintaining a supply of unused slots, so thechoice IT = 0 minimizes IIb. All the curves in Fig. 1 1 have aminimum, corresponding to an optimal choice of IT , regardlessof T . since no waiting of the handed-off calls is allowed.Figs. 10 an d 11 show that, for values of T 5 T . thebehaviors of n b an d II,,do not depend on the specific valueof T . In fact, in such a situation each call attempt can waitfor at least one carrier acquisition opportunity before its time-


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22 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 44, NO . I , FEBRUARY 1995

1.OE-1

p8a

I .OE-2Ps

1.OE-3 4 , , , , , , , , , , , ,0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2

U

Fig. 1 1 . II,, versus u in the GDCA, for different values of T , withr = O..j s, I I H O= 2 and .\-= 300.

1.OE-1p1.E8P 1.OE-2

- = 2.5s1.OE-31.0E-4

250 300 350 400 450 500 550 600average number of use s per cell, N

Fig. 13. n,r versus -Y in the GDCA for different values of T , withr = 0 . 5 s, I IHO = 2, u = 3 .

1 OE+O about 210 for T = 207- (1 0 s), to about 300 fo r T = 5.r (2.5 s) ,the performance target on n b being the more limiting. This isto be compared to the results in Figs. 6 and 7, where N,,,,is about 280, the performance target on II d being the morelimiting. Then, it is apparent that a proper choice of an d~ H Oan adequately outweigh the impairments due to a nonnegligible delay in carrier acquisition.

1 OE-1g8 1 OE-20 OE-3z - T = 2 5 s

- T = l O s VII. CONCLUSION250 300 350 400 450 500 550 600 In this paper a class D of DCA strategies, namely theinterference-free, timid, not conditioned class, is considered.

limited complexity and high reliability.

1 OE-4

avenge number of usem per cell ,NFig. 12 IIl, versus S in the GDCA for different values of T , with The inkrest in these strategies is motivated by their veryT = 0 5 S, I I H O= 2 , u = 3

Four DCA strategies belonging to class D are considered,out is expired; on the other hand, call blocking and droppingperformance are not sensitive to further decreases of T , incethere exist a high correlation between failures in consecutivecarrier acquisition attempts. Therefore, provided T 5 T,the delay in the information exchange and decision makingintroduced by the S CA algorithm does not impact performancein a significant way.For the performance evaluation carried out in the nextsection, we have selected 0 = 3; such a value guaranteesgood performance fo r all the considered values of T , s it canbe seen from Figs. 10 and 11.D. Performance Evaluation ofDCA With the SCA Algorithm the Geometric

Fig. 12 plots II, as a function of the average number ofusers per cell N fo r T = T , ~ T nd 20 T, 7- = 0.5 s, o =3 and 7 1 ~ 0 2. Fig. 13 plots II d versus N under the sameassumption as in Fig. 12. The bursty user mobility model isadopted, by choosing SN = 60 s an d 6~ = 600 s. All theother parameters have the values reported in Table 11. Theperformance targets are n b 5 0.02 and I I d 5 0.002.Le t N,,, be the maximum value of N for which both thecall blocking and dropping performance targets are met. Then,according to the results in Figs. 12 and 13, N,,,,, ranges from

characterized by different amounts of required informationand complexity of the relevant carrier choice algorithm. Inparticular, we propose a new DCA strategy, namely theGDCA, that exhibits sensitive performance improvementsover other proposed strategies belonging to class D . This isobtained by means of carrier acquisition and release preferencelists defined for each BS . Then, in each BS, the carrierselection is driven not only by the carrier utilization status in alimited number of neighboring BSs (see ADCA and CFDCAalgorithms), but also by the priority attributed to every carrierin the considered BS. Such a priority is semipermanentlyassigned in view of a network global long-term optimizationon the basis of the average expected offered traffic. So, inthe GDCA we can refer to an a priori information, that isenclosed in the carrier ordering.It is also shown that, as the offered traffic peakednessbecomes larger, the performance in terms of call blockingand dropping probabilities of the considered DCA strategies(especially of the GDCA) outperforms more and more the FCAscheme for a given value of the mean offered load.Lastly, it is shown that a simple synchronized carrieracquisition protocol, together with the proper tuning of a fewtraffic parameters, can cope with the effects produced by thefinite propagation delays in the information exchanges amongBSs.


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BAlOCCHl pf o l . : GEOMETRIC DYNAMIC CHANNEL ALLOCATION 23

It should be noted that the ideas underlying this paper (e.&.,the GDCA effort in maintaining a high packing of the carriersor the synchronized carrier acquisition p rotocol) are applicablein the framework of DCA classes more general than the oneconsidered in this paper.

REFERENCESJ . Same cki . C. Vinodrai , A. Javed. P . OK elly, and K. Dick. Microcel ldesign principles, I E E E Comniiiri. M u g . , pp . 76-82. Apr. 1993.S. Nanda and D. J . Goodman, Dynamic resource acquis i t ion: Dis-t ributed carrier al locat ion for TDM A cel lular sys tems, in Proc. GLOBE-COM 91 , Phoenix, AZ, Dec. 2-5, 1991, pp . 883-889.L. J . Cimini and G. J. Foschini , Dis tributed d ynamic channel al locat ionalgori thms for microcel lular sys tems, in Wireless Conimitrtic.atioiis:Fic-t i t w D i r e d o m . Boston, MA: Kluwer Academic, 1993, pp . 219-241.J. S. Yum an d W . S. Wong, Hot-spot traffic relief in cellular sys tems.IEEE J . Select. Areas Commun., vol. 1 I , pp . 934-940, Aug. 1993.R. A . Valenzuela, Dynamic Resource Allocat ion in l ine-of-s ight mi-crocells, IEEE J . Select. Areas Commuri., vol. l l . pp . 941-948, Aug.1993.Y. Akaiwa and H. Andoh . Chann el segregation-A self-organiz eddynamic channel al locat ion method: Applicat ion to T D M A F D M Amicrocel lular sys tem, IEEE J . Selecr. Areas Conimiui.. vol. 11 . pp .949-954. Aug. 1993.S. S . Kuek and W. C. Wong, Ordered Dynamic Channel Allocation./ E Trans. Vehicitlar Technol., vol. 41. pp . 271-277. Aug. 1992.J . Zander and H. Eriksson, Asymptot ic bo unds on the performance of aclass of dynam ic channel ass ignment algori thms, I J . Selecr. AreasCommiin., vol. 1 1 , pp . 926-933. Aug. 1993.J . C.-I . Chuang, Operat ion and performance of a self-organizingfrequency ass ignment method for TDMA portable radio, in Proc.GLOBECOM 90 , San Diego, CA, Dec. 2-5, 1990, pp . 1548-1552.J. F. Kiang, Characteristics of two al temative frequency channelass ignment methods for TD MA wireless access sys tems. in Proc.. ICC92. Chicago, IL, June 1992, pp . 355-358.F. P. Kelly, Re\,ersibilirJ mid Stochastic Networks. Ne w York: Wiley.1979.M. Mouly and M. B. Pautet , The G S M S w e n t f o r Mobile C o m m i r ~ i c a -riorl.7, published by the authors , 1992.A. Baiocchi , F. Delli Priscoli, F. Grilli. and F. Sestini, The geometricdynam ic channel al locat ion s trategy for high t raffic FDMDDMA mobilecommunicat ion networks , in Proc. IZS 94, Zurich, Switzerland, Mar.8-11, 1994.

Andrea Baiocchi r e ce i ve d t h e D r E n g k m m acu m Idude degree in electronic\ engineering dndDottore di Ricerca degree in Information andCommunicat ions Engineering in 1987 an d 1992.respect ively. both from the Univers i ty of R oma L aSapienza .From 1991 to 1992 he wd6 d Researcher dt theDepartment of Mathematical Methods and Modelsfor Applied Sciences of the Univers i ty of RomaL a Sapienza, where he held lectures in NumericalAnal yvs Since July 1992 he jo ined the INF OCOMDepartment in the same Univers i ty a\ a Researcher in Communicat ions .where he current ly works in th e area of Communicat ions Networks His mainwent ihc i n t e re \ t s lie in the held of traffic modeling, queuing theory andperformdnce evaluat ion of broddband an d mobile communicat ion\ network\Dr Baiocchi is a memb er of the IEEE Com municat io ns Society

Francesco Delli Priscoli grddudted in electronic en -gineering summa cum laude from the Univeni1)of Romd L a Sdpienzd in 1986 He receibed theDottore di Ricerca degree in sys tem engineeringfrom the Univers i ty of R o m a L a Sapienzd in 1991From 1986 to 1991 he worked in t he S tud-ies and Experimentat ion Department ot Tele\pazio( R o m e ) He was responsible for many t a A \ relevdntto s tudie\ . spon\ored by the European Space Agency(ESA). conceming the des ign of ddvdnced \dtellites y s t e m b a \e d o n F D M A , T D M A . A TM C D M AS ince 1987 he has been cooperat ing with the Dipart lmento di Intomiatic,i eSis temis t ica of the Univers i ty of Rome La Sapienzd uhere he has beenresearching in the non-linear control theory (addptive control. stdbilizdtion.robustness) dnd he has been teaching in the course Automdtic Control Since

1991 he i s a Re\ea rche r dt the Dipartimento di lnformatica e Sistemi\ticdof the Univers i ty of Rome La S apienm dnd he ha\ been cooperat ingwith INFOCOM Department of the Univers i t ) of Rome La Sapienzd Hi spresent resedrch interes ts con cem s the sys tem archi tecture de\ ign m d theperformance evaluat ion of radio cel luldr networks dnd sdtellite systems basedon TDM A and CDM A Moreover he researche5 in the held of robust trackingof non-l inear sy\ tems

include integration of mi

Francesco Grilli received the Dr. Eng. summacum laude degree in electronics engineering in1993 from the Univers i ty of Rome L a Sapienra.Since then and up to the beginning of 1994he joined the INFOCOM Department of the sameUniversity. focusing his research efforts on ac-cess techniques in cellular mobile radio systems.During 1994, after a brief experience within th eRadiomobile Direct ion of Ericsson TEI in Rome. hejoined Telespazio R&D group. where he is present lyinvolved in the RAC E program. His current interes tsabile satellite networks with terrestrial networks.

Fabrizio Sestini received the Dr Eng \umm dcum Iaude degree in electronic\ engineering andDottore di Ricerca degree in Infomut ion andCommunicat ion Engineering in 1989 an d 1993 re-spectively. both from the Uni\er\it) of Rome LaSapienzd Since 1989 he ha\ been involved in %\era1 dc -tivities related to the Telecommunicdt ion Project otthe Italian National Research Council Hi\ currentresedrch intere\t$ include the held\ of W D M / C D Mreconfigurable opt ical networks archi tecture\ and

\everdl d\pects conceming the de\ ign and performance e\dludt ioi i 01 cclluldrmobile communicat ion networks based on the TDM. CDM. and P RM accesstechnique\ .Dr Sestini I\ a member ot the IEEE Communicat ion\ Societ) I ot theIEEE Computer Society

the geometric dynamic channel allocation as a practical strategy

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