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

The Geometric Dynamic Channel Allocation as a Practical Strategy in Mobile

Networks with Bursty User Mobility Andrea Baiocchi, Francesco Delli Priscoli, Francesco Grilli, and Fabrizio Sestini

Abstract-In this paper we refer to a specific class of Dynamic Channel Allocation (DCA) strategies, namely the inferference- free, timid, not-conditioned class. The main concern of this work is to verify if and to what extent strategies belonging to this class can offer better performance than Fixed Channel Allocation (FCA). The interest in this kind of strategies is motivated by their feasibility with current TDM technologies, the limited amount of information required to carry out channel assignments and their intrinsic stability. In this framework we present a simple, but very attractive DCA strategy, the so-called Geometric DCA (GDCA).

A performance evaluation is carried out to compare some representative DCA strategies of the considered class, by using a user mobility model that accounts for the large fluctuations of the number of users in a cell coverage area expected in a microcellular environment. The effect of the non-null propagation time required by the information exchange in the DCA strategies is also taken into account.

It emerges that the proposed GDCA allows better perfor- mance than more sophisticated strategies already proposed, at the expense of a frequency planning carried out only at network configuration. This is due to the ability of GDCA to exploit the a priori information to maintain a tight geometric packing of used carriers. The reported results also show that DCA strategies in the considered class cope with large and sudden traffic fluctuations remarkably better than the FCA scheme does and that the advantage becomes more evident as the burstiness of the user mobility process (hence of the offered traffic) increases.

I. INTRODUCTION

SOLUTION TO the increasing spectrum efficiency de- A mand in Personal Communication Networks (PCNs) is the implementation of a Dynamic Channel Allocation (DCA) strategy with distributed control [ 11-[8]. The DCA strategy foresees that the assignment of radio resources to the various cells is dynamically rearranged on a real time basis, to meet the rapidly changing demand for communication channels. The distributed control entails that decisions are made by the Mobile Stations (MSs) and/or by the Base Stations (BSs) rather than by a centralized network control station. This reduces control information exchanges and increases system robustness.

Manuscript received November 30, 1993; revised March 9, 1994. This work was supported by the Italian National Research Council in the framework of the Telecommunication Project.

A. Baiocchi, F. Grilli, and F. Sestini are with the Dip. INFOCOM, University of Roma La Sapienza, 00184 Roma, Italy.

F. D. Priscolli is with the Dip. di Informatica e Sistemistica, University of Roma La 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 this paper we refer to a specific class ;I) of traffic adaptive DCA strategies, namely the interference-free, timid, not-conditioned class.

By interference-free we mean that no interference is allowed at any time beyond a given threshold, Le., channel reuse is subject to the constraint that the probability of the event C/I > [C/I],,i, at any point in the coverage area of a cell be greater than 1 - E . The values of [C/I],,irl and E are determined by the desired signal reception quality and the target percentage of over-threshold coverage area in a cell, respectively. Such a constraint leads to a conservative estimate of potential interference received by a user in a given cell: in fact, the channel reuse distance must be chosen so as to meet the prescribed requirement even in the worst interference scenario. Therefore, we do not take advantage of the actual user perceived C / I , e.g., considering its actual distance from its BS and/or the actual number of interferers and their distances from the interfered BS. On the counterpart, much less information is needed to dynamically assign radio channels and still maintain acceptable values of the C/I.

As for the timid characteristic, channels can be seized by BSs and/or MSs according to two basic strategies: either one refrains from using a new channel in case that should cause unacceptable interference to anyone else or such a caution is overlooked. The first case refers to the so called timid strategies, while the other is known as aggressive strategy [3]. It can be argued [3], [8] that better performance can be obtained by means of this last approach. However, instability can arise owing to consecutive channel reassignments in an effort to keep interference below a proper threshold. On the contrary, no instability is introduced by a timid strategy.

By not-conditioned we mean that a congested BS always acquires a new channel, provided one is available that does not cause intolerable interference to any other channel currently in use. Conversely, by conditioned we mean that a congested BS can refrain from acquiring new channels, even though there exist available channels that do not yield interference problems. So, the occurrence of some call blocking and/or dropping in the relevant cell is accepted to prevent heavier blocking and/or dropping phenomena in the medium/long term. The key problem of the conditioned DCA strategies is the assessment of such mediumbong term effects and hence the identification of the situations where it is convenient to

0018-9S4S/9S$04.00 0 1995 IEEE

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refrain from assigning a new channel. The not-conditioned DCA's and the FCA can be considered as two limit strategies into the conditioned strategy class.

The main concem of this work is to verify if and to what extent strategies belonging to this class can offer better perfor- mance than FCA does. The interest in this kind of strategies is motivated by their feasibility with current TDM technologies, the limited amount of information required to carry out channel assignments, and their intrinsic stability. In particular, we describe DCA strategies where carrier acquisition is performed according to a priority scheme. The simplest strategy of this kind is referred to as Priority List DCA (PLDCA) in the following. A more sophisticated priority scheme based on a prior^' information has been defined, namely the Geometric DCA (GDCA) strategy.

We consider both call and mobility processes. The adopted user mobility model accounts for the large fluctuations of the number of users in a cell coverage area expected in a microcellular environment; in this model offered traffic is modulated by a highly bursty migration process [ I l l .

Also, a distinctive feature of this study is to consider the effect of the non-null time needed to propagate the information the DCA strategy is based on. It is shown how some traffic handling mechanism can be set up to overcome that problem.

The main results are that: (i) in the considered network scenarios, the GDCA provides better performance than all the other considered strategies, including FCA; (ii) performance in terms of call blocking and dropping (due to unsuccessful hand-offs) worsens as the mobility process gets more and more bursty, but worsening is much larger for FCA than for the considered DCA strategies; (iii) increasing the burstiness of the user mobility process and/or increasing the overall mean offered load leads to smaller differences of the DCA strategies with respect to one another: and (iv) the negative effects of finite propagation delays in the information exchange can be overcome by introducing a carrier acquisition protocol and properly tuning a few traffic handling parameters.

As for the paper organization, Section I1 is devoted to the description of the reference network scenario. Section 111 outlines the adopted traffic and mobility models. In Section IV, four representative DCA strategies belonging to class D are outlined. A performance comparison among the FCA and the considered DCA strategies is carried out in Section V. Section VI deals with issues conceming the implementation of DCA strategies in the presence of non-negligible propagation delays. Finally, conclusions are drawn in Section VII.

11. REFERENCE NETWORK SCENARIO A cellular mobile radio network based on a mixed frequency

and time division access technique is considered. This access technique is used for example by the GSM pan-European mobile radio network [12]. The radio resource consists of a set of carriers, which can be assigned to cells independently of one another. Each carrier is organized in frames including a number of time slots. Each time slot can support a call.

In the following we assume that all time slots belonging to a carrier are assigned to the same cell, Le., the minimum

Cell belonging to the interference neighborhood of the reference cell

0 Other cells whose carrier utilization must be known by the reference cell in the CFDCA strategy

Fig. I . mation exchange.

Interference neighborhood of a cell and cells involved in the infor-

assignable bandwidth portion is that corresponding to a carrier. In a FCA strategy carriers are semipermanently assigned to cells. Instead, in a DCA strategy carriers can be acquired (or released) by the various cells in real time according to their present traffic load. We assume that the acquisition and release decisions are up to the BS's. Moreover, a one-to-one correspondence between BS's and cells is assumed for the sake of simplicity, Le., a cell (1 is served by the BS a.

Following [2], we define the interfewire neighbor-hood of a cell a as the set of cells which cannot reuse a carrier assigned to cell (1. because of potentially unacceptable interference: in the following this set is indicated as ,kr(o). We note explicitly that ,vi(.) does not depend on time t , since channel reusability is not assessed on a real time basis, but instead established once for all considering the worst case interference conditions resulting from cell layout, power control scheme, e.m. field propagation characteristics, etc.

If the cellular network is regarded as a regular grid of hexagonal cells, then all the interference neighborhoods have the same shape and include the same number of cells: more- over, it is possible to define a unique reuse distance. Let R be the cell radius and D be the reuse distance measured with reference to the cell centers. Since each cell has six nearest interferers in case of hexagonal cells, i t is easy to verify that the worst case C / I ratio in the up-link is given by [C/I],l,i,, = [ ( D / R ) - l]'/G, if a fourth-power law attenuation is assumed. For example, in Fig. 1 the reuse distance D is equal to 3&R, so that [C/I],,,,,, 17 dB. The interference neighborhood relevant to the black cell is depicted in dark gray. In general, in a real cellular network the interference neighborhoods can have different shapes and can include different number of cells. because of the irregular cell layout.

Further, a carrier which is neither assigned to cell ( I nor to any cell belonging to ,LT(a) at time t , is defined to be an ai*ai/able car-r-ier. at t with respect to cell (1. Let us define the set A(u. t ) including all available carriers at time f with respect to cell (1,.

Finally, we define the set S(a. t ) including the carriers assigned to cell n at time t . Obviously in the FCA strategy this set is independent of time. if we neglect long-term system management operations that can alter the carrier assi, Onment.

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

A DCA strategy belongs to class V if and only if BS n seizes a carrier belonging to d ( u , t ) , whenever it needs to increase its capacity at time t. While the set A(n, t ) is uniquely defined, there are many ways of choosing a carrier out of those belonging to d ( u , t ) (if any). Defining a DCA strategy in class 2) corresponds to defining that way.

111. MOBILITY AND TRAFFIC MODELS

The negative exponential probability density is widely used as a simple way to describe user cell crossing times, but it fails to account for highly variable user densities. In fact, sudden aggregations of users can be encountered within a cell area, especially in a microcellular environment, where cell sizes are such that we cannot rely on a significant spatial average. Then the cell crossing time statistics has to account for that variability, 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 high average values of the user speed and hence low cell crossing times; on the contrary, the other state (H state) corresponds to a hot cell, Le., a cell where some user congestion has occurred and/or stationary users prevail, so that average user speed is low and cell crossing takes a relatively long time. Each cell can dwell in either state for an exponentially distributed time, independently of one another.

In the end our mobility model is described by means of four parameters: the mean cell crossing time in the N state, SN; the mean cell crossing time in the H state, SH; the rate of change from the N to the H state, a; the rate of change from 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 model applies to all cells with the same values of the four parameters b . ~ , SH, cx and [j. The state of each cell is independent of all others.

As for the offered traffic, we assume that each user behaves as a Markovian source of call attempts. Therefore, as long as a user is not engaged in a call, time intervals between successive call attempts are independent of one another and of the system state and exponentially distributed with mean 1/X. A call attempt fails if and only if it cannot get through within a specified time-out 7, that corresponds to the maximum tolerable value of the pre-selection delay. Once a user is engaged, he holds the call for an exponentially distributed time with mean 1/p, unless the call has to be tom-down.

Further, we assume a handover takes place as soon as a MS with a call in progress crosses a cell boundary: this guarantees that C / I > [C/I]Il,in, if only the deterministic attenuation with distance is accounted for. The value of the maximum tolerable delay for handovers to be carried out is assumed to be negligible with respect to 7. Hence, an handover can be successfully performed if and only if sufficient radio resources are immediately found in the new cell. An unsuccessful handover causes the call to be dropped; in this model we neglect call droppings due to imperfect electromagnetic coverage of the cell area.

Fig. 2. Cell-to-label assignment example with 11 = 9

Finally, mobility and traffic behaviors are supposed to be independent of each other.

Iv . DESCRIPTION OF THE GDCA AND OTHER REFERENCE STRATEGIES IN CLASS v

The GDCA [I31 is described in Section IV-A. For per- formance comparison purposes other representative strategies belonging to class D are introduced: (i) the Anarchic DCA (ADCA), which is widely used as a simple reference DCA strategy (Section IV-B); (ii) the PLDCA, which is a trivial modification of the ADCA and can also be viewed as a simplified version of the GDCA (Section IV-C); (iii) the Cost Function DCA (CFDCA) [ 2 ] , by far the most sophisticated among the considered strategies (Section IV-D).

For each DCA strategy we outline the way carriers are selected, whenever a carrier acquisition or release has to be performed. The conditions leading to a carrier acquisition attempt or carrier release are detailed in Sections V and VI. Note that a carrier release is initiated only if the BS has enough unused slots so that it can give up to one or more carriers. Before any carriers are actually released, it could be necessary to reallocate some on-going calls by means of intracell handovers.

A. Geometric DCA

The GDCA strategy is based on the label and pool of car-rier-

Cell Labeling; Each cell in the mobile network is assigned

1) a cell cannot be assigned any of the labels already given to cells belonging to its interference neighborhood;

2 ) the number of different labels in the whole cellular network must be kept to the minimum compatible with rule 1.

Hereinafter, the labels will be indicated with capital letters (i.e., A: B , . . .). Moreover, the number of different labels will be denoted by v. As a matter of example, in Fig. 2 the cellular network is depicted as a regular grid of hexagonal cells and the reuse distance is 3 d R : in this case 11 = 9 labels (A-I) are sufficient for the whole cellular network.

In a real cellular network the cell-to-label assignment is no more immediate as in Fig. 2; nevertheless, it can be still performed with the same complexity as that required for the carrier-to-cell assignment in case of FCA. In particular, whenever a cell is added/removed to/from the network, a cell-to-label rearrangement could be necessary. Again, the

concepts.

a label according to the following two rules:

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2nd choice

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3rd 4th 5th 6th 7th 8th choice choice choice choice choice choice

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problem is equivalent to that of rearranging the carrier-to-cell assignment 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 the definition of a one-to-one association between labels and pools. In the following the i-th pool of carriers is indicated as P ( i ) . i = 0. . . . . v - 1. For instance, in the case of Fig. 2, the set of carriers is split into nine pools. Moreover, the carriers belonging to each pool are assigned a prioriry, thus forming an ordered list of carriers for each pool.

In a microcellular environment, it is likely that each pool contains the same number of carriers, since the high traffic variability prevents reliable traffic forecasts in single cells.

The GDCA strategy is based on preference lists for carrier acquisition and release. Such preference lists are diffeer-ent for BSs with diffei-ent labels, while the same lists are attributed to BSs with the same label. Let C d s be the carrier acquisition preference list associated to the label X , the first carrier appearing in the list being the highest priority one. Each list CAs consists of an ordered sequence of pools of carriers, the first one being that associated to the label X. In the following we associate a different integer number to each label as follows: A tf 0, B tf 1, C H 2 . . . Then, if I; denotes the integer associated to the label S, we let:

LA-\- = { P ( i ) . P ( [ i + I] i i l d v ) . P ( [ i + 21 1110~1 v). . . . . P( [ i + r/ - 11 iiiod v)} ( 1 )

where I I iiiotl 7ri denotes the remainder of the division of n by 7n. 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 carrier acquisition or performing a carrier release at time t . Then:

Carrier Acquisition Algorithm: The BS (i acquires the car- rier with highest priority (according to LA.\-) in the set A(a. t ) , if any.

Cui-i-ier Release Algorithm: The BS ii releases the carrier with lowest priority (according to LA-\-) in the set S(n. t ) .

As long as carriers are chosen among those belonging to the first pool of the preference list yirst choice cwriers), the GDCA 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 a BS.

The preference lists ensure that the system has an intrinsic tendency to maintain a tight carrier spatial reuse (dense geo- metric packing). thanks to the a priori network planning that is built in those lists. To this end, the qualifying element of the GDCA is the association of diffeimtfir.st choice pools to a BS a and to the BSs belonging to N(a). As for the second choice carriers, the definition adopted in (1 ) for the GDCA aims at maintaining a possibly geometrically regular assignment of carriers even for second choice ones. The sensitivity of the obtained performance to the specific carrier acquisition preference list is currently under study: the preliminary results indicate that the ordering of second choice carriers hardly affects traffic performance, provided the first choice carriers are assigned according to the GDCA criteria.

TABLE I CARRIER ACQUISITION PREFEREVE LIST I \ C;\SE OF N I \ E LABELS

I

93)

45)

The carrier acquisition preference lists are shown in Table I for v = 9. Let us assume that there be 45 carriers and let f ; denote the ith carrier, 1 5 i 5 45; we define the function p( .) by means of the correspondence =1 - 0, B - 1 . . . . . 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 ~ . f;. . . . . . j ~ ~ . f4:. f l . f ? . f ~ . f4. 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 4 4 . - . . . . f ; . . . f c } .

B. Anar-chic DCA

Carrier Acquisition: The BS (1 attempting a carrier acqui- sition at time t , chooses a carrier in the set d(u. t ) 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. t ) . say .f*: then, the on-going calls of the BS (1 are packed on all other carriers by means of intracell handovers and the carrier f * is released.

C. Priority List DCA

Each carrier is permanently assigned a priority. Le.. a unique carrier ordering C is defined. This strategy works essentially as the ADCA does, except that the carrier choice is driven by a predefined static priority rather than by chance.

Carrier Acquisitiori: The BS (1 attempting a carrier acqui- sition at time t seizes the carrier in the set d(i1. t ) with highest priority, according to the ordering C; obviously, the acquisition fails if the set d(a. t ) is empty.

Carrier Release: The BS (1 releasing a carrier at time f releases the carrier in the set S((1.t) with lowest priority according to the ordering C.

D. Cost Function DCA This 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 . t ) for a certain carrier ,J in a certain cell ii at time t . Let us consider the set I ( a . ,J. t ) of the cells belonging to the interference neighborhood of a cell (1 that at time t are already interfered on the frequency of carrier , j . Formally:

I ( ( / , . . J . f ) = {( E . & ( ( I ) I 3b : [ E .t,(h) and , j E S(b. / ) } . ( 2 )

I X

a 0 l/X 1 / ~ D v

C S

Then C ( a . j . t ) = I N ( u ) I - l I (a . j . t ) l , where the vertical bars indicate the set cardinality.

Carrier Acquisition: The BS a attempting a carrier acqui- sition at time t chooses the carrier in the set A(u, t ) having the minimum cost (in case of ties, the carrier with highest priority is chosen according to a unique predefined priority list L); obviously, the acquisition fails if the set d(a , t ) is empty.

Carrier Release: The BS a releasing a carrier at time t identifies the carrier in the set S ( a , t ) having the maximum cost, disengages it by means of a number of intracell handovers equal to the number of time slots currently in use and, lastly, releases it (in case of ties, the carrier with lowest priority is chosen according to the list C).

Rate of change from the "N" to the "H" state Rate of change from the "H" to the "N" state Mean call interarrival time of a single user Mean call holding time

Reuse distance 3R Number of labels in the GDCA Number of carriers 15 Number of slots per carrier

111 620 S-l 1/180 S-l 78 min 120 s

3

4

E. Information Required by the Considered DCA Strategies

In the ADCA, the PLDCA and the GDCA, the BS a is required to know which carriers belong to A(a, t ) at any time t ; this is equivalent to knowing which carriers are overall assigned in h f ( a ) . In the example shown in Fig. 1 the ADCA, the PLDCA and the GDCA strategies require that the BS of the black cell knows which carriers are assigned in the dark gray area. However, besides this real time information, the GDCA requires that each BS is provided with the non-real time information conceming the carrier acquisition and release preference lists. Such lists must be updated, whenever a new cell is added to the cellular network or an already existing cell is removed.

The CFDCA strategy requires knowledge of which carriers are currently assigned to each BS b such that ,V(a) n ,V(b) # 0, to compute the costs C(u. j . t ) . j E A ( u . t ) , for a BS a. Note that for all the other considered DCA strategies it does not matter to which BS a carrier is assigned within ,u(a). In the example in Fig. 1 the CFDCA strategy requires the BS of the black cell to know which carriers are 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 EVALUATION OF THE FCA AND OF THE CONSIDERED DCAS

We assume that cell sizes, shapes and e.m. field propagation are such that a constant reuse distance D can be defined. The cells are supposed to be hexagonal, with a radius R. To make simulations feasible, we choose a reuse distance D = 3R, although that corresponds to a rather low quality transmission channel ([C/I],;,, sz 4.2 dB in the up-link). By performing the cell-to-label assignment according to the rules described in Section IV-A, we get 11 = 3. In the FCA case, the cluster size equals just v. Table I1 summarizes the meaning and the values of the traffic and system parameters. Note that 20 voice channels would be assigned to each cell in case of FCA strategy 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 is supposed to be instantaneously updated by each BS as soon as any carrier acquisition or release is successfully performed.

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TABLE I1 ASSUMED VALUES FOR PERFORMANCE EVALUATION

This hypothesis is relaxed in the next section, where finite propagation delays are accounted for.

Finally, we assume that a carrier acquisition is attempted whenever a new call or a handed-off call requires a slot to a BS that has no available slots; conversely, a carrier release is performed, whenever the number of unused slots assigned to a BS grows up to S. Note that before a carrier release is carried out, it could be necessary to pack the on-going calls on the remaining carriers by means of intracell handovers.

I I b blocking probability, Le., the probability that a call attempt is 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 either blocked, or, once it has been set up, it incurs in a forced tear-down (call dropping): I I p = I I b + (1 - &)I&; Ih average rate of intracell handovers in each cell.

The aim of the presented performance evaluation is to assess the relative merits of the considered DCA strategies versus one another and versus FCA as a function of the mean offered traffic and of the user mobility burstiness. The quantity IIF gives an overall, not weighted characterization of the user perceived grade of service; therefore, such a parameter is used for a fair comparison between the considered scenarios and strategies.

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 sake of neatness.

The reported graphs plot either I I b or I I p as a function of the average number of users per cell N , for the FCA and the considered DCA strategies. Note that, on the average, only about N A / p = N / 40 users per cell are engaged in calls at any 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 hence IIp = I I b . Figs. 4 and 5 plot I I b and IIF respectively, when user mobility is considered, but there are no hot cells (Le., 6~ = 6~ = 60 s). Figs. 6 and 7 plot & and n p respectively, when both user mobility and hot cells are considered (Le.,

Three main conclusions can be drawn from the results in Figs. 3-7.

First, the overall performance advantage of DCA strategies belonging to class ;I) over the FCA increases as the offered traffic peakedness (variance to mean ratio of the offered

We introduce the following performance measures:

6~ = 60 S , 6~ = 600 s ) .

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CFDCA PLDCA GDCA

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16.6 13.5 20.2 15.9 16.2 13.3 19.2 15.2 15.2 12 5 19 9 1.5 7

TABLE 111 AVERAGE NUMBER OF INTRACELL HANDOVERS PER MINUTE

PER CELL IN THE DCA STRATEGIES (HC=HOT CELLS)

I N=400 I N=500 1 DCA strategy I I,, (no HC) I /h (with HC) I Ih (no HC) 1 /,,(with HC) ADCA I 12.1 I 9.8 I 13.5 I 10.9

network implementation. During transient phases the carrier pattern achieved according to such strategies can be quite far from their optimal working point, so that the occurrence of call blocking and dropping in a given time interval is heavier than in the stationary behavior.

Finally, Table 111 reports the average rate of intracell han- dovers I h (intracell handovers/min per cell) for two values of N and for the considered DCA strategies. The parameter I h is a significant measure of the control information burden caused by the various DCA strategies with respect to FCA. From Table 111 it can be seen that the PLDCA, the CFDCA and the GDCA require on the average similar numbers of intracell handovers, whereas the lower values of I,, for the ADCA result from the carrier release rule given in Section IV-B for that strategy.

VI. PRACTICAL IMPLEMENTATION OF THE DCA STRATEGIES

It is often assumed that every BS could instantaneously know the carrier utilization in neighboring BSs [ 2 ] , [3], so BSs synchronization in carrier acquisition would not be necessary. Here, we account for the finite propagation delays in the information exchange among the BSs.

In Section VI-A we present a simple distributed control solution to avoid colliding decisions in carrier acquisition, namely the Synchronous Carrier Acquisition (SCA) algorithm. Section VI-B is devoted to the introduction of traffic handling parameters that can improve performance in the presence of impairments due to the finite propagation times. In Sections VI-C and VI-D we apply these considerations to the GDCA strategy: first the dimensioning of the traffic handling pa- rameters is dealt with (Section VI-C), second the obtained performance results are presented (Section VI-D).

A. Synchronous Carrier Acquisition Algorithm

All DCA strategies here described require that the BSs be able to exchange information about carrier utilization. The BSs can get this knowledge in different ways: through a fixed signaling network connecting the BSs and/or the relevant switching centers, or simply listening to the carriers emitted by the neighboring BSs. In the latter case, BSs may simply make measurements of received carrier powers, or exchange radio signaling messages, following an appropriate protocol.

Whatever method is used, it takes a time Tbl ,~ for a BS to update its carrier utilization map. TMIN will range from less than a few ms (e.g., in the case of a MAN connecting the BSs) to a few seconds (e.g., in the case of radio C / I measurements).

Fig. 8. acquisition algorithm: decision time slot definition.

Organization of the time axis according to the synchronous carrier

In case of a not controlled (random) carrier acquisition, if at time t o the BS a acquires the carrier c, in the time interval between t o and to + T ~ ~ I N another BS belonging to N(a) could decide to utilize the same carrier c, eventually causing intolerable 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 can result in a performance worsening. In fact, the unpredictable delay in a random carrier acquisition due to collisions can give rise 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 in Section IV-A for the GDCA strategy: we associate each DTS to a label in a cyclic fashion, as shown in Fig. 8 in case of v = 9. The SCA algorithm requires the cells associated to a given label X to decide which carrier to acquire only at the end of the DTS associated to the label X . Carrier releases may be done regardless of the current DTS, as they cannot generate any collision.

Due to the rule (1) of cell-to-label assignment (see Section IV-A), all BSs associated with the same label may use the same carriers without collision, since they are not nearer than the reuse distance. As for BSs nearer than the reuse distance, they are labeled differently; therefore carrier acquisition colli- sions cannot occur, since these BSs decide in different DTSs.

Let T = V A be the interval between two consecutive decision opportunities for a given BS. Clearly, it results T > v T ~ ~ I N , where v is constrained to be as low as possi- ble by the rules of the cell-to-label assignment. It is worth noting that the acquisition delay 0 of an asynchronous carrier acquisition algorithm, where conflicting decisions may occur, is a random variable, whose mean could even be less than the delay T implied by the SCA algorithm. However, this last delay is constant and can be counterbalanced by introducing appropriate traffic handling parameters (see Section VI-B); on the contrary, the random delay 0 is hardly predictable and therefore cannot be adequately compensated for.

The implementation of the SCA requires a slight additional complexity, beside the label assignment described in Section IV-A. As the frequency of DTSs associated with the same label is quite low, BSs synchronization requirements are not critical: as an example, if T L ~ I N = 1 s and the uncertainty on the beginning of each DTS cannot exceed k 5%, 1 slip/day is obtained with a clock precision of about lop6, which is that of a good quartz clock.

B . Traffic Handling Parameters We introduce two parameters that are useful to improve call

blocking and dropping performance, when used together with the SCA algorithm:

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

8 1

1.OE4 4 0 1 2 3

"Ha

Fig. 9. for different values of T . with T = 0 . 5 s, o = 3 and -1- = 100.

nr, (solid lines) and n,, (dashed lines) versus I / I ~ O in the GDCA.

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

Let n ( t ) denote the overall number of time slots assigned to a given BS at time t and b ( t ) be the number of active calls in the considered BS at time t. Let also w( t ) denote the number of call attempts that are waiting to be assigned a channel and whose time-out has not yet expired at time t.

The parameter (T is used to maintain a supply of available slots, to accommodate call attempts offered in between two successive carrier acquisition opportunities (see Section VI- A). Such a supply is the more useful, the greater T is. In fact, resource acquisition can only take place once every T seconds and i t might be T > T . T being the maximum allowed pre-selection delay. Formally, let i l k = u( tO + k T ) , bl; = b ( t o + k?") and w k = rrl(to + AT) be the number of assigned slots, active calls and waiting call attempts respectively at the k-th resource acquisition opportunity for the considered BS. At that opportunity, if IT 2 ( i l k - bl; - u l l ; ) , the BS attempts to get x new slots with x = 0 - ( n k - bk - w k ) ; conversely, if IT < ( ? / , k - bk - (ilk), the BS releases ,y = nl; - 1)k - U I I ; - IT slots. To this end, in the former case K, = [x/Sl carriers are acquired, while in the latter case K, = Lx/S] carriers are released, where [.I*] ( L:I: ] ) denotes the least integer not less than . I ' (the largest integer not greater than .c). If less than ti carriers are available, all of them are taken by the BS. In any case the BS 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 for incoming handovers, i.e., only iiiax{ O.,n ( t ) - b( t ) - 7 1 ~ 3 0 ) slots are available to new calls, while up to ~ ( t ) - b ( t ) slots can be used to allocate incoming handovers. The handover reserved slots are useful, since we assume that calls that are handed off have to be immediately allocated (no waiting is permitted). otherwise they are dropped.

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

1 OE+Q

1 1.OE-1 f P I

21

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

U

Fig. IO. I I H O = 2 and .1- = 300.

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 carrier acquisition that restores a supply of IT available slot. This sug- gests that better performance should correspond to choosing

C. Parameter Selectiori for- the Geometric DCA

In this Section the parameters IT and nH30 are dimensioned with reference to the GDCA by assuming T = 0.5 s, h.,- = 60 s and b~ = 600 s (bursty user mobility); the values of all other parameters are reported in Table 11.

Fig. 9 plots & and IId as a function of 71HO for 0 = 3 (the sensitivity of these plots with respect to variations of (T is very low), ;li = 300 and various values of T . As one could expect, an increase in 7LHO yields a reduction of & and an increase in &.

For the performance evaluation carried out in the next section we have selected 7lHO = 2, which is the minimum value guaranteeing that, at least for T 2 2.5 s, the ratio I I b / n , l is not lower than 10.

As to IT, Figs. I O and 1 1 plot I I b and IId respectively, as a function of (T for various values of T , assuming i i H o = 2 slots and N = 300 userkell.

Fig. I O shows that, by reducing the SCA cycle time T, I I b reduces as well, since tracking of the traffic fluctuations is tighter. Due to the slots reserved for the incoming handovers, these considerations do not apply to n,, (see Fig. 11) .

Moreover, in case T > T , the curves in Fig. 10 have a minimum at IT = IT,,,'. As a matter of fact, decreasing (T from mOpt, I I b increases since the supply of available slots cannot cope with the new call attempts offered in between two carrier acquisition opportunities. For increasing values of (T from uopt, I&, increases due to the inefficiency caused by the over-dimensioned supply of available slots. For T 5 T , there is no use in maintaining a supply of unused slots, so the choice IT = 0 minimizes IIb. All the curves in Fig. 1 1 have a minimum, corresponding to an optimal choice of IT, regardless of T . since no waiting of the handed-off calls is allowed.

Figs. 10 and 11 show that, for values of T 5 T . the behaviors of n b and II,, do not depend on the specific value of T . In fact, in such a situation each call attempt can wait for at least one carrier acquisition opportunity before its time-

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

1.OE-1

p 8 a 8 I 1.OE-2 P s

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 , with r = O..j s, I I H O = 2 and .\- = 300.

1.OE-1 p 1 .E 8 P 1.OE-2

- T = 2.5s a 1.OE-3 1.0E-4

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

Fig. 13. n,r versus -Y in the GDCA for different values of T , with r = 0.5 s, I I H O = 2, u = 3 .

1 OE+O about 210 for T = 207- (10 s), to about 300 for T = 5.r (2.5 s), the performance target on n b being the more limiting. This is to be compared to the results in Figs. 6 and 7, where N,,,, is about 280, the performance target on IId being the more limiting. Then, it is apparent that a proper choice of and ~ H O can adequately outweigh the impairments due to a non negligible delay in carrier acquisition.

1 OE-1

g 8 I 1 OE-2 0 1 OE-3 z

- T = 2 5 s

-T= lOs VII. CONCLUSION

250 300 350 400 450 500 550 600 In this paper a class D of DCA strategies, namely the interference-free, timid, not conditioned class, is considered.

limited complexity and high reliability.

1 OE-4

avenge number of usem per cell, N

Fig. 12 IIl, versus S in the GDCA for different values of T , with The inkrest in these strategies is motivated by their very T = 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 dropping performance are not sensitive to further decreases of T , since there exist a high correlation between failures in consecutive carrier acquisition attempts. Therefore, provided T 5 T, the delay in the information exchange and decision making introduced by the SCA algorithm does not impact performance in a significant way.

For the performance evaluation carried out in the next section, we have selected 0 = 3; such a value guarantees good performance for all the considered values of T , as it can be seen from Figs. 10 and 11.

D. Performance Evaluation of DCA With the SCA Algorithm

the Geometric

Fig. 12 plots II, as a function of the average number of users per cell N for T = T , ~ T and 20 T, 7- = 0.5 s, o = 3 and 7 1 ~ 0 = 2. Fig. 13 plots IId versus N under the same assumption as in Fig. 12. The bursty user mobility model is adopted, by choosing SN = 60 s and 6~ = 600 s. All the other parameters have the values reported in Table 11. The performance targets are n b 5 0.02 and I I d 5 0.002.

Let N,,, be the maximum value of N for which both the call 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 information and complexity of the relevant carrier choice algorithm. In particular, we propose a new DCA strategy, namely the GDCA, that exhibits sensitive performance improvements over other proposed strategies belonging to class D. This is obtained by means of carrier acquisition and release preference lists defined for each BS. Then, in each BS, the carrier selection is driven not only by the carrier utilization status in a limited number of neighboring BSs (see ADCA and CFDCA algorithms), but also by the priority attributed to every carrier in the considered BS. Such a priority is semipermanently assigned in view of a network global long-term optimization on the basis of the average expected offered traffic. So, in the GDCA we can refer to an a priori information, that is enclosed in the carrier ordering.

It is also shown that, as the offered traffic peakedness becomes larger, the performance in terms of call blocking and dropping probabilities of the considered DCA strategies (especially of the GDCA) outperforms more and more the FCA scheme for a given value of the mean offered load.

Lastly, it is shown that a simple synchronized carrier acquisition protocol, together with the proper tuning of a few traffic parameters, can cope with the effects produced by the finite propagation delays in the information exchanges among BSs.

BAlOCCHl pf ol.: 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 carriers or the synchronized carrier acquisition protocol) are applicable in the framework of DCA classes more general than the one considered in this paper.

REFERENCES

J. Samecki. C. Vinodrai, A. Javed. P. OKelly, and K. Dick. Microcell design principles, IEEE Comniiiri. M u g . , pp. 76-82. Apr. 1993. S. Nanda and D. J. Goodman, Dynamic resource acquisition: Dis- tributed carrier allocation for TDMA cellular systems, in Proc. GLOBE- COM 91, Phoenix, AZ, Dec. 2-5, 1991, pp. 883-889. L. J. Cimini and G. J. Foschini, Distributed dynamic channel allocation algorithms for microcellular systems, 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 and W. S. Wong, Hot-spot traffic relief in cellular systems. IEEE J . Select. Areas Commun., vol. 1 I , pp. 934-940, Aug. 1993. R. A. Valenzuela, Dynamic Resource Allocation in line-of-sight mi- crocells, IEEE J . Select. Areas Commuri., vol. l l . pp. 941-948, Aug. 1993. Y. Akaiwa and H. Andoh. Channel segregation-A self-organized dynamic channel allocation method: Application to TDMAFDMA microcellular system, IEEE J . Selecr. Areas Conimiui.. vol. 1 1 . 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, Asymptotic bounds on the performance of a class of dynamic channel assignment algorithms, I J . Selecr. Areas Commiin., vol. 1 1 , pp. 926-933. Aug. 1993. J. C.-I. Chuang, Operation and performance of a self-organizing frequency assignment 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 altemative frequency channel assignment methods for TDMA wireless access systems. in Proc.. ICC 92. Chicago, IL, June 1992, pp. 355-358. F. P. Kelly, Re\,ersibilirJ mid Stochastic Networks. New York: Wiley. 1979. M. Mouly and M. B. Pautet, The GSM S w e n t f o r Mobile Commir~ica- riorl.7, published by the authors, 1992. A. Baiocchi, F. Delli Priscoli, F. Grilli. and F. Sestini, The geometric dynamic channel allocation strategy for high traffic FDMDDMA mobile communication networks, in Proc. IZS 94, Zurich, Switzerland, Mar. 8-11, 1994.

Andrea Baiocchi received the Dr Eng k m m a cum Idude degree in electronic\ engineering dnd Dottore di Ricerca degree in Information and Communications Engineering in 1987 and 1992. respectively. both from the University of Roma La Sapienza .

From 1991 to 1992 he wd6 d Researcher dt the Department of Mathematical Methods and Models for Applied Sciences of the University of Roma La Sapienza, where he held lectures in Numerical Analyvs Since July 1992 he joined the INFOCOM

Department in the same University a\ a Researcher in Communications. where he currently works in the area of Communications Networks His main wen t ihc intere\ts lie in the held of traffic modeling, queuing theory and performdnce evaluation of broddband and mobile communication\ network\

Dr Baiocchi i s a member of the IEEE Communications Society

Francesco Delli Priscoli grddudted in electronic en- gineering summa cum laude from the Univeni1) of Romd La Sdpienzd in 1986 He receibed the Dottore di Ricerca degree in system engineering from the University of Roma La Sapienzd in 1991

From 1986 to 1991 he worked in the Stud- ies and Experimentation Department ot Tele\pazio (Rome) He was responsible for many t a A \ relevdnt to studie\. spon\ored by the European Space Agency (ESA). conceming the design of ddvdnced \dtellite s y s t e m ba\ed on FDMA, TDMA. ATM CDMA

Since 1987 he has been cooperating with the Dipartlmento di Intomiatic,i e Sistemistica of the University of Rome La Sapienzd uhere he has been researching 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\earcher dt the Dipartimento di lnformatica e Sistemi\ticd of the University of Rome La Sapienm dnd he ha\ been cooperating with INFOCOM Department of the Universit) of Rome La Sapienzd His present resedrch interests concems the system architecture de\ign m d the performance evaluation of radio celluldr networks dnd sdtellite systems based on TDMA and CDMA Moreover he researche5 in the held of robust tracking of non-linear sy\tems

include integration of mi

Francesco Grilli received the Dr. Eng. summa cum laude degree in electronics engineering in 1993 from the University of Rome La Sapienra.

Since then and up to the beginning of 1994 he joined the INFOCOM Department of the same University. focusing his research efforts on ac- cess techniques in cellular mobile radio systems. During 1994, after a brief experience within the Radiomobile Direction of Ericsson TEI in Rome. he joined Telespazio R&D group. where he is presently involved in the RACE program. His current interests

abile satellite networks with terrestrial networks.

Fabrizio Sestini received the Dr Eng \ummd cum Iaude degree in electronic\ engineering and Dottore di Ricerca degree in Infomution and Communication Engineering in 1989 and 1993 re- spectively. both from the Uni\er\it) of Rome La Sapienzd

Since 1989 he ha\ been involved in %\era1 dc- tivities related to the Telecommunicdtion Project ot the Italian National Research Council Hi\ current resedrch intere\t$ include the held\ of WDM/CDM reconfigurable optical networks architecture\ and

\everdl d\pects conceming the de\ign and performance e\dludtioii 01 cclluldr mobile communication networks based on the TDM. CDM. and PRM access technique\.

Dr Sestini I\ a member ot the IEEE Communication\ Societ) I ot the IEEE Computer Society