NEW DYNAMIC CHANNEL AllOCATION ALGORITHMS

A set of tbree allocation algorithms is proposed and analysed. As opposed to a number of allocation algorithms, whose performance is greatly dependent on the traffic profile, these techniques are dynamically adaptable to the change of the traffic load, combining the features of dynanric channel allocation and fixed channel allocation, migrating smoothly from one to another technique to give the rigid way according to a given traffic distribution and a given grade of service, and Dynanric Channel Allocation (DCA), in which an arbitrary proportion of the channels is assigned on a demand basis. The performance of these techniques is greatly dependent on the traffic distribution and, in general, DCA performs less satisfactorily than FCA for high load [5-8]. In fact, in DCA, the continuous change of the usage pattern easily leads to spatial inefficiency because of the channel locking, a technique used to keep the cochannel interference within acceptable limits by impeding the channels to be reused unless the required minimum reuse distance is satisfied. If this is not appropriately handled, as the traffic grows the number of locked channels also gruws and the DCA techniques are outperformed by the FCA one, where the channels are packed into reuse groups and the reuse distance is kept to a minimum. This paper proposes tbree channel allocation algorithms dynanrically adaptable to the change of the traffic load. They conveniently combine the features ofFCA and DCA, migrating smoothly from one to another technique to always give the best performance in any circumstances. best performance in any circumstimces. Although the pro2. posed strategies assign the channels in a fully dynanric fashTHE TECHNIQUES ion, this is carried out in a disciplined way so that channels are packed into reuse groups and the reuse distance is kept to a minimum, increasing the reuse efficiency.


INTRODUCTION
Efficient nse of radio resources has always represented a major concern in wireless communications due to the scarcity of the frequency spectrum.A substantial effort has been spent towarda investigating techniques that lead to a better system performance with a direct impact on capacity.Channel allocation is certainly one of such techniques.
A great many channel allocation algorithms have been proposed and extensively explored in the literature (e.g.[1][2][3][4]).Essentially, these algorithms can be grouped into Fixed Channel Allocation (FCA), in which the channels are assigned on a The aim of the techniques to be proposed here is to assign the channels dynanrically but on an orderly and compact basis such that the channel locking is minimised.Because of the disciplined usage of the dynanric channels, as the traffic grows, the system evolves gradually and smoothly to the fixed allocation pattern, combining, then, the benefits of DCA for low traffic and of FCA for high traffic.
Before proceeding to the description of the techniques we explore the temtinology to be used and the basic procedures to be assumed in a dynanric allocation.Define : -I ( v) as the set of the cells interfering with cell v -D( v) as.the set of cells with the minimum reuse distance with respect to cell v -A; as the set of cells where channel i has been assigned -va as the cell where a new call arises In order to maintain the cochannel interference within the specification limits, the minimum requirement for a channel i to be assigned to a call arising in cell Va is the fnlfilment of the basic condition va if.A; and I(va) n.A; Revista da Sociedade Brasileira de Telecomunicact6es Volume 13, numero 1, junho 1998 = 0, where 0 denotes the null set.The new call will be blocked if Va ~ A; or I(va) n A; # 0 Vi E N, where N is the set of channels within the system.The algorithm choosing the first channel satisfying this basic condition is the well-known First Available (FA) algorithm, the simplest form of DCA.Some of the allocation techniques proposed here include the FA as part of their overall decision procedure.It must be emphasised, however, that many other forms of DCA, as available in the literatnre, could be used, instead.
The next subsectioos describe 1) the procedure common to the three proposed techniques, 2) the proposed techniques, named <> Algorithm, /3 Algorithm, and 'Y Algorithm, and 3) the call reshuffle process.

Common Procedure
In a procedure common to all of the proposed algorithms, the sets Z;(va) = A;nD(va) ViE N are built and a channel is chosen that satisfies the condition max IZ;(va) I Vi E N, where the module representation IX I signifies the number of elements within the set X.The chosen channel is then assigned to a new call.
Note that Z; (va) gives the cocells of cell va using channel i i at the minimum reuse distance and that max IZ; ( va) I gives the channel with the highest usage in the nearest cocells at the time of the assignment procedure.

a-Algorithm
This algorithm follows the common procedure whenever Z;(va) # 0. However, when Z;(va) = 0 Vi E N and Bm(va) :0:: GOS, where Bm(va) is the mean blocking probability of va and GOS is the specified grade of service, a channel j is assigned that satisfies the basic condition va ~ A; and I(va) n A; = 0.In case Z;(va) = 0 Vi E Nand Bm(va) > GOS but Ak # 0 such a call will be blocked even if a channel n exists that satisfies Va ~ A,. and I(va) nAn= 0 .. In essence, in Jhis algorithm a new call is assigned the channel with the highest usage in the nearest cocells at the time of the assignment procedure.In case no channel is found that satisfies such a condition and the mean blocking probability of the cell satisfies the specified grade of service the first available channel is allotted.If the mean blocking probability exceeds the required grade of service, a channel is selected among those not being used.If this fails, the call is blocked.

,13-Aigorithm
This algorithm follows the common procedure whenever Z;(va) # 0. However, when Z;(va) = 0 Vi E N and L(va)/N :0:: (r-l)jr, where L(va) is the number of locked channels in Va and r is the chosen reuse pattern, a channel j is assigned that satisfies the basic condition va ~ A; and I(va) n A; = 0.In case Z;(va) = 0 Vi E Nand L(va)/N > (r-l)jr, a a channel k is assigned that satisfies the condition Ak = 0.If Z;(va) = 0 Vi E Nand L(va)/N > (r-l)jrbutAk # 0 such a call will be blocked 46 even if a channel n exists that satisfies the basic condition Va ~ A,. and I( va) nAn = 0.
The motivation to choose the ratio ( r -"!) / r as a decision point is that, when FCA is used with a given reuse pattern r say r = 7, i.e. 7 cells per cluster) ouly a proportion l jr (117, for r = 7) of all the channels can be used within the cell; the (r-1)/r (617, for r = 7)) remaining proportion represents that of the locked channels.
In essence, in this algorithm a new call is assigned the channel with the highest usage in the nearest cocells at the time of the assignment procedure.In case no channel is found that satisfies such a condition and the proportion of locked channels of the cell is less or equal than the corresponding proportion for the chosen reuse pattern the first available channel is allotted.If the proportion of locked channels of the cell exceeds that of the chosen reuse pattern, a channel is selected among those not being used.If this fails, the call is blocked.

1'-Aigorithm
This algorithm follows the common procedure whenever Z;(va) # 0. However, when Z;(va) = 0 ViE N, a channel j is assigned that satisfies the condition Aj = 0.The call will beblockedinva if Z;(va) = 0andA; # 0Vi,j EN, even if a channel k exist that satisfies va ~ Ak and I( va) n Ak = 0.
In essence, in this algorithm a new call is assigned the channel with the highest usage in the nearest cocells at the time of the assignment procedure.In case no channel is found that satisfies such a condition, then a channel is selected among those not being used.If this fails, the call is blocked.Therefore, this algorithm keeps a rigid control of the reuse distance which is coostantly maintained to its minimum

Call Reshuffle
At the end of each call a call reshuffle procedure takes place aiming at increasing the number of active cocells using the same channel at the minimum reuse distance.Suppose a call using channel j in cell Va has ended and assume that k is the channel satisfying the condition min IZ;(va)l Vi E N, where Z;(va) = A; n D(va)• Areshuffle from the call using channel k to the released channel j will take place if the number of cocells at the minimum reuse distance using channel j is bigger than that of cocells at the mirtimum reuse distance using channel k.

SYSTEM UNDER INVESTIGA-TION
The performance of the proposed techniques has been assessed in several cellular network configurations with distinct traffic distributions [9] In particular, the results to be shown here consider the traffic to be uniformly distributed over an "infinite" system of 49 cells displaced on a toroidal surface, as shown in Figure 1.The parameters used as decision criteria in the algorithms are GOS = 5% and r = 7, with clusters Ailton A. Shinoda and Michel D. Yacoub New Dynamic Channel Allocation Algorithms having 105 channels.Traffic is considered to be Poisson, hoiding time has a negative exponential distnbution with mean equal to 2 minutes, and subscribers are assumed to be fixed.A Monte Carlo simulation has been used to assess the performauce, given in terms of the system mean blocking probability.

RESULTS
Broadly speaking, among the three proposed algorithms, there are two distinct strategies, namely those carried out in the <> and in the j3 Algorithms and those carried out in the 7 Algorithm.The 7 Algorithm is included in the other two and it is accomplished in the "' Algorithm when the mean blocking probability of the cell exceeds that of the required grade of service (GO 8), chosen as a decision parameter.In the same way, it is accomplished in the j3 Algorithm when the proportion oflocked channels of the cell (a function of the reuse pattern) exceeds that of the specified value for the chosen 'reuse pattern.In fact the perrormance of the "' Algorithm will approach that of the 7 Algorithm as the GOB, chosen as a threshold, tends to 0%.The same reasoning applies to the j3 Algorithm with the allowed proportion oflocked channels.
These threshold points can be set as required and this is a useful mechanism that can be exercised to check the simulation programs.for low traffic and for high load.It is interesting to note that all of the three algorithms lead the system asymptotically to the FCA performance with the increasing traffic.In the limit as the traffic tends to infinity the performance of the proposed algorithms coincides with that of the FCA.In other words, although the proposed techniques assign the channels in a fully dynamic fashion, this is carried out in a disciplined way so that channels are packed into reuse groups and the reuse distance is kept to a minimum, as in FCA.
It can be seen that among the proposed techniques the 7 Algorithm gives the best performance, followed by the j3 Algorithm, and the a Algorithm in this order.For a 2% system mean blocking probability, for instance, the traffic gain with respect to FCA is 35%, 32%, and 16% for the respective algorithms.(Note that in such a case FA is already outperformed by FCA.)The traffic gain is noticeably higher than this in au unbalanced traffic system [9].It is clear, from these results, that a flexibility in assigning the channels must be allowed and, at the same time, a careful control of the channel locking condition is mandatory in order for the system to adapt itself to the variationofthe traffic load to give the best performance.
An interesting point to be mentioned is that the best strategy, performed by the 7 Algorithm, presents decision rules that are rather simple to implement and are completely independent of any threshold parameter.
Figure 2 shows the system mean blocking probability as a function of the traffic load per cell normalised with respect 5.
to 8 erl..Because some of the allocation algorithms proposed

CONCLUSIONS
here (namely "' and {3) include the FA technique as part of their overall decision procedure we also compare their performances with that of FA.As mentioned before, it must be emphasised, however, that many otherforms of DCA, as available in the literature, could be used, instead of FA. Figure 2 also shows the perrormance of FCA for comparison.Note that, as quoted previously, FA performs better than FCA for low traffic but it is outperformed by FCA with high load.And this behaviour is noticed in a number of DCA techniques [5][6][7][8].Note also that all of the three algorithms proposed here perform substantially ~tter than FCA and FA both A set of three dynamic channel allocation algorithms have been proposed and analysed.A Monte Carlo simulation study has been carried out having an "infinite" cellular network with uniform traffic distribution as the system under investigation.In general, these techniques maximise the number of cochannels already in use and minimise the number of channels in a locked condition.
As opposed to a number of allocation algorithms, whose performance is greatly dependent on the traffic, these techniques are dynamically adaptable to the change of the traffic load.They combine the features of dynamic channel alloca-lion and fixed channel allocation conveniently, and a smooth migration from one to another technique occurs so that the best performance is accomplished in any circumstances.Although the proposed techniques assign the channels in a fully dynamic fashion, this is carried out in a disciplined way so that channels are packed into reuse groups and the reuse distance is kept to a minimum, increasing the reuse efficiency.Therefore, the techniques reqnire, as an input parameter, among others, the target reuse pattern, which is chosen to fulfil the interference specifications.In theory, if in the course of the system operation a new reuse pattern is found that snits the network more adequately, the algorithm can then be updated with the new input, and the new reuse pattern shall be targeted.(In practice, things are certainly much more intricate.) The proposed algorithms are rather simple and have their decision rnles based on the number of active cochannels, the specified grade of service, and the allowed proportion of locked channels.It is noteworthy that the best strategy, performed by 'Y Algorithm, is independent of any threshold parameter and bases its decisions on the target reuse pattern.
These techniques have been simulated in several network configurations, with different traffic distributions, and it has been observed that the qualitative results shown here are also applicable to these systems.