**4.1 Dynamic reservation versus static reservation**

There are several reasons for designing multi-tier cellular networks. One is to provide services for mobile terminals with different mobility and traffic patterns. The required performance measures can be met if the traffic and mobility patterns can be classified into more homogeneous parts and treated separately. Consider a system where there are two mobility classes. If the cell radii are optimized for low-mobility terminals, then the high-mobility terminals will have to make a lot of handovers during a communication session. On the other hand, if the optimization is made regarding the handover performance of high-mobility terminals, then the traffic load in each cell may exceed acceptable limits.

In multi-tier cellular networks, different layers offer the designer the opportunity of class based optimization. In case of a two-tier network we consider three or seven micro-cells overlaid by one large macro-cell offered calls from two mobility classes (Fig. 8). High-mobility 10 Will-be-set-by-IN-TECH

In queuing priority schemes, new calls and handover calls are all accepted whenever there are idle channels for that type of calls. When no idle channels are accessible, calls may be queued or blocked (i.e cleared from the system). Queueing priority schemes can be divided into three groups: new call queuing schemes (Chang et al., 1999), handover call queuing schemes (Yoon & Kwan, 1993); (Tian & Ji, 2001); (Agrawal et al., 1996), and all calls queuing schemes (Yoon &

Computational analysis has shown that waiting positions do not change the advantage of dynamic reservation strategy. Fig. 7 displays two pairs of curves: one pair is the same as in Fig. 6, the second one relates to a case with three waiting positions. Of course, the revenue is

Fig. 7. Waiting positions do not change the advantage of dynamic reservation strategy. One pair of curves is the same as in Figure 6, the other pair relates to the case with three waiting

There are several reasons for designing multi-tier cellular networks. One is to provide services for mobile terminals with different mobility and traffic patterns. The required performance measures can be met if the traffic and mobility patterns can be classified into more homogeneous parts and treated separately. Consider a system where there are two mobility classes. If the cell radii are optimized for low-mobility terminals, then the high-mobility terminals will have to make a lot of handovers during a communication session. On the other hand, if the optimization is made regarding the handover performance of high-mobility terminals, then the traffic load in each cell may exceed acceptable limits.

In multi-tier cellular networks, different layers offer the designer the opportunity of class based optimization. In case of a two-tier network we consider three or seven micro-cells overlaid by one large macro-cell offered calls from two mobility classes (Fig. 8). High-mobility

growing, but the preference of dynamic reservation keeps the place.

**3.3 On queueing effect**

positions.

**4. Two-tier network**

**4.1 Dynamic reservation versus static reservation**

Kwan, 1993); (Chang et al., 1999).

Fig. 8. A macro-cell covering (a) three and (b) seven micro-cells.

calls of intensity *A* are served by macro-cell only. Low-mobility calls of intensity *B* are served by the micro-cells as first choice and, if the reservation strategy admits it, by the macro-cell as second choice. Arriving calls are served as follows. The mobility class of the call is identified. High-mobility calls of intensity *A* are served by macro-cell only. Low-mobility calls of intensity *B* are served by the appropriate micro-cell as first choice, and if reservation strategy allows it by macro-cell as second choice. In both cases, our optimization criteria is the same: to maximize the revenue when each served A-call costs *K* units and each served B-call costs one unit (*K >* 1). When calls reach the macro-cell level, they are no longer

Fig. 9. A two-tier cellular network call flow model.

differentiated according to their mobility classes. Therefore, the calls of the high mobility class terminals and the overflowed handover calls from micro-cells are treated identically. New calls from micro-cells may not use the guard (reserved) channels upon their arrival. If no non-guard channel is available, then new calls are blocked. High mobility calls are blocked if all macro-cell channels are busy. Fig. 9 shows schematically how calls are served and what order is followed when serving them. As above in the case of single-tier network we compare two reservation strategies:

a) Dynamic reservation: The cutoff priority scheme is to reserve a number of channel for high-mobility calls in the macro-cell. Whenever a channel is released, it is returned to the common pool of channels.

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New calls Low Mobility

to 0.025%.

Micro-cells

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Overflow

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New calls High Mobility

Fig. 11. An illustration of channel rearrangement.

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New calls Low Mobility

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Overflow

Call Admission Control in Cellular Networks 123

Fig. 12. Dependence of revenue on channel rearrangement from macro-cell to micro-cell.

of arrangement could be implemented by modern DSP techniques.

channels in the second tier. In Fig. 13.b some kind of a homogeneous single tier network is depicted: each call has access to 9 channels equally distributed between streams. Such kind

Fig. 14 depicts the loss probability curves for these two schemes. Case (a) relates to pure loss system, case (b) relates to scheme with one waiting positions per stream. What is surprising? In case (a), beginning with a loss probability as low as 0.56% (less than 1%), it is advantageous to use the equally distributed scheme. Therefore, the traditional two-tier network could be recommended here at a very low call rates. Table 1 contains more detailed data on loss probability. When a single waiting position is added, the advantage of the equally distributed scheme increases even more and the cross point of curves occurs at the loss probability equal

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Take-Back

N<sup>1</sup> N<sup>2</sup>

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L<sup>1</sup> L<sup>2</sup> L<sup>3</sup>

... ...... ...

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N

........................................................................................................... .... ... .... ... ...... ... .......................... ........................................................................................................................................................................................................................................................

New calls High Mobility

...................... .. ..... ...... ... ... .....

...................... .. .. ... .. ...... ... ....

Macro-cell

b) Static reservation: Divide all macro-cell channels allocated to a cell into two groups: one for the common use by all calls and the other for high-mobility calls only (the rigid division-based CAC scheme).

Fig. 10. Dependence of the revenue on the reserved number of channels for two-tier networks: (a) Three micro-cells and one macro-cell, (b) Seven micro-cells and one macro-cell.

Numerical results for two two-tier network examples are obtained. They are not qualitatively different from the results of the one-tier model discussed above. Fig. 10.a (three micro-cells and one macro-cell) and Fig. 10.b (seven micro-cells and one macro-cell) show that the dynamic reservation strategy gives the higher maximum revenue in both cases if the reserved number of channels *R* is properly chosen. The parameters are as follows: *A* = high-mobility call flow, *B* = low-mobility call flow, *N*<sup>1</sup> = number of micro-cell channels for each cell, *N*<sup>2</sup> = number of micro-cell channels.

**Conclusion:** In case of two-tier network, the results of numerical analysis confirm that the optimal strategy is dynamic reservation.
