# Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks

## Summary (2 min read)

### Introduction

- Thus, the signaling capacity of the signaling processors (in the base stations and the mobile switching centers) can limit the call handling capacity of a cellular system as the cell size is decreased.
- The scenario that the authors are concerned with is that there is a macrocellular network, with a given frequency allocation to each cell.
- This aspect is also included in their model by allowing calls to undergomobility change; i.e., a fast call can become a slow call and vice versa.
- In Section IV, the authors provide numerical results that show how accurate the analysis is in comparison with simulations of the model.

### A. Handovers, Repacking, and Signaling

- The authors define a handoff (or handover) as any event that causes the system to seek a new channel for an existing call in the system.
- If this attempt fails, the call is not retained in the microlayer, but is dropped.
- Handovers are also caused by the repacking of slow calls occupying macrolayer channels; i.e., slow calls that are assigned channels in the macrolayer are moved back to the microlayer on availability of channels in their respective microcells.
- This increases the capacity of the system, but additional signaling will be incurred due to the channel reassignments.
- The set of events that contribute to the signaling traffic are new call arrivals, cell boundary crossings, mobility changes, and repacking.

### B. Model Parameters and Notation

- New call arrival processes for the various macrocells are independent Poisson processes.
- Furthermore, the intervals at which a mobile changes its mobility are also assumed to be exponentially distributed.
- The microcells in the th macrocell are numbered using double indexes .
- Probability that a call leaving macrocell enters macrocell ; probability that a call leaving microcell enters microcell, also known as The authors further define.
- The authors analyze the models to obtain thenew call blocking probabilityfor each call class (i.e., slow or fast); i.e., the probability that a new call of that class is blocked on arrival to the system.

### A. The Approximate Analysis Approach

- The authors define the following stochastic processes for .
- Hence, the authors have a finite state space for this process.
- In principle, the stationary blocking and dropping probabilities can be obtained from this stationary distribution.
- The authors resort to an approximate analysis technique similar to the one adopted by several previous researchers in this area (for example, [8] and [16]).
- The process in the cell, i.e., , is analyzed in isolation, assuming that the arrival process of handoffs from the neighboring cells is Poisson.

### B. Additional Notation for the Analysis of an Isolated Cell in the Homogeneous Model

- For the homogeneous model, in the stationary regime, the authors drop the superscript from the various notations.
- Define arrival rate of new fast calls in a macrocell; these are serviced in the macrolayer (thus, ); arrival rate of handed-off fast calls in the macrolayer; arrival rate of fast calls in the macrolayer due to mobility change of slow calls in the microlayer; and total arrival rate of fast calls in the macrolayer.
- The dependence of these rates on the various random variables defined in Section III-A is shown in Section III-B1.
- A handed-off call can enter any one of itsneighbors with equal probability.
- These arrivals occur from all theneighbors of a cell.

### C. Analysis of the Isolated Cell Model Without Repacking

- The isolated cell model comprises groups of servers each, corresponding to the microcells, and one group of servers corresponding to the macrolayer channels.
- The authors approximate this dependence by using the stationary probabilities obtained for and hence model as a Markov chain with state space .
- A fast call becomes a slow call and is retained in the macrolayer if all the channels in its corresponding microcell in the microlayer are occupied.
- There are two nodes, 1 and 2; node 1 represents the arrival process and node 2 the service process.
- With these new rates, the next iteration is performed.

### A. System Parameters for the Numerical Results

- The number of channels allocated to each cell is 80; with a reuse factor of three between the cells, this would mean that there are 240 channels available in the system.
- A reuse factor of four is assumed in the microlayer; hence, the set of channels allocated to the microlayer is partitioned into four sets.
- When a macrocell is divided into microcells, the area of the microcell is times the area of the macrocell.
- Assuming that fast mobiles are five times as fast as the slow mobiles, the sojourn rates of the fast and slow calls (in macrocells and microcells, respectively) are related by .
- Note that repacking of slow calls will always help to reduce the blocking probability of fast calls, but may increase or decrease the blocking probability of slow calls.

### C. Analysis and Simulation Results for the Multicell Model

- A multiple macrocell system is analyzed using their iterative a alysis and using a multicell simulation; graphs between the Erlang load and the blocking probability are plotted for the parameter values , and .
- Figs. 6–9 show the results without slow call repacking.
- K. Maheshwari, “Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks,” Master’s thesis, Indian Instit.
- Since 1988, he has been with the Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, where he is now a Professor.

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...A service request rejected by its first-choice network can just leave the system or further try to access the other network [1]....

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..., [13] and [16], provide the simulation results to verify the analytical results....

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...In particular, the overflowed traffic is approximated as Poisson traffic in [12] and [13], as interrupted Poisson process (IPP) traffic in [14] and [27], and as Markov Modulated Poisson Process (MMPP) traffic in [15], [16], and [23]....

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...For a slow mobile, its dwell times in microcell and macrocell, tsm and tsM , are different random variables and have the negative exponential distribution with the mean 1= sm and 1= sM , respectively....

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...1045-9219/03/$17.00 ß 2003 IEEE Published by the IEEE Computer Society free channel, even though its overlaid microcell has many free channels, the fast calls will terminate....

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##### References

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### "Performance analysis of microcelliz..." refers background in this paper

...Hence, the stationary distribution has the following product form (see [12])....

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1,654 citations

### "Performance analysis of microcelliz..." refers methods in this paper

...Consequently, we resort to an approximate analysis technique similar to the one adopted by several previous researchers in this area (for example, [ 8 ] and [16])....

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...Our approximate analysis approach is an extension of the iterative technique that has been used in the past for macrocellular networks (see, for example, [5], [ 8 ], [9], and [16])....

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### "Performance analysis of microcelliz..." refers background in this paper

...It is clear that the process has a product form stationary distribution since we have a multiclass resource sharing model with a coordinate convex partial sharingpolicy (see [11])....

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### "Performance analysis of microcelliz..." refers methods in this paper

...Our approximate analysis approach is an extension of the iterative technique that has been used in the past for macrocellular networks (see, for example, [5], [8], [9], and [16])....

[...]

...Consequently, we resort to an approximate analysis technique similar to the one adopted by several previous researchers in this area (for example, [8] and [16])....

[...]

494 citations