01 Lab Trunking

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Wireless Networks (teacher: G. Gelli, a.y. 2008/09) 1

Matlab laboratory # 1

Trunking in cellular systems

Introduction

For this lab you will need:

(a) to review Lecture 9, with particular attention to the part regarding trunking and Erlang B

model (BCC);

(b) to review your Matlab skills;

(c) to download from the course website some Matlab functions for performing calculationswith Erlang B and Erlang C models.

Please try to work cleanly, by writing one Matlab M-function for each exercise.

Exercises

(1) In a cellular network, the available channels (100 channels per cell) are equally dividedbetween two operators.

(a) Compute the number of users served in each cell by each operator if every user generates

0.1 Erlangs of traffic.

(b) Compare with the situation where one monopolistic operator uses all the 100 channels.

(Assume a BCC model and GOS = 5% in your calculations).

(2) For a N = 7 system with P(blocking) = 1% and an average call length of 2 minutes, findthe loss in trunking efficiency when going from omni-directional antennas to 60o sectoredantennas.

(Assume a BCC model and that the average number of calls made by each user is 1 per hour).

(3) A cellular operator decides to use a digital TDMA scheme which can tolerate a C/I ratio of

15 dB in the worst case. Find the optimal value ofN (cluster size) for:

(a) Omni-directional antennas

(b) 120o sectoring

(c) 60o sectoring

Should sectoring be used? If so, which case (60o or 120o) should be used?(Perform your analysis for a path loss exponent of = 3 and = 4 and consider trunkingefficiency, assuming GOS = 1%).


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(4) A cellular system can support a given traffic A with C = 100 channels per cell and GOS= 2%. Verify what happens to GOS if the traffic increases in some periods of the year by afactor 2, 5, or 10. How many channels would be needed to keep the GOS unchanged in thesesituations?

(5) This exercise explores some issues in non-uniform fixed channel allocation (FCA).

Consider a cellular system with cluster size N and Nc channels available in each cluster. Foreach cell of the cluster, let the triple (Ai, Ci, GOSi) represent the cell traffic Ai, the numberof channels Ci of the cell, and the grade of service GOSi (blocking probability) of the cell(i = 1, 2, . . . , N ). In the BCC model, these quantities are related by the Erlang B formula:

GOSi = f(Ai, Ci) =

ACiiCi!

Ci

k=0

Aki

k!

Note that

N

i=1

Ci Nc (where the equality holds when all the channels are used).

In uniform FCA, each cell is assigned the same number of channels, i.e., Ci = C = Nc/N(note that floor rounding is needed since C must be an integer number). This is clearlyoptimal ifAi = Aj , i = j (uniform traffic).

In non-uniform FCA, instead, each cell is assigned a different number of channels, i.e., more

channels are assigned to cells with higher traffic.

The problem considered here is how to allocate the channels to different cells according to

some performance measure. Since the GOS is not necessarily the same in all cells, we can

define an overall GOS at least in two different ways:

(a) Average GOS: a weighted sums of the GOSs

GOS =N

i=1

wi GOSi , wi =AiNi=1 Ai

where the coefficients wi weight the GOS in each cell according to relative traffic inten-sity.

(b) Worst-case GOS: the maximum value among all the GOSs

GOS = maxi=1,2,...,N

GOSi

For a given distribution of traffic (A1, A2, . . . , AN) among the cells, the optimal channelassignment can be found as the solution of the following optimization problem:

minC1,C2,...,CN

GOS subject to

N

i=1

Ci Nc


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This is a constrained nonlinear optimization problem, where moreover the optimization vari-

ables belong to a discrete set. Note that solving the problem by a brute-force approach is not

advisable (the number of configurations of channels to be tested increases exponentially with

N). However, the case N = 2 can be dealt with rather simple math (although the solutioncannot be written in closed-form, mainly due to the fact that the Erlang B formula cannot be

easily inverted).

Provide a simple mathematical formulation for N = 2, and try to solve it with the help ofMatlab, by using the two previous definitions of GOS (average GOS or worst-case GOS).

Compare the obtained solutions for different non-uniform traffic distributions between the

two cells, and compare them with the uniform assignment (you might assume Nc = 120channels and an overall traffic in the two cells equal to Atot = A1 + A2 = 100 Erlangs, butfeel free to experiment with other values, provided that the GOS of the system is reasonably

below 5%).

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01 Lab Trunking