1. Adv. Wireless Comm. Systems - Cellular Networks -
Objectives
Understand basic mathematical techniques to evaluate
radio resource allocation problems
Understand the principles of Fixed and Dynamic Channel
allocations
Outline
Fundamental mathematical tools
Fixed Channel Allocation for non-uniform traffic
Dynamic Channel Allocation for non-uniform
Lecture 4&5: Chan. alloc. for non-uniform traffic
Adv. Wireless Comm. Systems Cellular Networks -

2. Channel Allocation for Non-Uniform Traffic
Traffic Model & Channel Utilization
Generally, offered calls are not uniform across cells
Thus, the capacity is no longer a good measure
A measure for non-uniform traffic is Channel Utilization, U
(4.1)
- no. of busy channels at time t
The channel utilization in cell i, , is a function of
The offered calls process to the cell, and their duration there
The no. of channels allocated to that cell
Lecture 4&5: Chan. alloc. for non-uniform traffic
Adv. Wireless Comm. Systems Cellular Networks -

3. Channel Allocation for Non-Uniform Traffic
The M/M/c/c Loss System
- No. of channels
- Call arrival rate
Call arrivals
- Call completion rate
- Offered load (in Erlang units)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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4. Channel Allocation for Non-Uniform Traffic
The M/M/c/c Loss System (cont.)
Markov chain transition rates: c
The stationary (equilibrium)
Probabilities are
obtained by solving the
local balance equations: c j
In our case:
(4.2)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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5. Channel Allocation for Non-Uniform Traffic
Erlang–B Formula
For a Loss System with a Poisson arrival process and general
i.i.d holding times, a call is blocked with probability c
Truncated Poisson
Distribution
(4.3)
(4.4)
- System utilization (in Erlangs)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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6. Channel Allocation for Non-Uniform Traffic
Utilization and Blocking Prob. vs. Offered Load c
We need to
tradeoff between
utilization and
blocking prob. - e
- utilization (in Erlangs) 1
- blocking prob.
offered load (in Erlangs)
Rule 4.1: Given c, take the largest s.t.
Rule 4.2: Given take the smallest c s.t.
Lecture 4&5: Chan. alloc. for non-uniform traffic
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7. Channel Allocation for Non-Uniform Traffic
Computation With a Large Number of Channels
Definition: and are asymptotic equivalent
( denoted by ), if
Lecture 4&5: Chan. alloc. for non-uniform traffic
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8. Channel Allocation for Non-Uniform Traffic
Computation With a Large Number of Channels
Computing for large c & is numerically unstable
We can use its asymptotic equivalent expression:
(4.5)
- the density function of a standard Normal distribution
- the cdf of a standard Normal distribution
Lecture 4&5: Chan. alloc. for non-uniform traffic
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9. Channel Allocation for Non-Uniform Traffic
Large Scale Benefit
Increasing c while keeping fixed, yields: if
(4.6) if
Thus, scaling up the number of channels improves the
utilization w/o exceeding the blocking prob. Threshold
Conclusion: Sharing channels among cells (consolidation)
is better than splitting them (separation)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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10. Channel Allocation for Non-Uniform Traffic
Fixed Channel Allocation (FCA)
For uniform traffic we know that channels per
cell is best
Question: How do we allocate channels using an FCA
algorithm when traffic is non-uniform?
Step 1: Given the offered load to cell i
- the maximum blocking prob. in cell i
Calculate , the no. of channels required by
cell i, , by using rule 4.2.
Lecture 4&5: Chan. alloc. for non-uniform traffic
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11. Channel Allocation for Non-Uniform Traffic
Fixed Channel Allocation (FCA)
Note: For any practical system there are always some
fixed amount of channels that are solely
reserved for users in cell i.
That is – they are not shared by other cells.
Lecture 4&5: Chan. alloc. for non-uniform traffic
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12. Channel Allocation for Non-Uniform Traffic
Fixed Channel Allocation (FCA)
Step 2: Determine where the same channels can be reused
How do we do that for a general cell layout ?
We construct the Reuse Constraints Graph
Given a cell layout, define an undirected graph, where
each cell is represent by vertex of a graph
each vertex pair is connected iff the same channel
can’t be used both cells at the same time
Lecture 4&5: Chan. alloc. for non-uniform traffic
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13. Channel Allocation for Non-Uniform Traffic
Reuse Constraints Examples
Example 4.1:
Cells in tandem
Cell:
The graph for reuse distance = 1
Vertices:
The graph for reuse distance = 2
Vertices:
Lecture 4&5: Chan. alloc. for non-uniform traffic
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14. Channel Allocation for Non-Uniform Traffic
Reuse Constraints Examples (cont.) 1
Example 4.2: Hexagonal cells
in a single cluster 6 2 5 3 4 1 6
The graph for reuse distance = 1 5 2 4 3
Lecture 4&5: Chan. alloc. for non-uniform traffic
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15. Channel Allocation for Non-Uniform Traffic
Reuse Constraints Examples (cont.)
Example 4.3: Hexagonal cells in a 7 cluster
layout – with reuse distance = 2
reuse distance = 1
Part of the edges …
reuse distance = 2
Node degree =
Lecture 4&5: Chan. alloc. for non-uniform traffic
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16. Channel Allocation for Non-Uniform Traffic
Finding The Minimum Bandwidth FCA
The Optimal FCA Problem:
Given a layout of n cells and their required no. of
channels ,
What is the minimum total no. of channels, S, needed
with Fixed Channel Assignment (FCA) ?
The 1st algorithm we present is based on maximal cliques
In many cases it finds the optimum – but not always!
Lecture 4&5: Chan. alloc. for non-uniform traffic
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17. Channel Allocation for Non-Uniform Traffic
Maximal Cliques
Definitions:
A graph is complete if every pair of vertices is connected.
A clique of a graph is a complete subgraph.
A clique is maximal if it has the largest number vertices.
For an algorithm see, e.g:
D.R. Wood, “An algorithm for finding a maximal clique in a graph”,
Operation Research Letters, Vol. 21, pp , 1997.
Lecture 4&5: Chan. alloc. for non-uniform traffic
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18. Channel Allocation for Non-Uniform Traffic
Clique Examples
This graph
This graph
has 4 maximal cliques
has 3 maximal cliques
Lecture 4&5: Chan. alloc. for non-uniform traffic
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19. Channel Allocation for Non-Uniform Traffic
Clique Examples (cont.) 1 6
This graph 5 2
has 6 maximal cliques 4 3 1 3 5 2 4 6 2 4 6 3 5 1
Lecture 4&5: Chan. alloc. for non-uniform traffic
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20. Channel Allocation for Non-Uniform Traffic
Clique Examples (cont.)
Hexagonal cells in a 7
cluster layout
with reuse distance = 2 x x x x x x x
Each collection of 7 cells marked
With x form a maximal click x x x x x x x
Lecture 4&5: Chan. alloc. for non-uniform traffic
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21. Channel Allocation for Non-Uniform Traffic
Finding Small S for FCA using Maximal Cliques
For every maximal clique K, S must satisfy:
(4.7)
Reuse Constraints
Example 4.4: Hexagonal cells
with one cluster and
reuse distance 1
Lecture 4&5: Chan. alloc. for non-uniform traffic
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22. Channel Allocation for Non-Uniform Traffic
Finding Small S for FCA using Max Cliques (cont.)
Algorithm 4.1: Clique-Based, Cell-Independent,
Traffic-Dependent FCA (CB-CI-TD FCA)
Take Step 1 above to calculate the required ,
Take Step 2 above to form the Reuse Constraints
Set S to (NP-Hard)
For cells 1 to n, subsequently allocate channels by reusing channels that don’t violate the Reuse Constraints
4.1 If for some cell, the S channels are not sufficient, increase S by the missing amount
Lecture 4&5: Chan. alloc. for non-uniform traffic
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23. Channel Allocation for Non-Uniform Traffic
Finding Small S for FCA using Max Cliques (cont.)
Q: Why do we need step 4.1 of the CB-CI-TD FCA algorithm?
A: There are for which ,S - the total req. no.
A counter-example
(1)
(1)
(1)
But we need = 3 channels
(1)
(1)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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24. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring
For the case of , the (proper) coloring of the Reuse
Constraint Graph yields the minimum S, namely,
S = C x (Chromatic_number)
For C=1, it is clear. Assume it holds for C-1
For C, each vertex cannot use neither its previous
local colors (channels), nor its neighbors colors
Thus, new Chromatic_number of channels are needed
Lecture 4&5: Chan. alloc. for non-uniform traffic
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25. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
Example 4.5: 3-tier hexagonal cells with reuse distance = 1
Reuse Constraint Graph
Cell layout
Chromatic no. = 3
For C=1 we use 3 channels
None of these can be reused for C=2
Given a new color in we must have 2 additional colors
3xC is the no. of colors for any n-tier hexagonal cells with reuse dist. = 1
Lecture 4&5: Chan. alloc. for non-uniform traffic
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26. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
Example 4.6: n-tier hexagonal cells with reuse distance = 2
Reuse Constraint Graph
Cell layout
Chromatic no. = 7
For this reuse constraint graph
Chromatic no. = Max Clique size
Lecture 4&5: Chan. alloc. for non-uniform traffic
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27. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
How do we handle the case with non-uniform ?
Does do the job ?
For this case it does !
Indeed,
7 and 10 are a MUST
6 cannot be taken from the 7 and 10
(6)
(10)
(7)
(10)
(4)
S= = 23
(10)
(2)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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28. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
For this case however, it over shoots !
Indeed,
3 and 5 are a MUST
For node y, 2 can be reused
from node x that is far enough
Giving a total of =15
(7)
(3)
5+3+9 = 17
(3)
(5)
7+2 =
(9)
Node x
Node y
(3)
(3)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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29. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
The answer is by using the weighted coloring algorithm
Each vertex of the Reuse Constraints Graph is assigned
the weight
The weighted coloring problem (also called set coloring) is
to color with minimum colors each vertex i with distinct
colors so that adjacent vertices also receives distinct colors
Can be represented as a (proper) graph coloring
Replace vertex i with a fully connected graph with nodes
Connect each new node to the previous connected nodes
Lecture 4&5: Chan. alloc. for non-uniform traffic
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30. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
How about setting S to:
= Max Clique number
This may give us a too small number, since there are cases
where,
Chromatic number > Max Clique number
Example:
Chromatic # = 3
Max Clique # = 2
Lecture 4&5: Chan. alloc. for non-uniform traffic
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31. Channel Allocation for Non-Uniform Traffic
THE Min S for FCA using Weighted Coloring (cont.)
Algorithms for weighted coloring problem
C. McDiarmid and B. Reed, “Channel Assignment and Weighted Coloring”,
Networks, Vol. 36, No. 2, pp , 2000
A polynomial time algorithm that colors the graph with 4/3 times the
minimum number
M. Caramia and P. Dell’Olmo, “Solving the Minimum Weighted Coloring
Problem”, Technical Report, University of Rome, Italy.
A branch and bound algorithm capable of solving 90 vertices
Lecture 4&5: Chan. alloc. for non-uniform traffic
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32. Channel Allocation for Non-Uniform Traffic
Finding The Min S for FCA using Weighted Coloring
Algorithm 4.2: Weighted-Coloring-Based, Cell- Indep.,
Traffic-Dependent FCA (WCB-CI-TD FCA)
Take Step 1 above to calculate the required ,
Take Step 2 above to form the Reuse Constraints
Use a polynomial heuristic or an optimal algorithm (NP-Hard) to find the color sets (channels) for each cell i
For cells 1 to n, allocate the channels found by the algorithm
Lecture 4&5: Chan. alloc. for non-uniform traffic
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33. Channel Allocation for Non-Uniform Traffic
The Benefit of Detailed Traffic-Dependent FCA
Example 4.7: 5-tier hexagonal cells with reuse distance = 2
Question: By how much can we increase the network utilization
with frequency allocation based on the detailed
loads , , rather than based on the
average load ?
Network Data
49 cells in 5-tier hexagonal layout
Reuse distance = 2
Total offered load = 490 Erlangs
Blocking prob. = 0.05
4/7 of the cells have
3/7 of the cells have
Lecture 4&5: Chan. alloc. for non-uniform traffic
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34. Channel Allocation for Non-Uniform Traffic
The Benefit of Detailed Traffic-Dependent FCA
Solution 1: The Uniform Traffic
Suppose we use FCA based only on the average load
The no. of channels required per each cell is resolved from
C=15
The reuse constraints graph with C=1 is colored with 7
colors. Thus, a total of 7x15 = 105 channels is required
The average utilization per cell is then
Lecture 4&5: Chan. alloc. for non-uniform traffic
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35. Channel Allocation for Non-Uniform Traffic
The Benefit of Detailed Traffic-Dependent FCA
Solution 1: The Uniform Traffic - Summary
Cell Utilization
Frequency Allocation 15 15 15 15 15 x 15 15
Lecture 4&5: Chan. alloc. for non-uniform traffic
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36. Channel Allocation for Non-Uniform Traffic
The Benefit of Detailed Traffic-Dependent FCA
Solution 2: The Non-uniform Traffic Solution
Suppose we use FCA based only on the detailed loads
and
The no. of channels required for a cell with
C=22
The no. of channels required for a cell with
C=9
Lecture 4&5: Chan. alloc. for non-uniform traffic
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37. Channel Allocation for Non-Uniform Traffic
The Benefit of Detailed Traffic-Dependent FCA
Solution 2: The Non-uniform Traffic Solution (cont.)
The reuse constraints graph with the following mixture of
9 and 22 channel requirements is colored with
(4x9)+(3x22) = 102 colors (channels)
The cell utilization is then 22 9 9 9 22 x 22 9
Lecture 4&5: Chan. alloc. for non-uniform traffic
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38. Channel Allocation for Non-Uniform Traffic
The Benefit of Detailed Traffic-Dependent FCA
Solution 1 Vs. Solution 2
Solution 1
Solution 2
No. of Channels
105
102
Avg. Cell Util.
8.328
9.589
Conclusion
Detailed traffic-dependent FCA improves the system
utilization by more than 15% with 3 less channels
Lecture 4&5: Chan. alloc. for non-uniform traffic
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39. Channel Allocation for Non-Uniform Traffic
How To Best Use The Extra Channels ?
Suppose we want to maximize the utilization
The Erlang-B, as function C for any given
If is the same – we gain more for
lower C
If C is the same - we gain more for
lower 1
- blocking prob. c
no. of channels 1
- blocking prob.
offered load (in Erlangs)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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40. Channel Allocation for Non-Uniform Traffic
How To Best Use The Extra Channels ?
To maximize utilization
Gradually allocate each additional channel to a cell with
the largest marginal gain
To “equalize” blocking probabilities
Gradually allocate each additional channel to cell with the
largest blocking probability
A systematic methodology to allocate available channels is
presented below
Lecture 4&5: Chan. alloc. for non-uniform traffic
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41. Channel Allocation for Non-Uniform Traffic
Cell Occupancy with FCA
Suppose channels are allocated to cell i and the reuse
constraints in (4.7) are not violated.
If the mobiles stay put in their cells, the blocking prob. In
each is cell i is ,
By cell independence, the stationary pdf of the cell
occupancy vector is:
Q: Find K
(4.8)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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42. Channel Allocation for Non-Uniform Traffic
FCA: Further Considerations – Limited Channels
Usually, an operator is given a spectrum span (bandwidth)
that determines the no. of available channels, S, to allocate
On the other hand, traffic requirements and operator goal for
blocking prob. determine the ,
Thus, for a given reuse constraints we may not get a
feasible coloring with S colors
Two resolution paths:
Increase blocking prob. (less revenue for the operator)
Relax the reuse constraints (lower quality service )
Lecture 4&5: Chan. alloc. for non-uniform traffic
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43. Channel Allocation for Non-Uniform Traffic
FCA: Further Considerations – Adjacent Channel Interference
Reuse constraints reflect only co-channel interference
A lesser degree of interference to frequency f occurs by
adjacent channels using a near frequency g
typically: low |f - g| high interference
Clearly, adj. chan. interfer. Corresponds only the edges of
the reuse constraints graph
Lecture 4&5: Chan. alloc. for non-uniform traffic
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44. Channel Allocation for Non-Uniform Traffic
FCA: Further Considerations – Adjacent Channel Interference
Example
The values denote the minimum frequency
band separation distance with respect to
Intra-cell channels are separated by 4
Cells at 1-tier away - by 2
Cells at > 1-tier away - by 0
Leads into a new set of constraints
For any edge (v,w) in the reuse constr. 2 2 2 4 2 2 2
= the set of forbidden distances
Lecture 4&5: Chan. alloc. for non-uniform traffic
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45. Channel Allocation for Non-Uniform Traffic
FCA: Further Considerations – Adjacent Channel Interference
Up & down links used in the same cell may interfere
Thus, must be further separated
Assigned in two different bands sufficiently separated by up
down
Channels used to handle handover must also be separated
In GSM, BCCH (broadcast channel) are used by two BTS to
transmit to a mobile during its handover process
Thus, BCCH channels in adjacent cells should be separated too
Lecture 4&5: Chan. alloc. for non-uniform traffic
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46. Channel Allocation for Non-Uniform Traffic
FCA: Further Considerations – Adjacent Channel Interference
The T - Weighted Graph Coloring Problem
If two channels f and g, interfer or not depending on |f - g|
It lends itself into the T- weighted coloring problem
See the paper: F. S. Roberts, T-Colorings of graphs: Recent results and open problems, Discrete Mathematics 93 (1991), pp
Lecture 4&5: Chan. alloc. for non-uniform traffic
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47. Channel Allocation for Non-Uniform Traffic
FCA: Further Considerations – Restricted Channels
European countries and competing operators within a
country, often use the same system, e.g., GSM
A further restriction exist on their boundary cells:
They must be separated administratively
Further restrictions may be imposed by the army & military
Leads into a new set of constraints:
For any vertex (cell) v
= the set of feasible channels for cell v
Lecture 4&5: Chan. alloc. for non-uniform traffic
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48. Channel Allocation for Non-Uniform Traffic
FCA – An Integer Linear Program Solution (ILP)
Taking into account the following considerations of:
Pre-assigned channels
Intra and inter cell - channel separation distance
Cell-dependent list of feasible channels
Non-dichotomy of Interference
Leads into a penalty function approach:
For every edge (v,w) in the reuse constraints graph and a pair of
allocation frequencies and , we penalize the choice by
that depends on the interference level
Bang-bang type penalty: if > ; 0 otherwise
Lecture 4&5: Chan. alloc. for non-uniform traffic
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49. Channel Allocation for Non-Uniform Traffic
FCA – An Integer Linear Program Solution (ILP)
Determining the penalty function
User are mobiles not practical to use FCA for uplinks
Downlinks are allocated first, then symmetric alloc. from the
downlink band is used for the downlinks with a constant separation
The penalty function is taken as a function of the
SIRs (one/several locations & theoretical/measured) v w g f f g
SIR
BTS
BTS
SIR
Lecture 4&5: Chan. alloc. for non-uniform traffic
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50. Channel Allocation for Non-Uniform Traffic
Maximum Service FCA using ILP
- 1 if channel f is assigned to cell v; 0 otherwise
- the no. of channels assigned to cell v
- the no. of channels required by cell v
Lecture 4&5: Chan. alloc. for non-uniform traffic
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51. Channel Allocation for Non-Uniform Traffic
Maximum Service FCA using ILP
To avoid “unfair” allocation by the ILP, we may add the
constraints
Alternatively, we may replace the linear objective function
by the convex function (and minimize)
- the offered load weight of cell v
Lecture 4&5: Chan. alloc. for non-uniform traffic
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52. Channel Allocation for Non-Uniform Traffic
Other FCA Optimization programs
See the survey paper:
K. I. Aardal, S. P.M. Van Hoesel, A. M.C.A. Koster,C. Mannino and A. Sassano, Models and Solution Techniques for Frequency Assignment Problems, ZIB-Report 01–40 (December 2001), Konrad-Zuse-Zentrum fur Informationstechnik, Berlin.
Lecture 4&5: Chan. alloc. for non-uniform traffic
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53. Channel Allocation for Non-Uniform Traffic
Dynamic Channel Allocation (DCA)
The next question we address is: How much can be
gained by DCA compared with FCA?
With FCA, channels are not shared among the cells
With DCA, a cell can borrow channels from other cells
An architecture that supports handover can support DCA
Channels are shared within a Base Station Controller (BSC) domain
BSC
BTS
BTS
Telephone
Network
MSC
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54. Channel Allocation for Non-Uniform Traffic
Dynamic Channel Allocation (DCA)
The following “idealized” Maximum Packing (MP) DCA alg.
is the most one may hope for
Based on the paper D. Everitt and D. Manfield,
“Performance analysis of cellular mobile communication
systems with dynamic channel assignment”, IEEE JSAC,
Vol. 7, no. 8, pp , Oct
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55. Channel Allocation for Non-Uniform Traffic
Maximum Packing DCA
Consider a network layout of M cells and S channels
Define the Reuse Constraints graph
MP Algorithm
Upon every new call arrival to cell i at state
Accept the new call if the reuse constraint graph can be weight-colored with S colors, where the weights are given by
If accepted, re-arrange the channels accordingly
Lecture 4&5: Chan. alloc. for non-uniform traffic
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56. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
Example 4.8: 5-tier hexagonal cells with reuse distance = 2
Network Data
49 homogeneous cells
in a 5-tier hexagonal layout
Reuse distance = 2
Total of 350 channels
Blocking prob. either 0.02 or 0.05
To model spatial traffic we take
i.i.d
with known and ,where
is calibrated to give the required
blocking prob.
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57. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Optimal FCA for Uniform Traffic
Since cells are homogeneous the 7-color pattern is optimal
provides 50 channels per cell
Calibrating for the blocking prob. yields
We use various to get different degrees of spatial traffic
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58. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment
For every iteration draw the actual offered loads
using
For FCA, calculate the cell blocking prob. by the average
, where
Average over many iterations
Lecture 4&5: Chan. alloc. for non-uniform traffic
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59. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment (cont.)
Weighted coloring is computational complex
so we use the following approx. for MP DCA
Approximated MP
Construct the set of Maximal Cliques (done only once!)
When a call arrives to cell i in clique K at state :
accept the new call iff
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60. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment (cont.)
Remarks on the approximated MP
For where the weighted-chromatic # < S, it is OK !
Otherwise, a call is mistakenly accepted ! (rear events!)
The feasible state space of the Approximated MP are:
(4.9)
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61. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment (cont.)
E.g., for the single cluster case the states are the vectors
s.t.
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62. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment (cont.)
For Poisson call arrivals and Exponential holding times the
Markov chain is time reversible
The stationary state distribution is therefore solved from the
local balance equations:
Truncated
Poisson
Distributions
(4.10)
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63. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment (cont.)
The dist. Is not very practical for direct computation since
finding the normalization constant is NP-complete
However, for cases where the non-truncated distribution is
know (as here), we can use an efficient technique called
the “Monte-Carlo Simulation”
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64. Channel Allocation for Non-Uniform Traffic
The Blocking Probability with MP
The Experiment (cont.)
Monte-Carlo simul. to compute the blocking prob. Of MP
Every iteration, generate M independent values
If one of the reuse constraints in (4.9) is violated – ignore the sample
Otherwise, add to a counter, BC, the no. of cells in the cliques with
Repeat for a large number of iterations, T
MP_Block_Prob = BC / (49 x T)
Lecture 4&5: Chan. alloc. for non-uniform traffic
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65. Channel Allocation for Non-Uniform Traffic
FCA vs. DCA (ref point of blocking prob )
49 hexagonal cells with N=7 and
S =350 channels.
Blocking prob. produced with 200 independent spatial traffic distribution.
Top curve: FCA
Bottom curve: MP DCA operating with the same offered loads
Middle curve: MP DCA dimensioned to higher load as to meet the same blocking prob. as in the uniform traffic
Q: Why the top and bottom curves don’t coincide at variance 0?
Lecture 4&5: Chan. alloc. for non-uniform traffic
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66. Channel Allocation for Non-Uniform Traffic
FCA vs. DCA (ref point of blocking prob )
49 hexagonal cells with N=7 and
S =350 channels.
Blocking prob. produced with 200 independent spatial traffic distribution.
Top curve: FCA
Bottom curve: MP DCA operating with the same offered loads
Middle curve: MP DCA dimensioned to higher load as to meet the same blocking prob. as in the uniform traffic
Lecture 4&5: Chan. alloc. for non-uniform traffic
Adv. Wireless Comm. Systems Cellular Networks -

67. Channel Allocation for Non-Uniform Traffic
FCA vs. DCA – Experiment Conclusion
DCA may significantly reduce the blocking prob.
From 0.05 down to less than and
from 0.02 down to less than 0.002
DCA is significantly less sensitive to traffic variability
compared with FCA
The main benefit of DCA is that it is adaptive to the traffic
Important since the offered loads are not known!
Lecture 4&5: Chan. alloc. for non-uniform traffic
Adv. Wireless Comm. Systems Cellular Networks -

68. Channel Allocation for Non-Uniform Traffic
Other DCA Algorithm Families
Maximal Packing is an instance of Traffic Adaptive DCA
algorithms
Other families of DCA algorithms are those that are:
Adaptive to the received signal power
Adaptive to interference power
Lecture 4&5: Chan. alloc. for non-uniform traffic
Adv. Wireless Comm. Systems Cellular Networks -