1. Trunking & Grade of Service
Trunked radio system  radio system where a large # of users share a limited pool of channels
Channel allocated on demand & returned to channel pool upon call termination
Exploit statistical (random) behavior of users so that fixed # of channels can accommodate large # of users
Trunking theory used by telephone companies to allocate limited # of voice circuits for large # of telephone lines
Efficient use of equipment resources  $$ savings
Disadvantage is that some probability exists that mobile user will be denied access to a channel
Blocked call : access denied  “blocked call cleared”
Delayed call : access delayed & call put into holding queue for specified amount of time (5-15 seconds)
ECE 4730: Lecture #6

2. Trunking & Grade of Service
Grade of Service (GOS)
Measure of user access to a trunked radio system during busiest hour of the week
Specified as probability (Pr) that call is blocked or delayed
Busiest hour  typically 4-6 pm on Thu or Fri (cellular)
Erlang (erl) : unitless measure of traffic intensity
Example: 0.5 erl = 1 channel occupied 30 minutes during 1 hour
Table 3.3, pg. 76  Trunking theory definitions
ECE 4730: Lecture #6

3. Trunking & Grade of Service
ECE 4730: Lecture #6

4. Trunking & Grade of Service
Traffic Intensity (A)
Also called “Offered” Traffic Intensity
Offered?  not necessarily carried by system (blocked/delayed)
Each user Au = l H (erl)
System with U users  A = U Au = U l H (erl)
Intensity/channel  AC = U Au / C (erl/channel)
Maximum carried traffic load = total # available channels = C (erl)
ECE 4730: Lecture #6

5. Trunking & Grade of Service
Erlang B formula
Blocked Call Cleared (denied)  BCC
GOS = Pr [blocked call] =
A = total offered traffic
C = # channels in trunking pool (e.g. a cell or sector)
Program in calculator or use computer to calculate
ECE 4730: Lecture #6

6. Trunking & Grade of Service
Erlang C formulas
Blocked Call Delayed  BCD  put into holding queue
Probability that call is delayed greater than t seconds
Probability that call is initially denied access and put into holding queue
Program in calculator or use computer to calculate
ECE 4730: Lecture #6

7. Trunking & Grade of Service
Graphical form of Erlang Curves
Fig. 3.6 & pgs. 81, 82
Family of curves
Pr vs. A for many values of C
Provide approximate solutions
Errors due to “eyeball” interpolation
Numerical formulas provide exact values
ECE 4730: Lecture #6

8. Number of Trunked Channels ( C )
Erlang B Graph
Number of Trunked Channels ( C )
ECE 4730: Lecture #6

9. Trunking & Grade of Service
Example: How many users can be supported in a cell containing 50 channels for a 5% GOS (BCC) if the average user calls twice/hr with an average call duration of 5 minutes?
Fig. 3.6  For GOS = 5% and C = 50 then A = 45 erl
Twice/hr  l = 2
Call duration  H = 5 minutes
Au = l H = 2 (5 min / 60 min) = 1/6 erl (unitless!)
A = U Au  U = A / Au = 45 / (1/6) = 270 users
See additional examples in book
ECE 4730: Lecture #6

10. Trunking Efficiency
Trunking Efficiency  measure of # users supported by specific configuration of fixed channels
Table 3.4, pg. 79  Lets assume 1% GOS
1 group of 20 channels  12 erl or (12/20) · 100 = 60% efficiency
2 groups of 10 channels  2 · 4.46 = 8.92 erl or (8.92/20) · 100 = 44.6% efficiency
***Larger channel group supports [(12/8.92)  1] · 100 = 35% more traffic!!***
Allocation of channel groups can substantially change # users supported by trunked system
As trunking pool size  then trunking efficiency 
ECE 4730: Lecture #6

11. Trunking Efficiency
ECE 4730: Lecture #6

12. Improving Cellular System Capacity
Cell Sectoring
Method that  capacity by reducing CCI
Replace omni-directional antennas at base station with several directional antennas
3 sectors  120° antennas
6 sectors  60° antennas
Cell channels broken down into sectored groups
CCI reduced b/c only some of neighboring co-channel cells radiate energy in direction of main cell
Figs & 3.11, pgs. 90 & 91
Cell splitting (discussed next) keeps D / R unchanged (same CCI) but increases frequency reuse/area
ECE 4730: Lecture #6

13. Cell Sectoring ECE 4730: Lecture #6 3 sectors  3 @ 120° antennas

14. Cell Sectoring N = 7 cell cluster 6 CCI cells in first tier
io = 2 interfering cells
ECE 4730: Lecture #6

15. Cell Sectoring ECE 4730: Lecture #6 How is capacity increased?
By reducing CCI the cell system designer can choose smaller cluster size (N )
Smaller N  greater frequency reuse  larger system capacity
Much less costly than cell splitting
Only requires more base station vs. multiple new base stations for cell splitting
Primary disadvantage is available channels in a cell subdivided into sectored groups
Trunked channel pool   trunking efficiency 
*** Overall system capacity increased at the expense of reducing capacity of individual cells (w/sectors) ***
Why? Cluster size N is reduced  frequency reuse increases!!
ECE 4730: Lecture #6

16. Cell Sectoring Other Advantages : ECE 4730: Lecture #6
More antenna gain  sector antenna focuses signal energy
Forward/reverse link budgets improved
More Tx power delivered to coverage area
Better building penetration
Flexibility in controlling CCI and dropped calls from poor handoff execution
Downtilt antennas in certain sectors to reduce CCI in specific cells
Uptilt antennas in certain sectors to increase coverage at cell boundary to improve chance of successful handoff
ECE 4730: Lecture #6

17. Cell Sectoring Other Disadvantages : ECE 4730: Lecture #6
Must design network coverage with sectoring decided in advance
Can’t effectively (easily) use sectoring to increase capacity after setting cluster size N
Can’t be used to gradually expand capacity as traffic  like cell splitting
ECE 4730: Lecture #6

18. Improving Cellular System Capacity
Cell Splitting
Subdivide congested cell into several smaller cells
Must decrease antenna height & Tx power so smaller coverage results and CCI level is held constant
Each smaller cell keeps  same # of channels as the larger cell!!
Capacity  b/c channel re-use  per unit area
Smaller cells  “micro-cells”
Fig. 3.8, pg. 87
ECE 4730: Lecture #6

19. Cell Splitting Base stations placed at cell corner for illustration
purposes
ECE 4730: Lecture #6

20. Other Graphical Examples
Cell Splitting
Other Graphical Examples
ECE 4730: Lecture #6

21. Cell Splitting Advantages : Disadvantages : ECE 4730: Lecture #6
Only needed for cells that reach max. capacity  not all cells
Implement when Pr [blocked call] > acceptable GOS
System capacity can gradually expand as demand 
Disadvantages :
# handoffs/unit area 
Umbrella cell for high velocity traffic may be needed
**More base stations  $$ for real estate, towers, etc.**
ECE 4730: Lecture #6