1. Chapter 4 Circuit-Switching Networks
Traffic and Overload Control in Telephone Networks

2. Traffic Management & Overload Control
Telephone calls come and go
People activity follow patterns
Mid-morning & mid-afternoon at office
Evening at home
Summer vacation
Outlier Days are extra busy
Mother’s Day, Christmas, …
Disasters & other events cause surges in traffic
Need traffic management & overload control

3. Traffic concentration
Fewer
trunks
Many
lines
Traffic fluctuates as calls initiated & terminated
Driven by human activity
Providing resources so
Call requests always met is too expensive
Call requests met most of the time cost-effective
Switches concentrate traffic onto shared trunks
Blocking of requests will occur from time to time
Traffic engineering provisions resources to meet blocking performance targets

4. Fluctuation in Trunk Occupancy
Number of busy trunks
N(t) t
All trunks busy, new call requests blocked 1 2 3 4 5 6 7
Trunk number
active
active
active
active
active
active
active
active
active
active 4

5. Modeling Traffic Processes
Find the statistics of N(t) the number of calls in the system
Model
Call request arrival rate: l requests per second
In a very small time interval D,
Prob[ new request ] = lD
Prob[no new request] = 1 - lD
The resulting random process is a Poisson arrival process:
(λT)ke–λT k!
Prob(k arrivals in time T) =
Holding time: Time a user maintains a connection
X a random variable with mean E(X)
Offered load: rate at which work is offered by users:
a = l calls/sec * E(X) seconds/call (Erlangs)

6. Blocking Probability & Utilization
c = Number of Trunks
Blocking occurs if all trunks are busy, i.e. N(t)=c
If call requests are Poisson, then blocking probability Pb is given by Erlang B Formula
Pb = ac c! k!
∑ ak
k=0 c
The utilization is the average # of trunks in use
Utilization = λ(1 – Pb) E[X]/c = (1 – Pb) a/c

7. Blocking Performance a = 5 Erlangs requires 11 trunks
To achieve 1% blocking probability:
a = 5 Erlangs requires 11 trunks
a = 10 Erlangs requires 18 trunks

8. Chapter 4 Circuit-Switching Networks
Cellular Telephone Networks

9. Radio Communications 1900s: Radio telephony demonstrated
1920s: Commercial radio broadcast service
1930s: Spectrum regulation introduced to deal with interference
1940s: Mobile Telephone Service
Police & ambulance radio service
Single antenna covers transmission to mobile users in city
Less powerful car antennas transmit to network of antennas around a city
Very limited number of users can be supported

10. Cellular Communications
Two basic concepts:
Frequency Reuse
A region is partitioned into cells
Each cell is covered by base station
Power transmission levels controlled to minimize inter-cell interference
Spectrum can be reused in other cells
Handoff
Procedures to ensure continuity of call as user moves from cell to another
Involves setting up call in new cell and tearing down old one

11. Wireless Call
Slides are modified version of Digital Transmission Fundamentals Slides by Leon-Garcia/Widjaja

12. Isotropic antenna 2

13. Isotropic antenna 2

14. Isotropic Antenna 2

15. Isotropic Antenna Effective Area2

16. Free Space Loss 2

17. Antenna Gain 2

18. Antenna Gain 2

19. Frequency Reuse Adjacent cells may not use same band of frequencies2
Adjacent cells may not use same band of frequencies
Frequency Reuse Pattern specifies how frequencies are reused
Figure shows 7-cell reuse: frequencies divided into 7 groups & reused as shown
Also 4-cell & 12-cell reuse possible
Note: CDMA allows adjacent cells to use same frequencies (Chapter 6) 7 3 1 6 4 5 2 2 7 3 7 3 1 1 6 4 6 4 5 5

20. Reuse Factor k i
N=i2+ik+k2

21. Reuse Factor
Reuse Factor =3
Reuse Factor =4
Reuse Factor =9

22. Number of users Number of channels per cell =
total number of channels /reuse factor
Number of simultaneous users=
Number of users per channel* number of channels per cell * number of cells
Number of cells = Coverage area/Cell area
Number of subscribers ??
Use Erlang Tables

23. Reuse factor effect on the user
Small reuse factor
= more channels per cell
= more subscribers
Small reuse factor means closers interferers
= more interference
= less bit rate per channel
Reuse Factor =3
Slides are modified version of Digital Transmission Fundamentals Slides by Leon-Garcia/Widjaja

24. Sectoring Divide each cell into a number of sectors
Divide the channels on the number of sectors
Sectors could be 180, 120 and 60
Slides are modified version of Digital Transmission Fundamentals Slides by Leon-Garcia/Widjaja

25. Sectoring
Interfering cells =2

26. Number of interfering cells
Number of interfering cells depends on The reuse factor