Traffic Engineering
40
¨ Cells - deploy a large number of low-power base stations
- each having a limited coverage area
¨ Reuse the spectrum several times in the area to be
covered to increase capacity
¨ Issues:
¤ Capacity (traffic load) in a cell
n One measure = number of communication channels that are
available
¤ Performance
n Call blocking probability, handoff dropping probability, throughput
etc.
¤ Interference
Traffic Engineering (2)
41
¨ Questions:
¤ IfI want to place a call, what is the probability that I
will NOT get a communication channel?
n “New call admission”
¤ IfI am moving from cell to cell, what is the probability
that during a call, I will NOT find a communication
channel in the new cell to continue my call?
n “Handoff call admission”
Grade of Service
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¨ Grade of service
¤ Usually 2% blocking probability during busy hour
¤ Busy hour may be
1. Busy hour at busiest cell
2. System busy hour
3. System average over all hours
¨ Given c = T/K traffic channels per cell – what is
the grade of service (GoS)?
¤ How many users can be supported for a specific GoS?
¨ Basic analysis called Traffic Engineering or Trunking
¤ Same as circuit switched telephony
¤ Use Erlang B and Erlang C Models
Erlangs - 1
43
¨ Let there be c = T/K channels per cell
¨ In a given time period, suppose there are Q active
users
¤ If Q = c, any new call will be blocked with probability
1
¤ If Q < c, then your call may get a channel
¨ How do we quantify this better?
¤ Erlangs
Erlangs - 2
44
¨ How do you estimate traffic
distribution?
¤ Traffic intensity is measured in
Erlangs
¤ One Erlang = completely
occupied channel for 60
minutes
¨ Examples
¤ 30 kHz voice channel
occupied for 30 min/hour ¨ Agner Krarup Erlang
carries 0.5 Erlangs ¨ Scientist with the Copenhagen
¤ 100 calls in one hour each Telephone Company
lasting 3 minutes = 100 calls/ ¨ Studied data from a village’s
hour × 3/60 = 5 Erlangs telephone calls to arrive at his
conclusions
More on Erlangs
45
¨ Traffic intensity per user Au
¤ Au = average call request rate × average holding time = λ
× th
¨ Total traffic intensity = traffic intensity per user ×
number of users = Au × nu
¨ Example:
¤ 100 subscribers in a cell
¤ 20 make 1 call/hour for 6 min => 20 × 1 × 6/60 = 2E
¤ 20 make 3 calls/hour for ½ min => 20 × 3 × .5/60 =
0.5E
¤ 60 make 1 call/hour for 1 min => 60 × 1 × 1/60 = 1E
¤ 100 users produce 3.5 E load or 35 mE per user
Notation associated with queues
46
¨ Written as P/Q/R/S
¤ P: Description of arriving traffic
¤ Q: Description of service rates or times
¤ R: Number of servers
¤ S: Number of users that can be in the system (includes those
being served and those waiting)
¨ M => Markov (Poisson arrival times, exponential
service times)
¤ Commonly used as it is tractable and it fits voice calls
¨ If the number of users that can be in the system (S) is
infinite, it is dropped from the notation
Erlang B Model: M/M/c/c queue
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¨ To estimate the performance of a trunked system use the
Erlang B queueing model
¨ The system has a finite capacity of size c
¤ Customers arriving when all servers busy are dropped
¨ Blocked calls cleared model (BCC) (no buffer)
¨ Assumptions
¤ c identical servers process customers in parallel
¤ Customers arrive according to a Poisson process (average of λ calls/s)
¤ Customer service times exponentially distributed (average of 1/μ
seconds per call)
¨ The offered traffic intensity is a = λ/μ in Erlangs
Erlang B Formula or Blocking Formula
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¨ Probability of a call being blocked B(c,a)
ac
c!
B (c, a ) = c
an
∑n = 0 n!
¨ Erlang B formula can be computed from the recursive formula
a ⋅ B(c − 1, a)
B(c, a) =
c + a ⋅ B(c − 1, a)
¨ Usually determined from table or charts
Example of Erlang B Calculation
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¨ For 100 users with a traffic load of 3.5 E, how
many channels are need in a cell to support 2% call
blocking ?
¤ Use Erlang B tables or charts
¤ With a 2% call blocking, we need 8 channels
Sample Erlang B table
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Erlang B Chart
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N : n u m b e r o f c h a n n e ls
-1 1 2 3 5 7 9 15 25 35 95
10
8 channels
probability of bloc k ing
-2
10
-3
10
-1 0 1 2
10 10 10 10
Tra ffic lo a d in E rla n g s
Example: Using Erlang B for traffic
52
engineering
¨ Consider a single analog cell tower with 56 traffic
channels
¤ When all channels are busy, calls are blocked
¤ Calls arrive according to a Poisson process at an
average rate of 1 call per active user per hour
¤ During the busy hour ¾ of the users are active
¤ The call holding time is exponentially distributed with a
mean of 120 seconds
Example: Continued
53
¨ What is the maximum load the cell can support while
providing 2% call blocking?
¤ From the Erlang B table with c= 56 channels and 2% call
blocking, the maximum load = 45.9 Erlangs
¨ What is the maximum number of users supported by the
cell during the busy hour?
¤ Load per active user = (1 call/3600 s) × (120 s/call) =
33.3 mErlangs
¤ Number of active users = 45.9/(0.0333) = 1377
¤ Total number of users = 4/3 number active users = 1836
Another Example
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¨ Consider an AMPS system with 30 kHz channels, 4
sectors/cell, frequency reuse of K = 9, and 12.5
MHz of bandwidth.
¤ Number of channels = 12.5 × 106/30 ×103 = 416
channels
¤ Say 20 are control channels => total number of voice
channels = 396
¤ Number of channels/cell = 396/9 = 44
¤ Number of channels/sector = 44/4 = 11
Example (Continued)
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¨ For a 2% blocking probability, from the Erlang B
tables, the maximum traffic load is
¤ For AMPS: 5.84 E
¨ If the average call duration is 3 minutes, and each
call is 3/60 = 0.05 E
¤ AMPS can support 116 calls/hour/sector
