1. “Sizing the Direct Route”
Alternate Routing C
Alternate
Route
Any calls from A to B use the direct route (span A-B) unless blocking occurs, in which case traffic is rerouted on an alternate route (span A-C). A B
High Usage Route
(Direct Route)
Other H. U.
Other H. U.
Note: A-C may be an alternate route from point of view of A-B but may be direct route for its own traffic
Problem: How many trunks do we need on the direct route given an overflow route exists?
“Sizing the Direct Route”

2. Sizing the Direct Route
CD = Cost per trunk on direct route
CA = Cost per trunk on alternate route (CA > CD)
 = Estimated marginal capacity per overflow trunk, Erl/trunk
ND = Number of trunks on direct route
NA = Number of trunks needed on alternate route
Cost of direct route
Cost of alternate route

3. Sizing the Direct Route (2)ND
Cost
Total Cost
NACA
NDCD
When is total
cost minimum?

4. Sizing the Direct Route (3)
“Cost Ratio”
where
but we can show that ND $
NDCD
NACA
Total Cost
Optimal (lowest total cost)

5. Sizing the Direct Route (4)
How do we size the direct route?
Add H.U. trunks to the direct route one at a time until:
and let
i.e. all N trunks have
So what are we really doing?
Adding trunks to the direct route until the change in carried traffic by the additional span is less than
And what does mean?
Discounted Efficiency of the alternate route

6. Sizing the Direct Route (5)
Alternate route operates at an efficiency of  Erlangs per trunk but each trunk costs R times more than one on the direct route.
AN is the incremental efficiency of the Nth trunk on the direct route. so
means:
Add direct route trunks until they are less efficient on a cost basis than putting the extra traffic on the overflow route
Note:
“Overflow Route” = “Alternate Route” = “Final Route” = “Tandem Route”
“Direct Route” = “1st Choice Trunk Group” = “High Usage Route”

7. Sizing the Final (Overflow) Route
The final route must be sized to handle its total traffic load:
Its own direct route traffic, and
Overflow traffic from various other high usage routes
It must also meet its specified target probability of blocking
Does overflow traffic behave like conventional Poisson arrivals?
Overflow
TO to D.R.
Time
Directly
Routed
Overflow traffic is very “peaky”.
How do we characterize it?

8. Characterizing Overflow Traffic
Mean Intensity of ith overflow:
Variance of ith overflow:
If several direct routes overflow onto a single alternate route:
If the alternate route also contains its own direct traffic, be sure to add its Mi and Vi to the totals:
Peak Factor (“peakiness” or “peakedness”):

9. Equivalent Random Group (2)
Example:
H.U.#1 H.U.#2 A.R.
N1=6 N2=10 NAR=?
A1=8.25 E A2=13.25 E AAR=3 E
A.R.
H.U. #1
H.U. #2
How many trunks do we need on the alternate route for P(B) = 0.01?
Recall:
Using peaky traffic tables:
Find we need N = 22 trunks on alternate route

10. Equivalent Random Group (3)
But using ERG method, we can show that N*=11 and A*=21.1 E will give us an MTotal of E and VTotal of E.
How did we find this?
TrafCalc, or
Best fit search
How does TrafCalc do it?
Start with N=1 and A=0.1.
Increase A by 0.1 increment until we get blocking high enough to cause an overflow of what we’re looking for (MTotal).
Calculate Vi (using formula) and check if it’s what we want (VTotal).
If not, increment N by 1, reset A=0.1, and repeat.

11. Equivalent Random Group (4)
Now that we have N*=11 and A*=21.1 E:
Find m:
Alternate Route needs 22 trunks.

12. Full Tandem Routing
In some cases, offered traffic is so low that even when we test the first direct route trunk (using AN=A1), we find:
 Direct Route has N=0 trunks
“Full Tandem Routing”
This means it’s more efficient to have no direct route
Recall:
(see Erlang B equation)

13. Full Tandem Routing (2) Example: Full Tandem Routing
How many trunks do we need on the direct high usage route offered A = 1 E if =0.85 E/trunk and R = 1.6?
A.R.
H.U.
First check if full tandem routing:
check
 Direct Route has N=0 trunks
Full Tandem Routing

14. Full Direct Routing Example:
The other extreme is when we size the direct route and find N such that B(N,A) is smaller than the target A.R. P(B) before we reach a large enough N that we place trunks on the alternate route:
and
or some other P(B)
Example:
How many trunks do we need on the alternate route for P(B)=0.02 if D.R. offered A = 50 E if =0.6 E/trunk, R = 3.0?
A.R.
H.U.
First check if full direct routing.
from traffic tables:
Full Direct Routing
so check