1. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 1 Alternate Routing Other H. U. C Alternate Route AB High Usage Route (Direct 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). 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. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 2 Sizing the Direct Route C D = Cost per trunk on direct route C A = Cost per trunk on alternate route (C A > C D )  = Estimated marginal capacity per overflow trunk, Erl/trunk N D = Number of trunks on direct route N A = Number of trunks needed on alternate route Cost of direct route Cost of alternate route

3. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 3 Sizing the Direct Route (2) NDND Cost NDCDNDCD NACANACA Total Cost When is total cost minimum?

4. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 4 Sizing the Direct Route (3) where “Cost Ratio” but we can show that NDND $ NDCDNDCD NACANACA Total Cost Optimal (lowest total cost)

5. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 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. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 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. A N is the incremental efficiency of the N th 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

7. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 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? Directly Routed Overflow peaky Overflow traffic is very “peaky”.How do we characterize it? T O to D.R. Time

8. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 8 Characterizing Overflow Traffic Mean Intensity of i th overflow: Variance of i th 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 M i and V i to the totals: Peak Factor (“peakiness” or “peakedness”):

9. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 9 Equivalent Random Group (2) Example: A.R. H.U. #1 H.U. #2 H.U.#1H.U.#2A.R. N 1 =6N 2 =10N AR =? A 1 =8.25 EA 2 =13.25 EA AR =3 E 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. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 10 Equivalent Random Group (3) But using ERG method, we can show that N * =11 and A * =21.1 E will give us an M Total of 10.94 E and V Total of 18.07 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 (M Total ). –Calculate V i (using formula) and check if it’s what we want (V Total ). –If not, increment N by 1, reset A=0.1, and repeat.

11. Author: Wayne Grover (materials set in PowerPoint by J. Doucette 2002) 11 Equivalent Random Group (4) Now that we have N * =11 and A * =21.1 E: –Find m: Alternate Route needs 22 trunks.