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Alternate Routing

C. Alternate Route. A. B. High Usage Route (Direct Route). Other H. U. Other H. U. Alternate Routing. 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).

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Alternate Routing

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  1. C Alternate Route A B High Usage Route (Direct Route) Other H. U. Other H. U. Alternate Routing 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. Cost of direct route Cost of alternate route 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

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

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

  5. and let i.e. all N trunks have 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 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: So what are we really doing?

  6. so 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. means: Add direct route trunks until they are less efficient on a cost basis than putting the extra traffic on the overflow route

  7. TO to D.R. Overflow Directly Routed Time 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 traffic is very “peaky”. How do we characterize it?

  8. Characterizing Overflow Traffic Mean Intensity of ith overflow: • If several direct routes overflow onto a single alternate route: Variance of ith overflow: 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. A.R. H.U. #1 H.U. #2 Recall: Equivalent Random Group (2) Example: H.U.#1H.U.#2A.R. N1=6 N2=10 NAR=? A1=8.25 E A2=13.25 E AAR=3 E How many trunks do we need on the alternate route for P(B) = 0.01? 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 10.94 E and VTotal 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 (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.

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