1. Top Percentile Pricing and the Economics of Multi-Homing
Hanoch Levy
School of Computer Science, Tel Aviv University
Jointly with
Joseph Levy, Yaron Kahana
Alternative name: “Satellite-linked Web Caches”
March , 2005
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

2. The Internet revolution
A variety of network providers
Many Internet service providers (ISP)
Connect to the Internet via network providers
Net1
Ne2
Net3
ISP-A
ISP-B
Multi-homing: ISP connect to multiple nets (reliability)
Top percentile pricing
Network method of charging ISP
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

3. The Top Percentile pricing Paradigm
Approach (example):
Network provider allows ISP to send as much data as wants. Virtually No limits!
Charge:
Divide the month to about 3000 slots of 15 minutes
Measure Bandwidth over all slots
Cost is based on the top 150th slot
Advantages:
Flexible to buyer (ISP) – no commitments!
Protects seller (provider) from high peaks!
Status: An increasingly popular pricing used by network providers r
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

4. Operational Questions (ISP)
Which nets to connect to?
How much will I pay under top percentile
Should I use multi-homing
What will multi-homing cost me?
On which link should I send my traffic? Net1? Net3? Both?
Net1
Ne2
Net3
ISP-B
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

5. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Prior Work
Traffic engineering / network design / pricing:
Literature focuses on:
Fixed price : Pay for the pipe (cost per volume)
Cost function may be linear, non-linear…
Used in network design
Per bit (variable) price: Pay by the bit
Cost may be complex (by type, linear, non-linear)
Used in routing + traffic engineering
Top percentile pricing?
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

6. Operational strategy: Hard
Assume: ISP faces two identical providers
Ask: what will dual-homing cost compared to single-homing
Answers:
Per-bit cost: Same!
Fixed cost: Double!
Top-percentile cost:
If lucky: same…
Not lucky: close to double?
In reality: ???
Our objective
Net1
Net3
ISP-B
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

7. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Model (1)
Net1
Net3
ISP-B
Single ISP
Networks:
Each uses top-q percentile pricing
Time intervals: t=1, …, T
R.V – amount of traffic shipped on network i at slot t.
Charge:
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

8. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Model (2)
Net1
Net3
ISP-B
Traffic demands: I different streams. The demand of stream i at time t:
Network reliability: can fail with certain probability at time t.
Accounting in model: Probability that stream i is routed through network j at any time:
General model. Allows accounting for network failure and network control policies.
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

9. Operational strategies (1)
Given:
Stream demands
Networks and reliability
Question: where to route each demand.
Objective: minimize expected cost
Simplify : 2 demands (persons, applications, etc..), 2 nets (dual)
Common approach:
Demand i is assigned a primary network and a secondary network
Net1
Stream-A
Stream-B
Net3
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

10. Operational strategies (2)
Practical simple assignment strategies:
Same primary: A and B choose 1 as primary and 2 as alternate
Alternate primary: Primary(A)=1, Primary(B)=2.
General question: To concentrate or spread?
Theoretical (extreme) strategies:
Best assignment (lower bound)
Worst assignment (upper bound)
Net1
Stream-A
Stream-B
Net2
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

11. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Analysis – Stochastic
Consider network : Stream i is on network with Bernoulli probability
Use convolution of all streams  joint demand on :
(Network j at slot t)
Make use of: Large number of the R.V’s are i.i.d! (e.g. Traffic at 9:00, 9:15, 9:30….)
Let be the r largest of D(t)
For a group of i.i.d: is binomial with (r, number of slots, G(x))
For all slots – convolve the binomials! (approx by normal) 
Numerical with reasonable complexity (if # streams low)
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

12. Analysis – Deterministic: bounds?
Net1
stream1 ?
stream2
Net2
time
Where to route each traffic demand – to minimize cost?
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

13. Analysis – Deterministic: lower bound (best assignment)
Net1
Net2
SUM and SORT
Assume:
c1>c2
assignment
Net2 assignment
Net2 cost
Net1 cost (0) r r
2r intervals for free  a) use them, b) put highest values there.
Now – you end-up paying for the highest of the other slots .
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

14. Analysis – Deterministic: upper bound(worst assignment)
Net1
Net2 r
SUM and SORT
Assume:
c1<c2
assignment
Net2 assignment
Net2 cost
Net1 cost (0)
Worst case scenario applies only to certain traffic pattern
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

15. upper bound(worst assignment)
Net1
Net2 r
SUM and SORT
Assume:
c1<c2
assignment
Net2 assignment
Net2 cost
Net1 cost (0)
Cannot cost more than c2* X(T-r+1) + c1*X(T-r+2)
There are patterns where this cost is feasible.
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

16. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Numerical results
Consider “realistic like” traffic
Examined:
Multi homing with same primary
Multi homing with alternate primary
Lower bound
Upper bound
Relative cost (compared to no-multi-homing)
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

17. Numerical results (1) Gain as long as failure < 1-r 10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

18. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Numerical results (2)
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

19. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Numerical results (3)
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

20. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Numerical results (4)
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Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

21. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Concluding remarks
Top-percentile pricing is a new paradigm that needs to be studied further
Mutli-homing on top-percentile pricing is economically viable (usually)
Cost may go high if same primary is used and failure rate is high.
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

22. Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana
Thank you
10/14/2018
Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana