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

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

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

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

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

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

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: 10/14/2018 Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

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

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

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

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

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

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

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

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

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) 10/14/2018 Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

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

Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana Numerical results (2) 10/14/2018 Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana Numerical results (3) 10/14/2018 Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana Numerical results (4) 10/14/2018 Top-Percentile Pricing, J. Levy, H. Levy, Y. Kahana

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

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