How many tiers? Pricing in the Internet transit market

Vytautas Valancius, Christian Lumezanu, Nick Feamster, Ramesh Johari and Vijay Vazirani

This paper deals with the problem of ISPs selling contracts to other (customer) ISPs. Transit ISPs implement policies which price traffic by volume or by destination with volume discount and cheaper prices to destinations which cost them less. The paper studies destination based tiered pricing with the idea that ISPs should unbundle traffic and sell pricing in tiers according to destination to maximise profits.

The background section offers a useful taxonomy of current bundles sold by transit ISPs. This arises from discussions with ISPs.

  • “Transit” – conventional transit pricing, sold at a blended rate for all traffic to all destinations ($Mbpsmonth). Blended rates have been decreasing at 30% each year historically. (Note – conversation with authors confirms this is usually 95th percentile).

  • “Paid peering” – like conventional peering but one network pays to reach the other. off-net (destinations outside its network) and on-net (destinations within its network) may be charged at different rates. E.g. national ISPs selling local connectivity at a discount.

  • “Backplane peering” – an ISP sells global transit through its background but discounts traffic it can offload to peers at same Internet exchange. Smaller ISPs may buy this if they cannot get settlement-free peering at exchange.

  • “Regional pricing” – transit providers price different geographical regions differently. Rare that more than one or two extra price levels are used for regions.

Authors show that coarse bundling can lead to reduced efficiency. Providers lose profit and customers lose service. In an example the blended rate price which maximises profit gives both less profit and lower surplus to consumers than two rates for two demand curves. An example is also given with a CDN which wants to move demand intradomain between two PoPs. The traffic is local to the PoPs and hence has lower cost to the network than typical traffic but is high in volume. If charged at the blended rate the CDN is highly incentivised to buy a direct link itself although the ISP providing transit could have carried that traffic and made profit while still charging the CDN less than paying for its own link. (Figure 2).

Section 3 of the paper creates a model of ISP profit and customer demand. Profit is modelled as sum p_i Q_i - c_i Q_i where Q_i is the demand for traffic in flow i traffic given the price vector (over all flows), p_i is the price of class i traffic and c_i is the cost of serving traffic in flow i. Demand is modelled in two ways: Firstly with “constant elasticity demand” (CED) – Q_i = (v_i/p_i)^alpha where v_i is the valuation parameter and alpha in (1,infty) is the price sensitivity. Secondly with “logit demand”, u_{ij} = alpha (v_i - p_i) + epsilon_{ij} where u_{ij} is the utility of consumer j using flow i alpha in (0, infty) is elasticity and v_i is an average “maximum willingness to pay”. The epsilon_{ij} have a Gumbel distribution (standard in the logit model). The logit model then shares flows between customers with the share s_i for flow i (the probabiltity a given customer will use flow i) is s_i = (e^{alpha(v_i-p_i)}/(sum_j e^{alpha(v_j-p_j)} +1). The plus one is to allow a “no travel” decision s_0 such that the s_i sum to one. This, again, is standard from choice theory.

Profit maximising prices for logit and CED can be derived theoretically but in the logit case a heuristic descent algorithm must be used to find this optimum. Bundled prices are then tested by setting a number of pricing points and bundling flows.

ISP costs are approximated in seveal ways (as ISPs are reluctant to share this information).

  • Cost as a linear function of bandwidth used.

  • Transit cost changing with distance either as a linear cost with distance or as a concave cost with distance.

  • Cost as a function of destination region (assuming metropoliton, national, international, classified approximately as step functions based on distance).

  • Cost as function of destination type (related to on-net/off-net), approximated by making traffic to peers cost twice that of customers (traffic between customers allows the ISP to bill twice). This is approximated with a factor theta for each distance which splits traffic into customer or peer.

Bundling is done by several strategies:

  • Optimal (all combinations of a given number of bundles tried)

  • Demand weighted (tries to give bundles equal total flow demand but keep high demand flows in same bundle).

  • Cost weighted (Similar but with cost).

  • Profit weighted (Similar but with profit).

  • Cost division (bundles divided according to cost of flow).

  • Index division (as above but equal number of flows in each bundle).

Data sets:

  • EU ISP from 2009

  • flows from a CDN

  • Internet 2 data

The basic conclusion is that only a small number of tiers are required to get near to 100% of the possible profit. Contracts with only three or four tiers bundled on cost and demand works well. Contracts based on discounts for local traffic (standard practice) are sub optimal.

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