The Role of Switching Hub in Global Internet Traffic

1
The Role of Switching Hub in Global Internet
Traffic

• Chang-Ho Yoon
• Young-Woong Song
• Byoung Heon Jun

2
Introduction

• Internet traffic is growing fast.
• Connection between networks becomes important.
• Popular contents generates internet traffic.
• The role of switching hub becomes less important
  as regionalization of Internet traffic gains
  speed.
• Persistent asymmetry in bargaining power was a
  serious policy issue in late 1990s due to global
  digital divide, which shows changes only
  recently.
• This paper examines the role and the bargaining
  power of the switching hub, taking into account
  the above listed facts.

3
Findings

• Bargaining power of the local networks depends on
  the quality adjusted volume of net traffic (the
  difference between the outbound and inbound
  traffic weighted by the quality).
• Rent to the hub depends on total traffic between
  the local networks connected to the switching
  hub.
• When there is competition, capacity constraint
  destroys most of the rent for the constrained hub
  and offers more rent for the rival.
• This creates a tendency for excess capacity.
• Peering possibility reduces the rent of the hub.

4
Literature

• Shapley (1953), A Value for n-Person Games, in
  Kuhn and Tucker eds., Contributions to the Theory
  of Games II
• Laffont, Marcus, Rey, and Tirole (2001),
  Internet Interconnection and the Off-Net-Cost
  Pricing Principle, mimeo, Institut dEconomie
  Industrielle
• Milgrom, Mitchell, and Srinagesh (2000),
  Competitive Effects of Internet Peering
  Policies, in Compaine and Vogelsang eds., The
  Internet Upheaval
• Besen, Milgrom, Mitchell, and Srinagesh (2001),
  Advances in Routing Technologies and Internet
  Peering Agreements, AEA Papers and Proceedings

5
Model

• Networks are denoted by i ? I.
• Each network hosts one contents provider CPi, and
  serves ni identical consumers.
• Alternatively, we can assume perfect competition
  in each content market.
• A consumer in each network has a separable
  utility function
• ui(q,y) ?j(?jqj qj2/(2?ij)) y
• From the utility function of the consumers demand
  function for j is derived Qj(pj?j)?i?S
  ni ?ij(?j pj), where
• S is the set of networks connected to j,
• ?ij represents the preference of consumer i for
  contents j,
• ?j represents popularity or quality of content
  j.

6
Preliminary results

• Contents price pj(?j) ?j/2
• Consumers surplus CSij ?ij?j2/8
• Network operators charge prices so as to extract
  all the consumers surplus.
• Network is profit when connected to S TSiS
  ?j?S ni?ij?j2/8
• One can calculate Shapley value using this
  information.
• Shapley value determines the actual payoff of
  each network, and payments by each network is the
  difference between the total profit and the
  Shapley value.

7
Premium for the hub

• Proposition 1. The payment of the transit
  purchaser consists of two parts. The first part
  is proportional to the quality adjusted net
  inbound traffic. The second part is proportional
  to the quality adjusted total traffic between the
  non-hub networks.
• NP1 (?2?2?1 ?1?1?2) (?3?3?1 ?1?1?3)/8
  (?2?2?1 ?1?1?2)/24
• NP2 (?1?1?2 ?2?2?1) (?3?3?2 ?2?2?3)/8
  (?2?2?1 ?1?1?2)/24
• NP3 (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)/8
  (?2?2?1 ?1?1?2)/12 (Hub)

8
Competition of hubs

• Proposition 2. When there are two hubs, the
  premium payments are reduced to half the level
  when there is only one hub, and each hub receives
  one quarter of the premium received when there is
  only one hub.
• NP1 (?2?2?1 ?1?1?2) (?3?3?1 ?1?1?3)
  (?4?4?1 ?1?1?4)/8 (?2?2?1 ?1?1?2)/48
  (transit purchaser)
• NP3 (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)
  (?4?4?3 ?3?3?4)/8 (?2?2?1 ?1?1?2)/48
  (hub)

9
Collusion

• If the two hubs collude and act as a monopolist,
  then they collectively obtain the same premium
  that can be obtained when there is only one hub.
• NP1 (?2?2?1 ?1?1?2) (?3?3?1 ?1?1?3)
  (?4?4?1 ?1?1?4)/8 (?2?2?1 ?1?1?2)/24
  (transit purchaser)

10
Capacity constraint

• Now suppose that each hub can only host one
  transit purchaser.
• NP1 (?2?2?1 ?1?1?2) (?3?3?1 ?1?1?3)
  (?4?4?1 ?1?1?4)/8 (?1?1?2 ?2?2?1)/16
  (?1?1?3 ?3?3?1) (?1?1?4 ?4?4?1)/48
• NP3 (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)
  (?4?4?3 ?3?3?4)/8 (?1?1?2 ?2?2?1)/16
  (?1?1?4 ?4?4?1) (?2?2?4 ?4?4?2)/48
  (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)
  (?1?1?4 ?4?4?1) (?2?2?4 ?4?4?2)/96

11
Partial constraint

• Now suppose that only network 4 has capacity
  constraint in the sense it can host only one
  transit purchaser.
• NP1 (?2?2?1 ?1?1?2) (?3?3?1 ?1?1?3)
  (?4?4?1 ?1?1?4)/8 (?1?1?2 ?2?2?1)/24
  (?1?1?4 ?4?4?1)/48
• NP3 (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)
  (?4?4?3 ?3?3?4)/8 (?1?1?2 ?2?2?1)/12
  (?1?1?4 ?4?4?1) (?2?2?4 ?4?4?2)/32 (hub
  with no constraint)

12
Partial constraint

• NP4 (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)
  (?3?3?4 ?4?4?3)/8 (?1?1?4 ?4?4?1)
  (?2?2?4 ?4?4?2)/96 (hub with constraint)
• NP4 (?1?1?3 ?3?3?1) (?2?2?3 ?3?3?2)
  (?3?3?4 ?4?4?3)/8 (?1?1?4 ?4?4?1)
  (?2?2?4 ?4?4?2)/24 (transit purchaser)

13
Investment game
Hub 4
Do not invest Invest
Hub 3 Do not invest , ,
Invest , ,
14
Possibility of peering

• Proposition 3. If peering generates more benefit
  to the interconnecting networks than the
  construction cost, the premium to the hub network
  is reduced. The smaller is the peering cost, the
  smaller the premium becomes. There will be no
  premium if peering is costless.
• NP1 (?2?2?1 ?1?1?2) (?3?3?1 ?1?1?3)/8
  min(?2?2?1 ?1?1?2)/24, F/6 (F
  cost of peering)