P2P storage trading system

(A preliminary idea)

Presenter: Lin Wing Kai (Kai)

Model

Peers join the system to perform the file replication.The files have intrinsic popularities.When a peer replicate a file, he can earn some credits. Intrinsic popularities Number of peers replicating the file.

Each peer will have a fixed storage space.The goal of each peer is to replicate the set of files so that the peer can earn the most credits.

Assumptions (I)

An incentive system is possible for peers to earn credits based on replication.

Perfect information on the market. Peers can estimate the intrinsic file

popularities correctly. Peers know each other replication

decision.

Terminologies (I)

N peers in the system, indexed by i. P = {1, 2, … i, …, N} Peer has storage space si

K files in the system, indexed by j. F = {1, 2, … j, …, K}

Each file has intrinsic popularity lj L = [lj], j = {1… K}, lj =[0, 1]

File replication vector Ri Ri = [ri,j: ri,j = 1 when peer i replicate file j] Ri is a vector of length K.

Terminologies (II)

The file replication matrix M, is a NxK dimensional matrix. Row vector is the file replication vector Ri of peer i. Column vector Uj indicate the set of peers that replicate file j.

KNN

K

rr

r

rrrr

M

,1,

1,2

,13,12,11,1

...

.....

....

... =Ri

=Uj, uj = sum(Uj)

Terminologies (III)

uj is the number of peers replicate file j. File popularity normalized function f (lj, u

j) lj = f(lj, uj) Peers earn credits of a file equal to its nor

malized popularity lj.

Simulation setup

20 peers Each peer has 10 units of storage space.

500 files Each file cost 1 unit of storage space. File popularities are uniform in [0, 1]

Normalized function f() = lj/ uj

One peer makes his replication decision at each iteration.

Results (A - I)

The credits gained by each peer:

The credits converge

Results (A - II)

The normalized files credits:

These files are replicated

Simple observations

An equilibrium exists in the system. Peers earn approximate the same credits. Equilibrium converge very fast.

At equilibrium, the files can be divided into two types: Some files are replicated. These files have

similar normalized file popularities. Some files are not replicated.

Plausible explanation

In the homogeneous peers environment, we expect all peers can earn similar credits because: If peer i1 can find a “method” to earn

more credits than i2, i2 can simply use the same method to earn more credits than i1.

For example, copy cat strategy.

Simulation B

Partial information in the market. Peers can still estimate the file intrinsic

popularities. Peers do not know other peers decision.

The credits of a file are determined by the peers. Each peer can set the file credits a certain

value. Another peer join to the system and if he see

this price, he simply set the price lower by delta.

Results (B - I)

The credits gained by each peer:

Extension

Perfect information is unrealistic: Peers do not know the action by other

peers. Peers do not know the file popularities. The file popularities are estimated from

the peers demand characteristics.

How to characterize the system equilibrium in this case?

Thank you

~ END~