Page 175 - Proceedings of the 2017 ITU Kaleidoscope

Challenges for a data-driven society

1 − ρ m 4.1. Constraints for Feasibility of Contracts
π 0 = (8)
L m +1
1 − ρ m
Definition 1. Individual Rationality (IR) constraints are de-
where ρ m = λ/µ m .
fined to ensure that the utility U θ i of user θ i is non-negative
According to LRU cache strategy, the cache hit rate in node if the user chooses the contract (q (θ i ) , T (θ i )). We have
n m with cache capacity C m is hit(C m ). When the requested
contents are in the relay routing node n m , the transmission
1 1
delay can be defined by w ln 1 + θ i q (θ i ) + (1 − θ i ) q (θ i ) − T (θ i ) ≥ 0
d 1 d 2
m−1 m−1 (15)
X int X wai dat
int
int
d(m) =d MC + d MC,1 + d j,j+1 + (d j + d j+1,j )
j=1 j=1
Definition 2. Incentive Compatible (IC) constraints are to
+ d dat + d dat maximize the users’ utilities when the user chooses a contract
1,MC
MC
(9) (q (θ i ) , T (θ i )).
Thus, the cache hit rate in the relay routing node n m can be 1 1
w ln 1 + θ i q (θ i ) + (1 − θ i ) q (θ i ) − T (θ i ) ≥
described as follows: d 1 d 2

w ln 1 + 1 θ i q (θ j ) + 1 (1 − θ i ) q (θ j ) − T (θ j ) ,
m−1 d 1 d 2
Y
pr(m) = hit(C m ) (1 − hit(C j )) (10) ∀i, j ∈ {1, · · · , I} , i 6= j
j=1 (16)
Therefore, the delivery delay of the user achieving contents
from CCNs can be obtained by User θ i prefers to choose the contract designed specifically
for its own type to maximize its own utility. And the contract
M M is feasible only if the IR and IC constraints are all satisfied.
X Y
d 2 = d(m) × pr(m) + (1 − hit(C m )) × d (11)
m=1 m=1
The utility function of user θ i can be defined by: 4.2. Optimal Contract
= v (q (θ i )) − T (θ i ) (12) Firstly, we need to simplify the IR and IC constraints to re-
U θ i
duce the computational complexity. Then, the optimal edge
where v (q (θ i )) is the satisfaction degree of user θ i by ob- cache strategy is proposed based on Lagrangian function.
taining contents with the capacity of q (θ i ). User’s satisfac-
Step 1. Reduce IR and IC Constraints
tion degree v (q (θ i )) can be derived from
We can see that there are I IR constraints in this scheme.

1 1 Theorem 1. If the users’ IC constraints are satisfied, users’
v (q (θ i )) = w ln 1 + θ i q (θ i ) + (1 − θ i ) q (θ i )
d 1 d 2 IR constraints can be simplified by
(13)
1 1

Here, w > 0 which is an adjustment parameter. The us- w ln 1 + θ 1 q (θ 1 ) + (1 − θ 1 ) q (θ 1 ) − T (θ 1 ) ≥ 0
d 1 d 2
er’s satisfaction increases with the capacity of q (θ i ). On the
(17)
contrary, the user’s satisfaction will decrease when the trans-
mission delay increases. Given a contract (q (θ i ) , T (θ i )),
the operator will charge user θ i with the price T (θ i ). We de- Definition 3. Spence-Mirrless single crossing condition can
fine U to be the utility of the content provider, which can be reduce the number of constraints efficiently, which can be
defined by described as follows
I ∂ ∂u/∂q
X [− ] > 0 (18)
U = p i (T (θ i ) − c 1 θ i q (θ i ) − c 2 (1 − θ i ) q (θ i )) (14) ∂θ ∂u/∂T
i=1
where p i is the proportion of type θ i , c 1 denotes the loss coef- The number of IC constraints reduces significantly when the
ficient for SBSs to provide users with contents and c 2 denotes users’ utilities satisfy Spence-Mirrless single crossing pover-
the loss coefficient for CCNs to provide users with contents. ty.
Theorem 2. The monotony of the capacity q(θ i ) and the suf-
4. PROPOSED SOLUTION ficiency of local incentive constraints are established when
the Spence-Mirrless single crossing condition is satisfied.
In this section, we propose a contract theory based caching Definition 4. For the contract (q (θ i ) , T (θ i )) of user θ i ,
scheme to improve the performance of CCNs. ∀θ i > θ j , q (θ i ) > q (θ j ).

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