Table 1 List of notations used through the paper
From: Distributed algorithm under cooperative or competitive priority users in cognitive networks
n | Total number of time slots |
|---|---|
U and C | Number of users and channels respectively |
Si(t) | Observed state of the ith channel at slot t |
ri(t) | Reward obtained from the ith channel at slot t |
μ1 and μi | Availability of the best and ith channels respectively |
Δ(1,i)=μ1−μi | Difference between the best and worst channels |
β(t) | Channel selected at slot t using a policy β for single or multiple-users cases |
Ti(t) | Number of times the ith channel was sensed up to slot t |
Xi(Ti(t)) | Exploitation contribution of the ith channel that depends on Ti(t) |
Ai(t,Ti(t)) | Exploration contribution of the ith channel that depends on t and Ti(t) |
Bi(t,Ti(t)) | Index assigned of the ith channel that takes into consideration the availability |
α | Exploration-exploitation factor |
Sβ(t)(t) | Global reward obtained by all users at slot t from the selected channels β(t) |
Ii,j(t) | Non-collision in the ith channel under the jth user at slot t |
Pi,j(n) | Total number of non-collision in the ith channel under the jth user up to n |
qi(t) | Quality of ith channel at slot t |
Gi(Ti(t)) | Quality collected from the ith channel up to slot t |
Gmax(t) | Maximum expected quality over channels up to slot t |
Qi(t,Ti(t)) | Quality factor that depends on t and Ti(t) |
\(B^{Q}_{i}(t,T_{i}(t))\) | Index assigned of the ith channel that takes into consideration both availability and quality |
γ | Weight of the quality factor |
\(\mu ^{Q}_{i}\) | Global mean reward of the ith channel that takes into consideration both availability and quality |
OU(n) | Total number of collisions in U-best channels up to n |
p | Probability of non-collision in best channels |
Appendix | |
Δ(k,i)=μk−μi | Difference between the kth best channel and the ith one |
OC(n) | Total number of collisions in all channels up to n |
Oi(n) | Total number of collisions in the ith channel up to n |
Dk(n) | Total number of collisions under the kth priority user up to n |
\(T^{\prime }_{k}(n)\) | Total number of times where the kth user badly identifies its dedicated channel, the kth best one |
Ss | Needed time for a user to return to its prior rank |
\(T_{B_{i}>B_{k}}(n)\) | Total number of times in which the index of the ith channel exceeds the kth best one up to n |
\(T_{B_{m}<B_{k}}(n)\) | Total number of times in which the index of the kth best channel exceeds the mth best one up to n |