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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)=μ1μi 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)=μkμi 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