To show ( δ 4 ), assume that t n ↓ 0 and − ln ( α ( t n ) ) ≤ ln t n − ln t n + 1 ∀ n ∈ N. Then t n + 1 ≤ α ( t n ) t n for each n ∈ N. Since lim sup t → 0 + α ( t ) < 1, then there exist n 0 ∈ N and 0 < r < 1 such that α ( t n ) < r for n ≥ n 0. Thus, t n + 1 ≤ r t n for each n ≥ n 0, and so ∑ n = 1 ∞ t n < ∞.
By (12), we may find a sequence ( t n ), t n → ∞, such that inequality (13) is satisfied for each t n.
[19]Let {s n } and {t n } be two nonnegative sequences satisfying sn+1≤ s n + t n for each n ∈ ℕ.
In each time slot, the dynamic cost index V n (t) of each user is updated as follows, ∀ n ∈ N V V n ( t ) = V n ( t − 1 ) + δ ( Q n, target − Q n ( t ) ), (12).
Alternatively, we set a target queue length Qn,target for each user, and correspondingly a dynamic cost index V n (t) for each user.
( mathbb{G} ) is a tuple (V, ℕ, (S i ) i ∈ ℕ, (U i ) i ∈ N, T) at each time period t of gameplay.
Separate loess plots of the N t for each day-of-the-week verified that all significant day-of-the-week effects were captured by D t.
Assume that the MBS is equipped with N t m antennas; each RRH BS is equipped with N t r antennas and each user is equipped with a single antenna, as shown in Figure1.
The CBS has N t antennas, and each SU is equipped with N r antennas.
Since there are O(n T) subproblems and each subproblem can be solved in O time, | P ́ T ( v ) | can be obtained in O(n T Δ) time.
It is assumed that the eNodeB has N t antennas and each onboard transceiver has one single antenna.
