Exact(8)
The dynamic optimization procedure in optimal control theory provides the optimal time courses for "state variables", or the size of the subsystems among which finite resources are allocated, by finding the optimal time path for a "control variable", or resource allocation rate [48].
Under this scheduler, assume that every user's average resource allocation rate in macro-cell i is the same.
Under this setup, the average resource allocation rate and the average throughput of user k are r_{i,k} = w_{i,k} (11).
Under this scheduler, assume that every user's average resource allocation rate in small cell i is the same as r_{i,k} = frac{1}{|{mathcal{U}}_{i}|}.
In this case, assuming that each user in a given user set (({mathcal {V}}_{i}) or ({mathcal {W}}_{i})) has the same average resource allocation rate, the corresponding average resource allocation rate is given as r_{i,k} =left{ begin{aligned} &frac{ 1-alpha)}{|{mathcal{V}}_{i}|} ~~ text{if}~~ kin{mathcal{V}}_{i} &frac{ 1-alpha{mathcal{W}}_{i}|{mathcal{V}ext{if}~~ k in {mathcal{W}}_{i}|
Consequently, the average resource allocation rate of user k is equivalent to (17), and the average throughput for ({mathcal {V}}_{i}) and ({mathcal {W}}_{i}) are S_{i,k}({mathcal{V}}_{i},{mathcal{W}}_{i}) = sum_{bin{mathcal{A}}_{alpha}} H_{i,k,b} (28).
Similar(52)
In addition, from (11), we see that the average resource allocation rates among the users can be easily controlled by adjusting {w i,k } and their corresponding throughput performances.
For reference, we adopt a 1 Hz resource allocation update rate as the optimal update rate, i.e. the arrival process is statistically time-homogenous within in the interval of one second.
Finally we consider the effect of a non-optimal resource allocation update rate.
The work done in [16, 17] jointly addresses resource allocation and rate adaptation for Scalable Video Coding SVCC) traffic.
The impact of channel state information (CSI) uncertainty and non-optimal resource allocation update rate to the algorithm is studied.
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