Fair Resource Allocation in Virtualized O-RAN Platforms

O-RAN systems in virtualized platforms (O-Cloud) offer performance boosts but also raise energy concerns. This paper assesses O-Cloud's energy costs and proposes energy-efficient policies for base station (BS) data loads and transport block (TB) sizes. These policies balance energy savings and performance fairly across servers and users. To handle the unknown and time-varying parameters affecting the policies, we develop a novel online learning framework with fairness guarantees that apply to the entire operation horizon of the system (long-term fairness).


SYSTEM MODEL AND FAIRNESS REGRET
The assignment policy is updated at the beginning of each slot  subject to a simplex constraint for each vBS and shapes the system performance during that slot.If the controller assigns more load to a server than its capacity, then (part of) this data will not be processed before its deadline, and the associated vBSs will suffer reduced throughput.We use the cost reduction function   to model the energy cost savings for the servers at each slot.The goal of the controller is to devise a sequence of assignment policies {}   =1 to achieve a two-sided fairness criterion: (i) fairness w.r.t. the average utility   perceived by the vBSs over the horizon T ; and (ii) fairness w.r.t. to the average energy cost savings of servers.For the fairness criteria, we employ the generalized -fairness function: We evaluate the efficacy of the assignment policies using the metric of static regret which is extended here to capture the two-sided horizon fairness as follows: where  ★ is a hypothetical benchmark that could be only devised with access at  = 0 to all loads, capacities, and functions.Unfortunately, off-the-shelf (online) convex optimization algorithms cannot be applied directly to this problem, due to the time-averaging in the argument of functions   (•) and   (•), which does not allow the necessary (for these techniques) decomposition over time.
, which we will tackle with a saddle-point algorithm that updates the primal and dual variables successively.We start with the analysis of the learning in the dual 1 spaces.The proposed Optimistic FTRL update for this problem is   +1 = arg min  ∈Θ  1: ( ) +  ⊤ ( 1: + κ+1 ) , where  1: ( ),  1: are the aggregate dual regularizing function and dual gradient; and κ+1 denotes the gradient prediction.The dual Algorithm 1 Fair and Balanced Assignment Policy (non-RT RIC) where      ,1: +   ,1: + g , +1 + w , +1 .8: end for The dual regret is bounded as This result improves the optimistic regret bound of quadratic regularizers by enabling constant regret O (1) in the case of perfect predictions.For the primal update, we employ entropic regularization due to the multi-simplex structure of X.The update for this problem is   +1 = arg min  ∈ X  1: () −  ⊤  1: +  1: + g+1 + w+1 where  1: (),  1: and  1: are the aggregate regularization and aggregate primal-space gradients; and g+1 and w+1 are the gradient predictions.The proposed entropic regularizer for this multi-  even when the predictions are maximally inaccurate.Moreover, we perform the primal and dual updates in a closedform manner (step 8).This allows us to run the updates with O (1) memory and computation time.The detailed steps are summarized in Algorithm 1 and the regret guarantee is described next.
Theorem 2.1.Algorithm 1 attains regret: Discussion.Observe the last two terms in the regret bound depend on the type of the adversary, and remain sublinear under certain general conditions.The first three terms of the regret bound are eliminated when the predictions are perfect.This reveals that predictions expedite the learning process while we retain the worstcase guarantees when they are inaccurate.At the same time, the Algorithm 2 Fair and Cost-efficient minTB Policy (near-RT RIC) Compute gradients   ,   , obtain predictions s+1 ,   +1 5: Compute   +1 and   +1 using the dual update of Algorithm 1. 6: end for s 2 a A i 4 T e 0 6 q 9 e P W N 5 0 0 P p q e + e k E M U 4 j w h k m q M 2 P S j I B V E x 2 S 8 N e l y i U y L o Q H K J D e z E t a n k j J t b m O b I 7 i z K 8 9 D / a j k n p S O q 0 6 x f A l T 5 W E P 9 u E Q X D i F M l x D B W r A A O E e H u H J u r U e r G f r Z V q a s 3 5 6 d u G P r N d v 3 R K P + w = = < / l a t e x i t > 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " p q j I d u Z l 7 S J D  algorithm is oblivious to user demands, system state (e.g., costs and available capacity), and channel conditions.These two features, along with its general convergence properties, make the proposed framework particularly useful from a practical point of view.As a last note, we wish to stress that our work advances the stateof-the-art by using closed-form expressions and predictions, and importantly by combining two different fairness metrics.

FAIR SERVICE OF USERS AND VBS COST MINIMIZATION
Now, we study how to minimize the energy cost at the O-Cloud while the users are served fairly in terms of latency, by controlling the radio resource assignment, i.e., the TB size.Setting a threshold for the minimum TB size, the vBS prevents short TB transmissions that increase the energy cost.On the other hand, such thresholds introduce waiting times for users to accumulate data to fill the TBs.The minTB strategy   is decided by the vBS at the beginning of each slot in order to balance the service latency and its energy cost when processing the transmitted data.We consider a general model where the utility function   denotes the performance perceived by user  when the minTB strategy is   .Furthermore, we denote with   the vBS energy cost.  .
Discussion.The regret bound in the above Theorem verifies that the proposed OFTRL framework can deliver, also for this scenario, the desirable performance.The execution of Algorithm 2 is lightweight as one can readily devise closed-form updates and is suitable for the near-RT RIC.

R𝒖
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