{'fraction_non_alphanumeric': 0.03322784810126582, 'fraction_numerical': 0.007383966244725738, 'mean_word_length': 4.77181633688483, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 5, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Resource Management for 5G NR Integrated Access and Backhaul: a Semi-centralized Approach

The next generations of mobile networks will be deployed as ultra-dense networks, to match the demand for increased capacity and the challenges that communications in the higher portion of the spectrum (i.e., the mmWave band) introduce. Ultra-dense networks, however, require pervasive, high-capacity backhaul solutions, and deploying fiber optic to all base stations is generally considered to be too expensive for network operators. The 3rd Generation Partnership Project (3GPP) has thus introduced Integrated Access and Backhaul (IAB), a wireless backhaul solution in which the access and backhaul links share the same hardware, protocol stack, and also spectrum. The multiplexing of different links in the same frequency bands, however, introduces interference and capacity sharing issues, thus calling for the introduction of advanced scheduling and coordination schemes. This paper proposes a semi-centralized resource allocation scheme for IAB networks, designed to be flexible, with low complexity, and compliant with the 3GPP IAB specifications. We develop a version of the Maximum Weighted Matching (MWM) problem that can be applied on a spanning tree that represents the IAB network and whose complexity is linear in the number of IAB-nodes. The proposed solution is compared with state-of-the-art distributed approaches through end-to-end, full-stack system-level simulations with a 3GPP-compliant channel model, protocol stack, and a diverse set of user applications. The results show how that our scheme can increase the throughput of cell-edge users up to 5 times, while decreasing the overall network congestion with an end-to-end delay reduction of up to 25 times.


I. INTRODUCTION
Future generations of cellular networks will provide groundbreaking network capacity, in conjunction with a significantly lower delay and ubiquitous coverage [1]. 5th generation (5G) and beyond deployments will support new mobile broadband use cases, e.g., Augmented (AR) and Virtual Reality (VR), and expand into new vertical markets, enabling an unprecedented degree of automation in industrial scenarios, Vehicle-to-Everything (V2X) communications, remote medical surgery and smart electrical grids.
To this end, the 3rd Generation Partnership Project (3GPP) has introduced various technological advancements with the specifications of the 5G Radio Access Network (RAN) and Core Network (CN), namely NR and 5G Core (5GC) [2]. In particular, NR features a user and control plane split, a flexible Orthogonal Frequency Division Multiplexing (OFDM) frame structure, and the support for millimeter wave (mmWave) communications, while the CN introduces virtualization and slicing [3].
Specifically, the mmWave band, i.e., the portion of the spectrum between 30 GHz and 300 GHz, represents the major technological enabler toward the Gbit/s capacity target. These frequencies are characterized by the availability of vast chunks of contiguous and currently unused spectrum, in stark contrast with the crowded sub-6 GHz frequencies. However, mmWaves exhibit unfavorable propagation characteristics such as high isotropic losses and a marked susceptibility to blockages and signal attenuation [4], [5]. These issues can be partially mitigated using beamforming through large antenna arrays, thanks to the small wavelengths and advances in lowpower Complementary Metal-Oxide Semiconductor (CMOS) RF circuits [6]; nevertheless, their introduction alone is not enough for meeting the high service availability requirement. Therefore, mmWaves networks also need densification, to decrease the average distance between mobile terminals and base stations and improve the average Signal-to-Interference-plus-Noise Ratio (SINR). The theoretical effectiveness of this technique is well understood [7]; however, achieving dense 5G deployments is extremely challenging from a practical point of view. Specifically, providing a fiber backhaul among base stations and toward the CN is deemed economically impractical, even more so in the initial 5G deployments [8].
Recently, wireless backhaul solutions for 5G networks have emerged as a viable strategy toward cost effective, dense mmWave deployments. Notably, the 3GPP has promoted Integrated Access and Backhaul (IAB) [9], i.e., a wireless backhaul architecture which dynamically splits the overall system bandwidth for backhaul and access purposes. IAB has been integrated in the latest release of the 3GPP NR specifications. Prior research has highlighted that IAB represents a cost-performance trade-off [8], [10], as base stations need to multiplex access and backhaul resources, and as the wireless backhaul at mmWaves is less reliable than a fiber connection. In particular, IAB networks may suffer from excessive buffering (and, consequently, high latency and low throughput) when a suboptimal partition of access and backhaul resources is selected, thus hampering the benefits that the high bandwidth mmWave links introduce [8], [11]. Therefore, it is fundamental to solve these non-trivial challenges to enable a smooth integration of IAB in 5G and beyond deployments.

A. Contributions
This article tackles the access and backhaul partitioning problem by proposing an optimal, semi-centralized resource allocation scheme for 3GPP IAB networks, based on the Maximum Weighted Matching (MWM) problem on graphs. It receives periodic Key Performance Indicator (KPI) reports from the nodes of the IAB deployment, constructs a spanning tree that represents the deployment, and uses a simplified, low-complexity version of the MWM to partition the links between access and backhaul. After a feedback step, each node can then schedule the resources at a subframe-level among the connected devices. To the best of our knowledge, this is the first MWM-based resource allocation framework for 3GPP IAB networks at mmWaves, designed with three goals, i.e., it is flexible, integrated with the 3GPP specifications, and has low complexity.
The flexibility makes it possible to easily adapt the resource allocation strategy to different requirements, use cases, and classes of traffic for 5G networks. We achieve this by developing a generic optimization algorithm, which identifies with a configurable periodicity the access and backhaul partition that optimizes a certain utility function. The selection of the utility function prioritizes the optimization of different metrics, e.g., throughput or latency, which in turn can be mapped to different classes of traffic. To achieve the second goal, i.e., the compliance with the 3GPP IAB specifications, the resource allocation framework relies only on information that can be actually exchanged and reported in a 3GPP deployment. In this regard, we also review the latest updates related to the 3GPP IAB standardization activities.
Finally, the algorithm operates with a low complexity, i.e., we propose a version of the MWM algorithm that can be applied on spanning trees with linear complexity in the number of nodes in the network infrastructure, and demonstrate its equivalence to the generic (and more complex) MWM. Additionally, the proposed framework also relies on a feedback exchange that is linear in the number of base stations, and is thus decoupled from the number of users.
Furthermore, we evaluate the performance of the proposed scheme with an end-to-end, fullstack system-level simulation, using the ns-3 mmWave module [12] and its IAB extension [11].
This represents the first evaluation of an optimized resource allocation scheme for IAB with a simulator that is based on a 3GPP-compliant protocol stack, uses 3GPP channel models, and integrates realistic applications and transport protocols. The extended performance evaluation highlights how the proposed scheme improves the throughput of a diverse set of applications, with a 5-fold increase for the worst case users, with different packet sizes and transport protocols, while decreasing the latency and buffering at intermediate nodes by up to 25 times for the smallest packet sizes.

B. State of the Art
This section reviews relevant research on resources allocation in a multi-hop wireless network, deployed through either IAB or other wireless mesh solutions [13].
The literature adopts different approaches to model and solve the resource allocation problem.
The first, discussed in [14]- [20] is based on conventional optimization techniques. Specifically, the authors of [14] present a simple and thus tractable system model and find the minimal number of Next Generation Node Bases (gNBs) featuring a wired backhaul that are needed to sustain a given traffic load. Their work is further extended in [15], which provides an analysis of the performance benefits introduced by additional, fiber-less gNBs. In [16], the mobile network is modeled as a noise-limited, k-ring deployment. Such model is then used to obtain closedform expressions for the max-min rates achieved by User Equipments (UEs) in the network.
Moreover, [17] proposes a system model which leads to an NP-hard optimization problem, even though it considers single-hop backhaul networks only, and uses deep Reinforcement Learning (RL) to reduce its computation complexity. In [18], the joint routing and resource allocation problem is tackled via a Linear Programming (LP) technique. Notably, this work assumes that data can be transmitted (received) toward (from) multiple nodes at the same time. Similarly, the authors of [19] formulate a Time Division Duplexing (TDD), multi-hop resource allocation optimization problem which leverages the directionality of mmWave antennas, albeit in the context of Wireless Personal Area Networks (WPANs). Since such problem is also NP-hard, a sub-optimum solution is found. Finally, [20] focuses on joint link scheduling, routing and power allocation in multi-hop wireless networks. As in previous cases the obtained optimization problem is not tractable: in this instance such obstacle is overcome by studying the dual problem via an iterative approach.
The second approach relies on stochastic geometry to model IAB networks [10], [21]. Specifically, [21] determines the rate coverage probability of IAB networks and compares different access/backhaul resource partitioning strategies. Similarly, [10] provides a comparison of orthogonal and integrated resource allocation policies, although limited to single-hop wireless networks.
Another significant body of literature leverages Markov Chains (MCs) to study IAB networks; some of these works can be interpreted as a direct application of such theory [22], [23], while others [24]- [27] exploit a more complex framework. The papers which belong to the former class are based on the pioneering work of [28], which inspects the stability of generic multi-hop wireless networks and formulates a throughput-maximizing algorithm known as back-pressure. In particular, [22] focuses on the optimization of the timely-throughput, i.e., takes into account that packets usually have an arrival deadline. Such problem is then addressed by formulating a Markov Decision Process (MDP), leading to a distributed resource allocation algorithm. Similarly, [23] proposes an algorithm that also targets throughput optimality but, contrary to the back-pressure algorithm, manages to avoid the need for per-flow information. On the other hand, the body of literature which belongs to the latter class uses the MC-derived Network Utility Maximization (NUM) framework first introduced in [29] and [30]. Specifically, the authors of [24] focus on satisfying the Ultra-Reliable Low-Latency Communication (URLLC) Quality of Service (QoS) requirements by jointly optimizing routing and resource allocation. Then, the problem is solved using both convex optimization and RL techniques. In [25], an in-depth analysis of a mmWave, multi-hop wireless system is presented, proposing and comparing three different interference frameworks, under the assumption of a dynamic TDD system. This work is extended in [26] and [27], which consider respectively a Spatial Division Multiple Access (SDMA) and a Multi-User (MU)-Multiple Input, Multiple Output (MIMO) capable system. Finally, only a small portion of the literature [8], [11], [31] analyzes the end-to-end performance of IAB networks. Specifically, the authors of [11] extend the ns-3 mmWave module, introducing realistic IAB functionalities which are then used to characterize the benefit of deploying wireless relays in mmWave networks. Their work is extended in [31], where path selection policies are formulated and their impact on the system performance is inspected. A further end-to-end analysis of IAB networks is carried out in [8], providing insights into the potentials of this technology and the related open research challenges.
Concluding, the literature exhibits the presence of algorithms relying on a varying degree of assumptions on the network topology and the knowledge of system. Furthermore, most of the aforementioned studies lack an end-to-end, full-stack system-level analysis of the proposed solution. Conversely, this paper proposes a semi-centralized resource allocation scheme, which also has a low complexity, both computationally and in terms of required feedback. Moreover, we provide considerations on how our proposed solution can be implemented and deployed in standard-compliant 3GPP IAB networks, and compare such solution to the state of the art with an end-to-end, realistic performance analysis.

C. Paper structure
The remainder of this paper is organized as follows. Sec. II describes our assumptions and the system model. Then, Sec. III presents a novel scheme for resource partitioning in mmWave IAB networks, along with considerations on how it can be implemented in 3GPP NR. Finally, Sec. IV describes the performance evaluation results and Sec. V concludes this paper.

II. IAB NETWORKS
The following paragraphs identify the characteristics and constraints of mmWave IAB, according to the 3GPP design guidelines presented in [9] and the specifications of [32].

A. Network topology
In general, an IAB network is a deployment where a percentage of gNBs (i.e., the IAB-nodes) use wireless backhaul connections to connect to a few gNBs (i.e., the IAB-donors) which feature a wired connection to the core network, as can be seen in Fig. 1. Moreover, these deployments exhibit a multi-hop topology where a strict parent-child relation is present. The former can be represented by the IAB-donor itself or an IAB-node; the latter by either UEs or downstream IABnodes. In [9], no a priori limit on the number of backhaul hops is introduced. As a consequence, 3GPP argues that IAB protocols should provide sufficient flexibility with respect to the number of backhaul hops. Moreover, the Study Item (SI) on IAB [9] highlights the support for both the topologies depicted in Fig. 1a, i.e., Spanning Tree (ST) and Directed Acyclic Graph (DAG) IAB.
Clearly, the former exhibits less complexity but, at the same time, poses some limits in terms of (a) ST and DAG topologies.
(b) System model notation. Figure 1. Comparison of the IAB network topologies analyzed in [9] and related notation.
network performance: the possible presence of obstacles may result in a service interruption, due to the unique backhaul route established by the UEs. On the other hand, a DAG topology offers routing redundancy, which can be used not only to decrease the probability of experiencing a "topological blockage," but also for load balancing purposes.

B. Multiple access schemes and scheduling
An in-band, dynamic partitioning of the access and backhaul spectrum resources is currently preferred by 3GPP [9], [32], together with half-duplex operations of the IAB-nodes. Moreover, most of the literature suggests that 5G mmWave systems will operate in a TDD fashion [4], [33].
This choice is mainly driven by the stringent latency requirements which the next generation of mobile networks will be required to support, and by the usage of analog or hybrid beamforming. The usage of Frequency Division Duplexing (FDD), in conjunction with the presence of large chunks of bandwidth, would lead to severe resource under-utilization and make channel estimation more difficult.
Based on these considerations, the system model exhibits a TDD, Time Division Multiple Access (TDMA)-based scheduling where the access/backhaul interfaces are multiplexed in a half-duplex manner. It follows that at any given time instant, each node of the IAB network cannot be simultaneously involved in more than one transmission or reception. In particular, IAB-nodes cannot schedule time and frequency resources which are already allocated by their parent for backhaul communications which involve them. Finally, the introduction of resource coordination mechanisms and related signaling is explicitly supported in the IAB specification drafts [9], [32]. Nevertheless, these solutions must reuse as much as possible the available NR specifications and require at most minimal changes to the Rel.15 5GC and NR.

C. System model
According to these assumptions and referring to Fig. 1b . . e |E| } ≡ {e n j →n k } j,k , where the edge e n j →n k originates at the parent node n j and terminates at the children n k , comprises in all the active cell attachments, either of mobile terminals to a gNB or from IAB-nodes towards their parent node. Since the goal of this paper is to study backhaul/access resource partitioning policies, this generic model can be actually simplified: in fact, all the UEs connected to a given gNB can be represented by a single node in G without any loss of generality. Similarly, the same holds true for their links toward the serving gNB, which can then be represented by a single edge. Furthermore, this work focuses on ST topologies only. Nevertheless, the proposed framework can be easily extended to the case of a DAG IAB network: it suffices to introduce a preliminary routing step where an ST G is computed from the actual DAG network G, for example by using the strategies presented in [31]. Such process can be possibly repeated at each allocation instance, effectively removing any constraint on the network topology.
We define as feasible schedule any set of links E ⊆ E such that none of them share a common vertex, i.e., ∀ e n j →n k = e n l →nm ∈ E it holds that n j = n m and n l = n k . Let then f u be a utility additive map, namely, a function such that the overall utility experienced by the system when scheduling edges e 1 and e 2 satisfies f u (e 1 , e 2 ) = f u (e 1 ) + f u (e 2 ). Let also W ≡ {w 1 , w 2 , . . . w |E| } be the set of positive weights whose generic entry w j represents the utility which is obtained when scheduling the j-th edge, namely, w j ≡ f u (e j ). Then, the overall utility of the system is U ≡ e k ∈ E f u (e k ) = e k ∈ E w k . The goal is to find the feasible set E * which maximizes the overall utility, i.e., argmax E U. In computer science, this task is typically referred to as the Maximum Weighted Matching problem [34].
Finding the MWM of a given graph, in the general case, is not trivial from a computational point of view. In fact, the fastest known MWM algorithm for generic graphs has a complexity of O(|V ||E| + |V | 2 log |V |) [35], posing serious limitations to the suitability of such algorithm to 5G and beyond networks, which target a connection density of 1 million devices per km 2 .
However, we argue that under the aforementioned assumptions on the system model, which restrict the network to an ST topology, it is possible to design an MWM-based centralized resource partitioning framework which exhibits linear complexity with respect to the network size and which, as a result, is able to satisfy the scalability requirements highlighted by 3GPP in [9].
III. SEMI-CENTRALIZED RESOURCE ALLOCATION SCHEME FOR IAB NETWORKS This section presents an MWM algorithm for ST topologies (Sec. III-A), an efficient and MWM-based centralized resource partitioning framework for IAB networks (Sec. III-B) and some considerations about its implementation (Sec. III-C).

A. MWM for ST graphs
As the first of our contributions, we present an algorithm, hereby called T-MWM, which computes the MWM of an ST in linear time. In particular, T-MWM is a bottom-up algorithm which, upon receiving as input a weighted ST G described by its edge list E and the corresponding weight list W, produces as output a set of active edges E * which are an MWM of G. Furthermore, E is from now on assumed to exhibit the following invariant: each IAB parent precedes its children in the list, hence avoiding the need for a recursion. This is automatically obtained as each IAB child connects after its parent, and is thus added to the list in a subsequent position.
Nevertheless, this assumption can be easily relaxed, albeit at the cost of losing as a side-effect the bottom-up design.
As can be seen in Alg. 1, the T-MWM algorithm basically performs two traversals. During the first one, the utility yielded by the various nodes and their children is computed. Then, during the second traversal, this knowledge is used for computing an MWM of the network.
The correctness of this procedure can be easily proved. Consider the sub-tree of G whose root is represented by the generic node n k . Let also F(n k ) be the utility yielded by a MWM of such sub-tree which activates a link originating from n k , and G(n k ), conversely, the utility provided when the MWM contains no links which originate from such node. Then, the correctness of the first phase of the algorithm, namely the computation of the F and G vectors, follows directly from the following Lemmas.
Lemma 1. Let n k be an arbitrary internal node of G and {n j } k be the set of its children. Then, any MWM of G must contain an edge which has as one of its vertices either n k or an element of {n j } k .

Algorithm 1 Tree-Maximum Weighted Matching
Input: A weighted ST G encoded by a list E, which associates each node in G to its edges, and the corresponding weights list W.
Output: An MWM E * of G.
Initialize the utility vectors to zero vectors 3: Initialize the set of active edges as empty 4: for each node n k ∈ E do Iterate over the various nodes, in ascending order w.r.t. to their depth in G 5: for each edge e k,j ≡ (n k , n j ) do Iterate over its edges 7: if currU til > maxU til then 10: maxU til ← currU til; maxEdge(n k ) ← e k,j 11: for each node n k ∈ E do Iterate over the various nodes, in ascending order wrt to their depth in G 16: if F(n k ) ≥ G(n k ) then 17: Lemma 2. For any internal node n k : where the set {n j } k comprises all the children of n k . Conversely, for leaf nodes F(n l ) ≡ G(n l ) ≡

0.
Proof: This lemma can be proved by induction over the height h k of the sub-tree corresponding to node n k . The base case is h k = 0, i.e., when n k is a leaf node; in this case, trivially, both F(n k ) and G(n k ) are zero since no links exhibit n k as parent node and the sub-tree of G which originates in n k consists of n k only, respectively.
Consider then the node n k having a sub-tree of height h k > 0. From Lemma 1 we know that either n k or (at least) one of its children must be included in any MWM. If on the one hand we do not activate any edge which originates from n k , then no constraints on the children's activation are introduced. Therefore, in this case the maximum utility is obtained when all the On the other hand, if we activate an edge from n k to one of its children n m then no additional edges which originate from the latter can be added to E * . It follows that the utility obtained in this instance reads: and can be rewritten as: Such utility is maximized when n m is chosen as argmax Finally, the validity of the last phase of T-MWM follows from Lemma 3.
Lemma 3. Given an ST G, let G k be its sub-tree of root n k . Then, an MWM of G can be computed by performing, in a recursive fashion and starting from the root, the following procedure: , add to E * the edge from n k to n m , where the latter is defined as Then, repeat recursively on all the sub-trees corresponding to n k 's children {n j } k s.t. n j = n m and on the children of n m itself.
2) If F(n k ) < G(n k ), repeat recursively on all the sub-trees which exhibit the children of n k as their root.
Proof: This Lemma follows directly from the definitions of F and G and the previous Lemmas. Specifically, the above procedure always yields a feasible activation, i.e., a matching of G. In fact, in either options we never recurse on a node which has already been activated, hence no pair of edges ∈ E can share any vertices. Furthermore, due to the properties of F and G and their validity for each sub-tree in G, the edges of E * comprise a maximal matching, i.e., they yield the maximum possible utility among all the feasible schedules.
Regarding the computational complexity of the proposed algorithm, it can be observed that instance by using the policies of [31], and assume that a central controller is installed on the IAB-donor. It is important to note that since G contains only the IAB-nodes, the donor and at most one

C. Implementation of centralized allocation schemes in mmWave IAB networks
The remainder of this section discusses how the proposed scheme can be implemented in IAB deployments, with references to how the 3GPP specifications can support it.
Basically, the resource allocation framework requires (i) a central controller, which is installed on the IAB-donor, or could be deployed in a RAN Intelligent Controller (RIC) following the O-RAN architecture [36]; and (ii) a scheduler which exchanges resource coordination information with the former and computes the weights for the resource allocation. In particular, referring to the aforementioned phases of the proposed scheme, the following implementation considerations can be made.

1) Initial setup:
The setup of the various centralized mechanisms is subdivided into two subphases: an initial configuration, where the relevant entities are initialized, and a periodic update of the topology information. The former takes place when the IAB-nodes are first connected to the network. During this phase, the controller acquires preliminary topology information, by leveraging the configuration messages which are already exchanged during the usual Rel.16 IA procedure, generating a map which associates the depth in the IAB network to a pair of child-parent global identifiers (which from now on will be referred to as "IDs"). Since this phase takes place when no UE has performed its IA procedure yet, the exchanged topology information concerns the donor and IAB-nodes only.
Moreover, the central controller is in charge of periodically updating the topology information.
In order to minimize the signaling overhead, this process does not require any additional control information: in fact, the status information which is already collected in a periodic manner can be leveraged in such regard. Specifically, the periodic info received from the various IAB-nodes, which will carry a list of ID-value pairs, is analyzed. The child-parent associations are then compared with the ones known by the controller, updating the latter whenever the two topology information happens to differ. In particular, the CQI and BSR information is generated by analyzing the corresponding CEs which are received by the host gNB, and checking whether the source Radio Network Temporary Identifier (RNTI) belongs to an IAB-node or to a UE. In the first case, the corresponding ID is retrieved and an entry carrying such identifier along with its CQI/BSR value is generated.  2) Backlog Avoidance (BA). This resource partitioning strategy aims at avoiding congestion. Therefore, the system utility is: where the weight w i, k reads q i, k , namely, the amount of buffered data which would reach its next hop in the IAB network by crossing the link e i→k .
3) Max-Rate Backlog Avoidance (MRBA). This represents the most balanced option among the three, since it exploits favorable channel conditions while also preventing network congestion and favoring network fairness. The weight assigned to link e i→k is: where η, µ thr and k are arbitrary parameters and µ represents the number of subframes which have elapsed since the last time edge e i→k has been marked as favored.
Once For instance, the gNBs are free to override these indications whenever the buffer of the favored child is actually empty, due to discrepancies between its actual status and the related information available to the controller. In such a way, the unavoidable delay between the information collection and the reception of the scheduling does not lead to any resource underutilization.
Moreover, this is achieved with minimal changes to the state of the art schedulers, making the proposed scheme relatively easy to implement and deploy in real-world networks.

IV. PERFORMANCE EVALUATION
We implemented the proposed resource allocation scheme in the popular open source simulator ns-3, exploiting the mmWave module [12] and its IAB extension [11], to characterize the systemlevel performance of the proposed solution with realistic protocol stacks, scenarios, and user applications.
The ns-3 mmWave module is based on [39] and introduces mmWave channel models, including the 3GPP channel model for 5G evaluations [40], and highly customizable PHY and MAC layer implementation, with an NR-like flexible OFDM numerology and frame structure. Additionally, the IAB module [11] models wireless relaying functionalities which mimic the specifications presented in [9]. Specifically, this module supports both single and multi-hop deployment scenarios, auto-configuration (within the network) of the IAB-nodes and a detailed 3GPP protocol stack, allowing wireless researchers to perform system-level analyses of IAB systems in ns-3.
It is of particular relevance to understand how the scheduling operations are implemented in the IAB module, since they offer not only the baseline for the proposed scheme, but also valid guidelines for real-world deployments. The current ns-3 IAB schedulers exhibit a TDMA-based multiplexing between the access and backhaul interfaces. Moreover, scheduling decisions are undertaken in a distributed manner across the IAB network, i.e., each gNB allocates the resources which its access interface offers (to both UEs and IAB-nodes) independently of the other gNBs in the network. In fact, in an IAB network these scheduling decisions are almost independent of one another: if a parent node schedules the backhaul interface of a downstream node, clearly the latter will be constrained in its own scheduling decisions, as it will not be allowed to allocate the time resources which have already been scheduled for backhaul transmissions by its parent.
Therefore, in a tree-based, multi-hop wireless network the various gNBs need to know in advance the scheduling decisions performed by their upstream nodes: to solve this problem, the authors of the IAB module for ns-3 introduced a "look-ahead backhaul-aware scheduling mechanism" [11]. any node from the donor. In such a way, the DCIs will have time to propagate across the IAB network and reach the farthest node at time T − 1, thus allowing its scheduler to perform the resource allocation process at least one radio subframe in advance.

A. Simulation scenario and parameters
The purpose of these simulations is to understand the performance of the proposed resource partitioning framework in the context of its target deployment, i.e., a multi-hop IAB network.
As a consequence, the reference scenario consists of a dense urban deployment with a single IAB-donor and multiple IAB-nodes, as depicted in Fig. 4a. In particular, the various gNBs are distributed along an urban grid where the donor is located at the origin while the IAB-nodes are deployed along the street intersections, with a minimum inter-site distance of 100 m. The IAB-nodes attachments are computed using the so-called HQF policy presented in [31]; however, this choice does not introduce any loss of generality since such parameter is fixed for all the runs. A given number of UEs are deployed within the surroundings of these base stations, with an initial position which is randomly sampled from circles of radius ρ and whose centers are the various gNBs.
Both the IAB-donor and the IAB-nodes are equipped with a phased array featuring 64 antenna elements, and transmit with a power of 33 dBm; conversely UEs are equipped with 16 antenna elements and their transmission power is restricted to 23 dBm. Notably, the presence of additional antenna elements at the gNBs is a key (but reasonable) assumption, as it allows base stations to achieve a high beamforming gain. In turn, it is possible to achieve a high capacity, which is fundamental to avoid performance bottlenecks, given the absence of a fiber backhaul. The UEs download data which originates from sources that are installed on a remote host; both the User Datagram Protocol (UDP) and the Transmission Control Protocol (TCP) are used. For the UDP simulations, the rate of the sources is varied from 4 to 40 Mbps to introduce different degrees of saturation in the network. Therefore, in these simulations only DL traffic is considered. Finally, the performance of the proposed policies is hereby compared with the baseline of [11], indicated as "Dist." by examining end-to-end throughput, latency, and a network congestion metric.

B. Throughput
The first metric which is inspected in this analysis is the end-to-end throughput at the application layer. As a consequence, only the packets which are correctly received at the uppermost layer of the destination node in the network are taken into account. In particular, for each UE and each simulation run, the long-term average throughput is computed as follows: where B(t, j) is the cumulative number of bits received up to time t by the k-th UE, during the n-th simulation run. Then, the distribution of S APP , namely, the vector containing the collection of the S APP k,n values across the different runs and UEs, is analyzed. Figs. 5a and 5b report the Empirical Cumulative Distribution Function (ECDF) of S APP , for a UDP packet size of 100 and 500 bytes, respectively, and the policies introduced in Sec. III-C. In the former, we can notice that the introduction of the centralized framework increases by up to 15% the percentage of UEs whose throughput matches the rate of the UDP sources. Moreover, by focusing on the leftmost portion of Fig. 5a we can observe another interesting result, concerning the throughput experienced by the UEs which do not fulfill their QoS requirements. In fact, with respect to the first quartile the distributed scheduler achieves the worse performance, with 25% of the UEs obtaining a throughput smaller than 3.3 Mbps. The centralized framework significantly improves these results, even though the extent of such improvements varies quite dramatically across the different policies. Compared with the distributed case, the MSR policy achieves a higher throughput with respect to all the percentiles, albeit exhibiting the same high variance of the former. Instead, the BA and MRBA policies have a dramatic impact on the system performance, introducing a 5-fold increase of the worst case throughput coupled with a significantly lower variance.  By increasing the UDP packet size to 500 bytes, the network becomes noticeably saturated, as depicted by Fig. 5b;  (b) Third quartile. Figure 6. End-to-end throughput quartiles, for sUDP ∈ {50, 100, 200, 500} B.
Moreover, we can say that in a saturated network the congestion is so severe that prioritizing the bottleneck links is not enough: we also need to take into account the channel conditions and prioritize the links which not only are congested, but also have the "biggest chance" of getting rid of the buffered data due to the temporary better channel quality.
Finally, Fig. 6 presents the first and third quartiles of S APP as a function of the UDP packet size s U DP . It can be noted that, with respect to the first quartile, the MRBA outperforms all the other policies by delivering a throughput which is up to 90% higher than the one obtained by the distributed scheduler. In fact, Fig. 6b shows how MRBA achieves also the best third quartile, albeit the improvement over the distributed solution is less dramatic. Furthermore, we can observe how the positive impact of the BA strategy is inversely proportional to the saturation in the network. We can then conclude that the bias it introduces loses its effectiveness as the buffering phenomena start to affect the majority of the IAB-nodes.

C. Latency
Just like the aforementioned metric, the latency is measured end-to-end at the application layer.
Thanks to this choice, the resulting delay accurately represents the system-level performance, as it includes the latency which is introduced at each hop in the IAB network.
In particular, for each packet correctly received at the uppermost layer of its final destination, the following quantity is traced:  These trends are exacerbated by Fig. 7b, which shows the third quartile of D APP as a function of the UDP packet size s U DP . In fact, we can notice that the effectiveness of the BA policy is inversely proportional to the network saturation; the opposite holds true with respect to the MSR strategy. It follows that, for UDP rates in the order of 5 to 10 Mbps, the network is mainly plagued by local congestion which causes the insurgence of buffering in some of the nodes.
Conversely, as the rate of the UDP sources increases the system shifts to a capacity-limited regime, a phenomenon which explains the dominance of the MSR and MRBA policies.

D. Network congestion
The network congestion is measured by collecting, every T alloc subframes, the RLC buffers status of the various nodes into the vector B RLC . It must be noted that, since RLC Acknowledged Mode (AM) is used, these values will indicate data which is related to both new packets and possible retransmissions.  Figs. 8a and 8b show the median of B RLC , for traffic flows whose next hop in the network is represented by either UEs or IAB-nodes respectively. The BA strategy achieves the worst performance in this metric, leading to unstable systems in the cases of s U DP = {200, 500} B. A reason for this behavior can be found in the "locality" of the BA policy criteria and the lack of influence of the past allocations on the weights. These characteristics may lead to favoring the same link in a repeated manner, hence offering little remedy to the end-to-end congestion. On the other hand, the buffer occupancy achieved by the MSR strategy depicts a system behavior which, in accordance with previous observations, is extremely similar to that of the distributed case. Interestingly, with these configurations the network congestion occurs primarily at the donor and, in general, on the backhaul links towards IAB-nodes. This phenomenon can be explained as follows: even though, on average, the channel qualities of the backhaul links experience a better SINR, the maximum number of such links which can be concurrently activated is limited, due to the TDD configuration. Therefore, the MSR policy may introduce a bias towards the access links instead, since their activation yields the highest sum capacity, despite their lower channel quality. Finally, the MRBA policy achieves the lowest amount of RLC buffering. Specifically, Fig. 8b shows that, compared to the MSR and distributed strategies, the median buffer occupancy among backhaul links is up to 60% smaller, albeit at the cost of slightly more congested UE buffers.
Finally, Fig. 8c depicts the third quartiles of B RLC as a function of the depth of the corresponding gNB in the IAB network. It is possible to notice that, regardless of the policy in use, 500 1,000 1,500 2,000 0   prioritization of the most congested links and of the channels featuring a higher quality results in performance benefits in the average case, although it also causes a decrease of the network fairness. On the other hand, the MRBA policy manages to optimize the backhaul/access resource partitioning, while introducing an increase in the throughput fairness at the same time.

F. Further considerations
It is of particular relevance to analyze the performance of the centralized policies when relaxing the most restrictive hypothesis, i.e., the capability of reliably exchanging feedback information in a timely manner, and to understand how restrictive such assumption actually is. To such end, Fig. 10a shows the performance of the proposed framework as a function of the centralized allocation period T alloc . In particular, each of the depicted points represents the joint end-to-end throughput and delay achieved with the different configurations. As expected, in general the effectiveness of the various centralized policies progressively deteriorates as the frequency of the scheduling indications decreases. Interestingly, the BA policy exhibits the lowest performance degradation with respect to an increase of the allocation period, which suggests that this phenomenon has a slower evolution over time compared to the one exhibited by the channels quality. Nevertheless, the key takeaway is that all of the proposed allocation strategies outperform the distributed solution, across both metrics. However, the trend depicted by Fig. 10a also suggests that there exists a threshold value of T alloc after which the performance of the proposed frameworks brings only marginal performance benefits.
Additionally, the running time of the MWM algorithm presented in Sec. III-A was analyzed, in order to understand whether it may partially invalidate the timely feedback assumption.
Specifically, Fig. 10b presents the statistics of the various MWM execution times, obtained on a machine equipped with an i7-6700 4-core processor clocked at 3.4 GHz. The first observation which can be made is that this empirical analysis confirms the previously estimated asymptotic complexity, depicting a running time which exhibits a linear dependence on the number of gNBs in the network. Furthermore, it can be noted that the runtime of the MWM algorithm does not exceed 6 µs, even for a significant number of IAB-nodes connected to the same IAB-donor. As a consequence, we can conclude that the execution times of the centralized allocation process do not pose any threat to the timely feedback assumption, since they are reasonably smaller than the duration of the minimum centralized allocation period.

V. CONCLUSIONS
In this paper we proposed a centralized resource partitioning scheme for 5G and beyond IAB networks, coupled with a set of allocation policies. We showed that the introduction of this light resource allocation cooperation dramatically improves the end-to-end throughput and delay achieved by the system already, preventing (or at the very least limiting) the insurgence of network congestion on the backhaul links. Specifically, the MRBA policy exhibits the most promising results, offering up to a 5-fold increase in the worst-case throughput and approximately a 50% smaller worst-case latency, compared to the distributed scheduler. On the other hand, the effectiveness of the BA and MSR policies varies quite significantly across the specific system configuration and inspected metric.
We provided considerations on the implementation of a centralized resource allocation controller in real world deployments. In particular, we acknowledged that the proposed scheme relies on the assumption of IAB-nodes being capable of exchanging timely feedback information with the IAB-donor. Even though the amount of signaling data which the proposed solution requires is quite low, and its performance is quite robust with respect to an increase of the central allocation period, we argue that this remains a significant constraint. Moreover, such drawback is exacerbated by the unfavorable mmWaves propagation characteristics. As a consequence, we deem that centralized solutions, which rely on timely exchange of control information with the IAB-donor, are likely to require dedicated control channels, possibly at sub-6 GHz, in order to grant the utmost priority and reliability to the feedback information. Therefore, we can conclude that the aforementioned framework can bring dramatic performance benefits to IAB networks, although its introduction in 5G and beyond deployments requires additional research efforts.
For this reason, as part of our future work we plan to design machine-learning algorithms which predict the network evolution at the IAB-donor. This improvement will allow us to relax the timely feedback assumption, by increasing the minimum centralized allocation period which leads to performance benefits over distributed strategies. Moreover, we foresee to implement mechanisms which adapt the parameters of the MRBA policy to the system load and configuration, and additional resource partitioning strategies. Finally, the generalization of the proposed framework to SDMA systems will be studied. The use of such multiple access scheme should significantly improve the performance of mmWave wireless backhauling by introducing the possibility of concurrently serving multiple terminals, provided that they exhibit a sufficient distance among them.