Cost-Aware DU Placement and Flow Routing in 5G Packet xHaul Networks

Packet-switched xHaul networks based on Ethernet technology are considered a promising solution for assuring convergent, cost-effective transport of diverse radio data traffic flows in dense 5G radio access networks (RANs). A challenging optimization problem in such networks is the placement of distributed processing units (DUs), which realize a subset of virtualized baseband processing functions on general-purpose processors at selected processing pool (PP) facilities. The DU placement involves the problem of routing of related fronthaul and midhaul data flows between network nodes. In this work, we focus on developing optimization methods for joint placement of DUs and routing of flows with the goal to minimize the overall cost of PPs activation and processing in the network, which we refer to as the PPC-DUP-FR problem. We account for limited processing and transmission resources as well as for stringent latency requirements of data flows in 5G RAN. The latency constraint makes the problem particularly difficult in a packet-switched xHaul network since it involves the non-linear and dynamic estimation of the latencies caused by buffering of packets in the switches. The latency model that we apply in this work is based on worst-case calculations with improved latency estimations that skip from processing the co-routed, but non-affecting flows. We use a mixed-integer programming (MIP) approach to formulate and solve the PPC-DUP-FR optimization problem. Moreover, we develop a heuristic method that provides optimized solutions to larger PPC-DUP-FR problem instances, which are too complex for the MIP method. Numerical experiments performed in different network scenarios indicate on the effectiveness of the heuristic in solving the PPC-DUP-FR problem. In particular, the heuristic achieves up to 63% better results than MIP (at the MIP optimality gap equal to 76%) in a medium-size mesh network, in which the MIP problem is unsolvable for higher traffic demands within reasonable runtime limits. In larger networks, MIP is able to provide some results only for the PPC-DUP-FR problem instances with very low traffic demands, whereas the solutions generated by the heuristic are at least 83% better than the ones achieved with MIP. Also, the analysis performed shows a significant impact of the PP cost factors considered and of the level of cost differentiation of PP nodes on the overall PP cost in the network. Finally, simulation results of a case-study packet xHaul network confirm the correctness of the latency model used.


I. INTRODUCTION
The evolution of mobile communication networks has been accompanied by gradual centralization of radio access The associate editor coordinating the review of this manuscript and approving it for publication was Bilal Khawaja . networks (RANs), in which traditional radio base stations are disaggregated into radio modules placed near antennas and baseband processing units (BBUs) located at a central (hub) site. The 5th generation (5G) mobile networks [1] allow for further split of BBU functions into a distributed unit (DU) and a central unit (CU), whereas a radio unit VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ (RU) realizes low-level physical functions at the antenna site [2]. Virtualized DU and CU functions can be performed on general-purpose processors (GPPs) available at processing pool (PP) facilities located at different network sites [3]. The disaggregation and distribution of radio processing functions leads to the existence of multiple data flows that have to be exchanged between the 5G RAN elements, including, fronthaul (FH -between RU and DU) and midhaul (MH -between DU and CU) flows. These flows have diverse bandwidth and latency requirements, which are related both to characteristics of the radio system as well as to specific functional split options applied for RU-DU and DU-CU [4]. A scalable and cost-efficient solution for convergent transport of diverse data flows in 5G-RANs, especially in dense networks that require the connectivity with a large number of antennas / RUs, is a packet-switched xHaul network [5], [6], [7]. Such a network may be implemented using the well-known packet-based Ethernet technology, which has been adapted for xHaul in the IEEE standards 802.1CM [8] and 1914.1 [5]. Ethernet allows for efficient utilization of link bandwidth thanks to statistical multiplexing of multiple xHaul data flows as well as the traffic related to other services, such as 4G, enterprise, and residential services. The transmission of 5G radio data by means of Ethernet frames is enabled by the enhanced CPRI (eCPRI) protocol [9]. Concurrently, time-sensitive networking (TSN) mechanisms related to prioritized transmission of frames have been proposed for Ethernet-based xHaul networks in [8] to support the transmission of latency-sensitive fronthaul traffic.
Various deployment scenarios, which differ in the localization of DU and CU entities, are considered for 5G RANs [5], [6], [10]. One of the possible cases, depicted as the first option in Fig. 1 in [5], assumes that the CU functions are performed at a hub site, whereas the DU functions can be realized on the PPs available at different sites of the access network, in the proximity of cells. In this scenario, a basic network design problem concerns the selection of PPs for the placement of DU entities, and the latency-aware routing of FH and MH data flows between RUs, PPs, and the hub. In this study, we focus on such a network planning problem. Namely, we assume that the network planning process (i.e., the selection of PPs and the routing of related xHaul flows) is performed for a worst-case network utilization scenario, namely, where the bit-rates of data flows and the PP processing loads correspond to full utilization of radio resources (i.e., the transmission capacities of RUs). It translates into a static network planning problem, where there are no temporal demand changes during network optimization. Such an assumption assures that the transmission and processing resources are available and the latencies of flows are acceptable in the xHaul network even when the radio network is fully utilized. Note that all the constraints are also satisfied if the network utilization is lower. In the following, we discuss in detail the contributions of this work.

A. RESEARCH CONTRIBUTION
In a network in which the cost of using PPs is diversified at particular locations, for instance, due to different space rental prices or the availability of renewable energy sources, it is desirable to design the network in such a way that it would entail the lowest investment and operational costs for the network operator. However, in prior works concerning a similar problem [11], [12], the assumption was that all PPs involve the same cost and optimization of the use of PPs was not addressed. Therefore, to fill the research gap, this work focuses on the PP cost-aware DU placement and FH/MH flow routing (PPC-DUP-FR) problem. The problem is particularly challenging in packet-switched xHaul networks, where dynamic, non-deterministic latencies of data flows caused by buffering of packets in the switches have to be accounted for during DU placement and flow routing decisions [11]. In this regard, the network optimization process can be supported by applying analytical latency estimators. In this work, we use a reliable worst-case flow latency model that assures a tighter estimation of flows latencies than the model used in our previous works [11], [12].
The main goal of this work is to develop methods for cost-oriented optimization of packet-switched 5G xHaul networks. The second objective is to analyse the impact of different PP cost scenarios on the network cost. The main novelty concerns formulating and solving the PPC-DUP-FR problem, which focuses on optimization of the PP-related network cost and an improved latency estimation model. The optimization methods proposed allow to solve a real-life engineering problem related to the planning of an xHaul access network, in which an Ethernet-based packet-switched network is used for transporting fronthaul and midhaul radio data flows between the 5G RAN elements. The main benefit for a network operator from using the methods is the assurance that the transport network will satisfy the latency requirements of latency-sensitive flows, which is not a trivial task in a network incurring dynamic latencies due to the packet buffering. Additionally, the methods are oriented on selecting the best (cheapest) locations for the activation of the PPs and the allocation of the DU workloads, which will let the operator to optimize the network cost. Detailed contributions of this work include: 1) application of the latency model based on worst-case calculations with improved latency estimations that skip from processing co-routed, but non-affecting flows (see Section III-C), 2) formulation of an MIP optimization problem for solving the PPC-DUP-FR problem in a packet xHaul network (see Section V), 3) development of a heuristic method for generating optimized solutions to larger instances of PPC-DUP-FR (see Section VI), 4) analysis of methods performance and overall PP cost in different network and PP cost scenarios (see Section VII), and 5) validation of the latency model by means of an event-driven simulation of a case-study packet-switch xHaul network (see Section VII-G).
The paper is organized as follows. In Section II, we discuss related works. In Section III, we present the network scenario as well as the cost and latency models considered in this work. In Section IV, we define the cost-aware DU placement and flow routing problem and, in Section V, we formulate it as an MIP optimization problem. In Section VI, we describe the heuristic method that generates optimized solutions to PPC-DUP-FR. In Section VII, we report and discuss numerical results. Finally, in Section VIII we conclude this work.

II. RELATED WORKS
The majority of research concerning optimization of resource allocation in RANs have focused on the conventional centralized radio access network (C-RAN) scenario, which is used currently in the 4G/LTE networks. In this scenario, radio frequency signals are transmitted using fronthaul links between remote radio heads (RRHs), located near antennas, and a central site, at which a pool of baseband units (BBUs) is available for the radio signal processing. In C-RANs, a basic optimization problem concerns the placement and allocation / mapping of BBUs to particular RRHs, e.g., see [13] and [14]. Research works have been also focused on optimization of optical fronthaul networks, including such issues as provisioning of connectivity and minimization of transmission resource usage [15], [16], assuring network survivability [17], [18], and achieving energy efficiency [19], [20]. More related works regarding resource allocation in C-RANs can be found in a survey presented in [21].
The 5G RAN architecture allows for splitting the BBU processing functions into two separate units, namely, DU and CU. This makes the resource allocation problem more complex since it requires decisions on the placement / allocation of both entities as well as it involves multiple xHaul radio data flows that have to be transported between the 5G RAN elements. In the vast majority of studies, it is assumed that the xHaul connectivity is provisioned by an optical transport network. For instance, reinforcement learning-based algorithms were proposed for the DU/CU placement [22] and the DU/CU placement with lightpath provisioning [23] problems with the aim to minimize the number of active PPs and bandwidth consumption in an optical xHaul network. An optical aggregation network based on wavelength division multiplexing (WDM) was assumed in [24], where the DU/CU placement problem was formulated as an MIP optimization problem. The authors analysed performance gains of the RU-DU-CU architecture in comparison to the RRH-BBU approach. In [3], an optical transport network was used to connect the BBU processing entities, which were flexibly split and distributed over different network locations. The minimization of power consumption and bandwidth usage with functional split selection in a hybrid C-RAN network connected using direct fronthaul and midhaul links was studied in [25] and [26].
The authors of [27] proposed a min-max fair resource allocation framework that dynamically allocates transmission and DU/CU resources in a multi-tenant open RAN (O-RAN) architecture connected by means of direct links established over a passive optical network (PON). Similarly, a dynamic bandwidth allocation algorithm for the transport of xHaul flows over a PON was proposed in [28].
The next generation fronthaul interface (NGFI), defined in the IEEE 1914.1 standard [5], as well as technical specifications of the open RAN (O-RAN) architecture [29] enable the use of packet-switching technologies in xHaul transport networks. The major concern in such networks are non-deterministic latencies caused by packet buffering in switches. In latency-sensitive xHaul networks, resource allocation and network optimization tasks should take this effect into account, e.g., by making use of reliable latency estimation models [8]. The authors of [30] have analysed the trade-off between the network cost and the level of CU centralization in a 5G RAN deployment scenario, in which the DUs are collocated with the RUs and the placement of CUs is subject to optimization. A packet-based network was assumed for the transport of midhaul traffic between the DUs and CUs, however, with a simplified static latency model, without considering the buffering of packets. In [31], the analysis of latencies in a packet-switched fronthaul network is performed using M/M/1 queuing model and Jackson network theory. Since the latency model proposed estimates average end-to-end delays, and not maximum possible delays, it makes it unsuitable for the network design tasks in which strict latency requirements are imposed. In [32], a packetswitched network with fronthaul and backhaul flows was considered, however, buffering latencies were not accounted for. Heuristic algorithms were developed in [33] and [34] to solve the problem of routing with latency and flow scheduling constraints in a packet-switched (bridged) network, but the algorithms did not consider the optimization of the DU/CU placement. In [11] and [12], MIP models were proposed to optimize the allocation of DU and DU/CU entities, respectively, in packet-switched xHaul networks. However, these works were oriented on straight minimization of the number of PP sites, which did not comprise a more realistic scenario in which PP activation and processing costs are diversified in the network. Other simplifications concerned the unlimited PP processing capacity in [11] and the lack of path selection sub-problem in [12]. Eventually, a simplified latency model was used, which accounted for an excessive amount of interfering flows in the estimation of buffering latencies.
In this work, we focus on joint optimization of the DU placement and flow routing in packet-switched xHaul access networks, with considering the activation and processing costs of the PP nodes. This is a realistic scenario that can be implemented in a real-world infrastructure and that goes beyond previous studies (e.g., see [11], [12], [22], [23]) in which just the number of active PPs was subject to optimization without accounting for their costs, which in fact might be diversified in the network (as discussed in Section III-B). VOLUME 11, 2023 We make use of a latency model (described in Section III-C) that includes buffering latencies and which allows for a more precise estimation of maximum flows latencies than the model used in [11] and [12]. To the best of our knowledge, the cost-aware packet-switched xHaul network planning problem addressed and the optimization model and method presented in this work have not been considered in the literature so far.

III. NETWORK SCENARIO
In this Section, we present the main assumptions concerning the packet-switched xHaul network scenario. Also, we describe the cost and latency models used in this work.

A. MAIN ASSUMPTIONS
We assume a similar network and traffic model as in [11]. Namely, a convergent packet-switched xHaul network, which implements NGFI architecture defined in [5], is used to transport the radio data traffic in a 5G RAN. The elements of the 5G RAN considered include the RUs located at antenna sites, PP nodes performing virtualized DU functions, and a hub node containing a PP dedicated for realization of CU functions. The PPs may have various processing capacities and are spread over different sites of the network. Subsets of RUs requiring joint DU processing, for the purpose of multicell coordination [35], are grouped into clusters.
The packet transport network makes use of Ethernet switches for multiplexing and routing of FH and MH flows [8], respectively, between RUs and DUs (PPs), and between the DUs and the CU (hub). The flows are realized both in uplink (RU→DU→CU) and downlink (CU→DU→hub) directions. Specific one-way latency limits are imposed on the transport of FH and MH flows over the network. Namely, the latencies are guaranteed on the level of particular network flows, what is expected from the transport network as discussed in [5] and [36]. Note that the network model might be further extended and include the latencies introduced at the 5G service level due to the processing of DU workloads at the PPs (e.g., see [37] and [38]). Considering such service latency constraints would require a proper latency model corresponding to a specific implementation of the PP hardware. Such extensions are out of scope of this study and are left for future work.
We assume that the radio data of each flow are transmitted with constant bit-rates corresponding to a full utilization of radio resources. Similarly as in [39], the traffic model assumes that the data are sent periodically as bursts of Ethernet frames (packets), where each frame in the burst has a fixed size of 1542 bytes [8]. The bursts are handled in the network and switched as entire. The switches select the bursts for transmission based on their priority, where FH data has the highest priority (HP) and MH data has the lowest priority (LP). Preemption of a burst (even of a lower priority) that is in transmission is not allowed. We consider that there is no time-scale of flows and their parameters are fixed throughout the network planning process to convey a worst-case resource utilization scenario in the network, where all antennas are fully operational and transfer the maximum amount of data.

B. COST MODEL
In this work, we focus on the optimization of the cost related to the use of PPs in the network. We aim at such placement of DUs at selected PP locations that minimizes the overall PP cost. We assume a cost model that entails two factors: • PP activation cost (κ activ ), which is a fixed cost related to the activation and utilization of a PP at the given location, and • PP processing cost (κ proc ), which is a variable, loaddepended cost related to the volume of DU processing performed at the node.
Accordingly, the cost of using PP node v is expressed as: where κ activ (v), κ proc (v), and ρ(v) are the activation cost, the processing cost of a DU unit, and the DU processing load at node v respectively. The PP activation cost may reflect the cost of building a room or renting the space for server placement. The PP processing cost may represent the cost of energy consumed by servers when processing the radio data by virtualized DUs. In real-life scenarios, PP locations may differ with both κ activ and κ proc . Activation costs will be significantly higher if hardware is stored in the city centre rather than in the suburbs, and processing costs will be lower if the location allows for the use of renewable energy sources.
In Section VII-F, we analyse the impact of both PP cost factors and of the level of differentiation of PP costs on the overall network cost.

C. LATENCY MODEL
The latency model used in this work accounts for both static and dynamic delays that the bursts of Ethernet frames experience during their transmission through the network.
The static latencies include propagation delays in links (at speed 2 × 10 5 km/s), storing and forwarding delays in switches (5µs per a switch [11]), and burst transmission times in network links. The static delay calculated for a given transmission link is expressed by Constraint (18) in the MIP model formulated in Section V, and it is used in estimation of the flow latency in Constraint (19).
The dynamic latencies are related to buffering (queuing) delays of bursts of frames at the output links of switches, which are caused by prior transmission of other (interfering) bursts. To assure the estimations of dynamic latencies are reliable, we calculate worst-case queuing delays. As in [8], we assume that such delays are produced by: 1) the bursts that belong to other flows of either higher or equal priority (HEP), which might be selected for transmission before the burst of the given flow, and 2) the largest burst of a lower priority (LP) flow, which might be in transmission. In both cases, the burst for which estimation is performed might need to be buffered by the time required for the transmission of interfering bursts at the switch output link, which is expressed by Constraints (15)- (17) in the MIP model.
In this work, we assume that the interfering HEP flows include all HEP flows that come from other input links. In addition, they include the co-routed flows, i.e., such that come from the same input link as given flow, which may affect the flow latency. In particular, a co-routed HEP flow 1 affects flow 2 if the transmission time of burst 1 in the output link (T out 1 ) is higher than the transmission time of burst 2 in the input link (T in 2 ). Such situation happens if the bursts have the same length, but input bit-rate is lower than the output bitrate, as shown in Figure 1-(b). It is also the case of the same input and output bit-rates, but longer burst 1 than burst 2, as illustrated in Figure 1-(c). The co-routed flows for which T out 1 ≤ T in 2 are non-affecting and can be excluded from the set of interfering HEP flows since the transmission of burst 1 at the output link terminates before burst 2 is received at the input link. In such a case, burst 2 can be transmitted without buffering as shown in Figure 1-(a).
Remark: The novelty of the above-presented model consists of the assumption of excluding the co-routed, but non-affecting HEP flows, which assures a tighter estimation of worst-case latencies than when using the model applied in our previous works [11], [12]. Previously, all co-routed flows were considered as interfering, which led to unnecessary overestimation of latencies. The use of an improved latency model requires its adequate mathematical representation in the optimization model. To this end, we formulate a novel MIP model in Section V. Eventually, in Section VII-G, we validate the model using an event-driven simulator of a packet-switched xHaul network.

IV. COST-AWARE DU PLACEMENT AND FLOW ROUTING PROBLEM
The PPC-DUP-FR problem addressed in this work concerns selecting a subset of PP nodes, from a given set of candidate PPs, for realization of DU processing for a given set of RUs. In addition, it concerns the selection of routing paths, from a given set of candidate paths in the packet-switched xHaul transport network, for routing of FH and MH flows, respectively, between each RU and the PP at which its DU is placed, and between the PP and the hub, where the CU is located. The placement of DUs should be such that the overall cost of activating PPs and processing of DUs at PPs, denoted by z and reflecting the cost model defined in Section III-B, is minimized in the network given the below listed constraints that must be satisfied.
1) the DUs associated with a cluster of RUs must be placed at the same PP; 2) the volume (bit-rate) of traffic in a network link cannot exceed the link capacity; 3) the processing load in a PP node cannot exceed the node processing capacity; 4) the latency of each flow in the network, estimated using the model presented in Section III-C, cannot exceed the latency limit given for this flow.
In Figure 2, we illustrate the PPC-DUP-FR problem by an example representing two different DU placement and flow routing configurations. In the example, two RUs, three PPs, and the hub are connected by means of a packet-switched xHaul transport network consisting of five switching nodes. The PPs have different activation (κ activ ) and processing (κ proc ) costs, which are shown in the figure. In case (a), the DUs of both RUs are placed at node PP3 and the overall cost of using PPs in the network is equal to z = 50 + 2 × 3 = 56. This is the lowest possible cost since PP3 has the lowest activation and processing cost in the network. However, the latency of the FH flow of RU1 is above an acceptable limit due to too large distance between RU1 and PP3, which makes configuration (a) unacceptable (infeasible). In case (b), the DUs are placed at node PP2 and the overall PP cost, which is equal to z = 60 + 2 × 4 = 68, is higher than in case (a). Nevertheless, the FH transmission paths between RU1/RU2 and PP2 are shorter and FH latencies are on acceptable levels. Since the cost of PP2 is lower than of PP1, this solution to the PPC-DUP-FR problem is optimal. In Section V and Section VI, we present two methods, namely, based on solving an MIP model of the problem and an heuristic approach, which aim at generating such optimal solutions.

V. MIP MODELLING OF PPC-DUP-FR PROBLEM
In this Section, we formulate a MIP model of the PPC-DUP-FR optimization problem addressed in this work. We begin by introducing the notions and notation used to model the problem and, afterwards, we present the MIP model. The formulation of MIP allows us to solve the problem using an MIP solver, such as CPLEX [40]. In Section VII, VOLUME 11, 2023 we evaluate the scalability of the MIP method, in particular, its effectiveness in solving larger problem instances.

A. NOTATION
Let directed graph G = (V, E) represent a packet-switched xHaul network, where V is the set of network nodes and E is the set of links. Set V comprises four disjoint subsets of nodes: RU nodes (V RU ), PP nodes (V PP ), CU nodes (V CU ), and switching nodes (V S ). Let C denote the set of clusters of RUs. Each cluster includes a subset of RUs that require their DU functions to be placed and performed at the same PP node, e.g., for multi-cell coordination purposes. We assume that the clusters are disjoint and each RU belongs to a cluster. Let κ activ (v) and κ proc (v) denote, respectively, the cost of activation of PP node v ∈ V PP and the unit cost of DU processing at PP node v. Let E S+ denote the set of links outgoing from the switches and let E S-(e) denote the set of incoming links of the switch that is the origin of link e ∈ E S+ . Let H (e) be the transmission capacity (bit-rate) of link e ∈ E, C(v) be the processing capacity of PP node v ∈ V PP , L P (e) be the propagation delay in link e ∈ E, and L SF (e) be the storeand-forward delay of the switching node that is the origin node of link e ∈ E S+ .
There is a pair of traffic demands associated with each RU, namely, an uplink demand from RU towards DU and CU, and a downlink demand in the opposite direction. The set of all demands (uplink and downlink) is denoted as D. The processing load of the DU of demand d is denoted as ρ DU (d). Let c(d) denote the cluster comprising the RU of demand d.
For each demand d ∈ D, a pair of traffic flows has to be realized in the network: (a) a fronthaul flow between the RU node and a selected PP node at which the DU functions of the RU are performed, and (b) a midhaul flow between the PP node and a CU node. Let set F = {FH, MH} include both types of traffic flows. Let L max (f ) denote the maximum one-way latency allowable for flow f ∈ F. The bit-rate of In Table 1, we summarize the above described notation.

B. MIP MODEL
In Table 2, we present the MIP formulation of the cost-aware DU placement problem addressed in this paper. The MIP model uses the problem variables defined in Table 1. Hereafter, we explain the meaning of problem constraints. The optimization objective (2) is to minimize the overall activation and processing cost of PP nodes in the network. Constraint (3) assures that each cluster of demands has assigned a PP node for DU processing, and Constraint (4) assures that the demands of a cluster are processed in the assigned PP node. Constraint (5) assures that a PP node is active if there is a cluster of demands that makes use of this node for DU processing. Constraint (6) assures the selection of a single routing path for each FH and MH flow of each demand, which has an end in the PP node selected for DU processing of this demand. Constraint (7) allows to determine the links over which the flows are routed. Constraints (8)- (10) are used to determine if two specific flows are routed over the same network link. Constraint (11) allows to determine if the latency of a flow (denoted by f ) is affected by another flow (denoted byf ) in a switch outgoing link (denoted by e). Namely, the latency is produced if both flows are routed over the outgoing link and, in case the flows come from the same switch input link (denoted by g), the burst transmission latency of flow f at the incoming link is smaller than the burst transmission latency of flowf at the outgoing link (what is specified by parameter γ ). Constraint (12) calculates the overall DU processing load at a PP node, and Constraint (13) assures that the processing load does not exceed the node processing capacity. Constraint (14) assures that the overall traffic load at a network link does not exceed the link capacity. Constraints (15) and (16) allow to estimate, for a switch outgoing link, a worst-case buffering latency of packets belonging to a flow caused by, respectively, the packets belonging to all higher and equal priority flows, and the largest burst of packets belonging to a lower priority flow. The sum of these two sources of dynamic latency is calculated in Constraint (17). The static latency introduced at each network link is calculated in Constraint (18) as the sum of link propagation delay, store-and-forward delay produced in the origin node of the link (if the node is a switch) and burst transmission delay. Constraint (19) estimates a worst-case latency of a flow as the sum of estimated dynamic and static latencies. Finally, in Constraint (20), it is checked wether the flow latency does not exceed the allowable limit. VOLUME 11, 2023 (2)-(20) is N P-hard as it comprises, among others, Constraints (6) and (14) that represent the single-path allocation problem (see problem (4.2.4) in [41]).
Remark 2: The MIP formulation makes use of flow routing Constraints (7)-(11) and flow latency Constraints (15)- (20), which number depends on the number of network links. Such a modelling approach differs with the one used in our prior work [11], in which the problem constraints corresponded to particular candidate routing paths, and not to network links. In general, the set of possible routing paths between a pair of nodes grows exponentially with network size. Therefore, MIP model (2)-(20) (20), which grows linearly with the network size (i.e., the number of links), is more scalable than the mathematical model formulated in [11].
Remark 3: The MIP model extends the formulation used in [12] by incorporating a route selection sub-problem (through consideration of a set of candidate paths), which was not accounted for in [12]. Besides, the estimation of latencies is more accurate than in our prior work due to the introduction of additional problem variable x aff dfdf e and Constraint (11). Finally, a different optimization goal, which is minimization of the cost of DU node activation and processing, is considered in this work.

VI. HEURISTIC ALGORITHM
The heuristic proposed in this paper is called Move and Swap Cluster's Assignment -Repeated Algorithm (MaSCA-RA). First, we present the overall idea, followed by explanation based on the flowchart (Figure 3). Next, we go into details of two Pseudocodes used in the flowchart (Procedure 1, Procedure 2). At the end, we explain Procedure 3, which is a part of Procedure 2.
The idea of the algorithm is presented in Figure 3. It consists of two parts: 1) MaSCA -an algorithm that solves the optimization problem by iteratively modifying cluster assignments (thus creating a possible solution), and 2) RAa mechanism that ensures calling MaSCA multiple times to get as many results as possible in a given time limit. In more detail, if -for an example topology -MaSCA takes 20 minutes to solve the optimization problem, and there is time limit of 60 minutes for calculations, RA will call MaSCA 3 times, giving 3 results. The best result of all MaSCA calls is the final solution for that topology. MaSCA-RA is a single-thread algorithm.
MaSCA has two parameters that will be tuned in Section VII-B: SWAP and MULT. As presented in the Figure 3, we start by setting parameters and loading a given topology. We call Procedure 1 to create a Proximity Ranking that will rank all PP nodes for each cluster based on distance between them. Proximity Ranking is a tool that helps to create the first feasible solution (default solution), but is also used in Procedure 2 to determine which PP node is closer/further than the currently assigned one (detailed explanation in following paragraphs). We use MaSCA parameters to set two other parameters: a) MULT to calculate maxIterations that sets the maximum number of iterations (number of demands depends on the size of a loaded topology); b) SWAP to calculate swapCondition that sets a condition when algorithm should switch between moveAssignment and swapAssignment operators (explained below). Next, we create a default solution (a feasible one), that will be the entry point and the first best known solution (bestSolution). The default solution is defined with the usage of Proximity Ranking -we assign each cluster to its closest PP that can serve this cluster. We set a new variable moveFailed as zero. Then, we start the timer and repeat Procedure 2 maxIterations times or until time runs out (time < timeLeft). Procedure 2 slightly modifies assignment of PP node to a cluster in every iteration (detailed explanation in following Procedure 1 MaSCA -Creating Proximity Ranking of PP Nodes for Each Cluster (based on the Average distance) Require: Network topology with candidate paths between each pair of nodes. Ensure: Ranking of PP proximity for each cluster based on the average distance between all RU nodes in a cluster and any PP node (non-descending order). for v RU in V RU (c) do // iterate through RUs in the c 7: for v PP in V PP do // iterate through all PPs 8: path ← the shortest path from hops ← number of hops in path 10: latency ← static latency of path 11: countUsage(v PP ) += 1 12: countHops(v PP ) += hops 13: countlatency(v PP ) += latency 14: end for 15: end for 16: // Iterate through all PPs to calculate the average 17: // number of hops and static latency for ProxRank(c) 18: for v PP in V PP do 19: usage ← countUsage(v PP ) 20: avHops ← countHops(v PP ) / usage 21: avLatency ← countLatency(v PP ) / usage 22: add {v PP , avHops, avLatency} to ProxRank(c) 23: end for 24: Sort ProxRank(c) in the non-descending order, first by average hops then by average static latency. 25: end for paragraphs). At the end, the procedure stops the timer and saves the best solution (bestSolution). The target of MaSCA is to find the best solution expressed as a minimum sum of activation cost and processing costs of PP nodes as defined in (2). Each solution stored as bestSolution at any point always fulfils requirements mentioned in Section V. The feasibility of solutions is evaluated in Procedure 3, which is called from Procedure 2 (in line 19). Procedure 3 is responsible for selecting the paths (from the set of candidate paths) for routing of FH and MH flows for all demands such that the allocation of transmission resources in network links is feasible and the latencies of all flows are within acceptable levels.
In Procedure 1, we present ranking part of MaSCA which requires information about network topology and candidate paths between each pair of nodes, and ensures creating Proximity Ranking.
First, for any given cluster c, we define an empty ProxRank(c) as a list of triples (line 2). A single triple consists Procedure 2 MaSCA Single Core Iteration Require: The best result at the moment (bestSolution); The number of iterations in which moveAssignment operator failed to find a better solution (moveFailed); Condition when algorithm should switch to swapAssignment operator (swapCondition). Ensure: Create newSolution based on the bestSolution, and modify it with one of two operators (moveAssignment or swapAssignment) to find the new best result.
1: newSolution ← bestSolution 2: if movedFailed < swapCondition then //moveAssignment operator on newSolution 3: ppList ← All PP nodes that serve the least number of clusters 4: pp ← random from ppList 5: clusterList ← all clusters connected to the pp 6: cluster ← random from clusterList 7: possibleJumps ← list of all active PP nodes besides pp that could serve cluster 8: roulette ← create a roulette from possibleJumps // roll closer PPs with higher probability 9: rolledPp ← PP node randomly rolled from roulette 10: make rolledPp the new PP to serve cluster 11: if pp does not serve any more clusters then 12: deactivate pp 13: end if 14: else // swapAssignment operator on newSolution 15: cluster1, cluster2 ← random clusters served by different PP nodes. 16: pp1, pp2 ← PP node that serves cluster1/cluster2 17: swap clusters -now cluster1 is served by pp2 and cluster2 is served by pp1 18: end if 19: if Procedure3(newSolution) is feasible and z newSolution <= z bestSolution then 20: bestSolution ← newSolution 21: moveFailed ← 0 22: else 23: if moveAssignment operator has been used in this iteration then 24: moveFailed + + 25: end if 26: end if of: a) analysed PP node; b) the average number of hops to the analysed PP; c) the average static latency to analysed PP. Both b) and c) are based on the shortest path between each RU in c and analysed PP. The first PP node in ProxRank(c) will be a node that (on average) is the closest one to cluster c. To achieve that, we define three lists: 1) countUsage; 2) countHops; 3) countLatency, that store information about all PPs in relation to all RUs in the cluster c (lines 3-5).
We find the shortest paths between every RU in cluster c (v RU ) and every PP (v PP ). We save both number of hops and static latency from those paths (lines 8-10). Then, we fill the previously prepared lists to sum: 1) number of RUs that can reach v PP ; 2) number of hops in the shortest paths between those RUs and v PP ; 3) static latency of those paths (lines [11][12][13]. Afterwards, we iterate through all PPs once more to calculate the final distance between c and v PP , by adding the average number of hops (avHops) and average static latency (avLatency) of all shortest path between RUs in c and v PP , to the ProxRank(c) (lines [19][20][21][22]. Finally, we sort ProxRank(c) in the non-descending order, first by the average number of hops, and then by the average static latency (line 24).
The idea of Procedure 2 is to create a newSolution based on current bestSolution, and modify it with one of two operators: moveAssignment or swapAssignment to find a better solution. The procedure requires: the best known solution bestSolution, moveFailed that counts how many times moveAssignment operator already failed, and swapCondition that is calculated based on MaSCA-RA parameter SWAP, and which controls when the algorithm should switch to swapAssignment.
First, we create a newSolution, based on the given bestSolution (line 1). Next, based on the information how many times moveAssignment operator failed already, we choose an operator that will modify newSolution (line 2).
The target of the moveAssignment operator is to lower the number of active PP nodes, by freeing those nodes that serve the smallest number of clusters. From the list of such nodes (ppList), we choose one pp randomly (lines 3-4). Next, we extract clusterList that contains all clusters connected to the pp and randomly choose one cluster of them (lines 5-6). Next, we find a new PP to serve the cluster. To this

Procedure 3 MaSCA -Evaluation of a Given Solution
Require: Network topology with candidate paths between each pair of nodes, and a proposed solution where every cluster is assigned to a PP node. Ensure: Evaluation whether the given solution is feasible or not.
1: for f in F = {FH, MH} do // iterate through flows 2: for d in D do // iterate through demands 3: v ← PP node that is assigned to demand's d cluster 4: for p in P(d, f , v) do // iterate through cand. paths 5: fail ← 0 6: if placing d(f ) on p will exceed any limits then 7: fail ← 1 8: else 9: place d(f ) on p and update network's latencies 10: break 11: end if 12: end for 13: if fail != 0 then 14: return solution is NOT feasible 15: end if 16: end for 17: end for 18: return solution is feasible end, we create possibleJumps list, which contains all PP nodes, besides pp, that are active and could potencially serve the cluster. We are using the fitness propotionate selection (a.k.a. roulette wheel selection) to choose a new PP. Proximity Ranking estimates the average distance between the cluster and all PPs in possibleJumps. We roll closer PPs with higher probability. Rolled PP, named rolledPP, is the one that will now serve the cluster (lines 7-10). If pp does not serve any more clusters, we deactivate it.
The aim of the swapAssignment operator is to change search space by choosing two random clusters (cluster1, cluster2), that are served by differend PP nodes (pp1, pp2), and swapping them. Now cluster1 is served by pp2, and cluster2 is served by pp1 (lines [15][16][17].
After modifying the newSolution by one of the operators, we apply Procedure 3 to check if the obtained solution is feasible (Procedure 3 will be explained below). If the newSolution is feasible, and its cost (z newSolution ) is lower or equal than the cost of the bestSolution, it becomes a new bestSolution. Additionally, moveFailed is set to zero, to ensure that in the following iterations, the moveAssignment operator will be called. If any of the conditions are not met, and the moveAssignment operator has been used in this iteration, we increment moveFailed so that after multiple failed attempts by this operator, the algorithm can change the search space (lines [19][20][21][22][23][24][25][26]. Procedure 3 represents a method for evaluation of solutions and method for choosing candidate paths for each demand in the network. It requires a network topology with candidate paths, and a proposed solution, where every cluster is assigned to a PP node. Procedure 3 returns information whether a solution is feasible or not. First, we iterate through flows (f ∈ F), first by fronthaul and then by midhaul. The idea is to place all fronthaul demands in the first place, because they have more strict time limit. Following, we iterate through all demands (d ∈ D), and define v as PP node that is assigned to demand's d cluster (lines 1-3). We extract all candidate paths (p ∈ P(d, f , v) for the flow f of demand d (d(f )), that goes through PP v. We set the fail flag to zero. Then, if d(f ) placed on path p exceeds any constraint in the network (mentioned in Section III), we set the fail flag to 1. If the placement on p was successful, we accept p as path for d(f ), update all network latencies, and break the loop (lines 4-12). Solution is not feasible if for at least one d(f ) it is not possible to find a feasible path.
The complexity of MaSCA is bounded by the maximum number of candidate paths between any pair of nodes maxP, the maximum number of hops from a single path maxH , number of demands in the network |D|, and maximum number of iterations maxIterations = MULT · |D|, where MULT is a parameter. In more detail, the complexity of MaSCA is equal to: Formula (21) consists of the following elements: 1) complexity of creating Proximity Ranking (Procedure 1), where number of clusters multiplied by number of RUs in those equals number of demands -O(|D| · |V PP |); 2) complexity of solution's evaluation (Procedure 3) -O(|D| · maxP); 3) complexity of updating network's latencies during every evaluation, based on latency model (Procedure 3, line 9). During placement, we update latency/capacity of every link/node in the path, and queuing latency of all conflicting demands on every switching node in the path -O(maxH · |D|).

VII. NUMERICAL RESULTS
In this Section, we evaluate the MIP model and MaSCA-RA algorithm using an extensive set of numerical experiments. We start with a presentation of an evaluation scenario for the following tests. Thereafter, we tune the MaSCA-RA parameters, namely SWAP and MULT, to assure the best algorithm performance. Afterwards, we assess the scalability of the MIP model by comparing it with MaSCA-RA in larger network scenarios.
Next, we analyse the impact of different metrics, such as: additional candidate paths, increased PP processing capacity, and weighing of activation and processing costs, on overall network performance (with usage of MaSCA-RA).
Eventually, we make use of an event-driven network simulations in order to verify the latencies of individual Ethernet frames carrying FH and MH data flows in an example urban network optimized using the proposed method.

A. EVALUATION SCENARIO
The analysis is performed in two reference mesh network topologies, namely MESH-20 and MESH-38, that were considered in the literature in analysis of 5G C-RAN [18]. The connectivity between the switching nodes (SW) and a CU node in particular networks is shown in Figure 4. In each network, a random number of RUs is connected to each switching node. Moreover, in the proximity of each switching node, there is a candidate PP node that can be activated and used for DU processing. The lengths of links (random values within given limits) and their capacities are shown in Table 3.
We assume that the RUs operate with a specific radio system which has a certain demand on processing resources to realize the radio functions of DU. The processing capacity of a PP is equal to ρ max × i, where ρ max represents the overall processing demand of the DUs of the largest cluster of RUs in the network, and i is a random number from [C min , C max ]. We consider two different PP processing capacity scenarios assuming (C min , C max ) ∈ {(1, 3), (1, 5)}, which we denote as scenarios C [1,3] and C [1,5] , respectively. If not mentioned otherwise, the activation (κ activ ) and processing (κ proc ) costs of PP nodes are uniformly distributed from 50 to 100 and 5 to 10 of cost units, respectively.
To estimate the bit-rates of traffic flows, we applied the model presented in [42] assuming a radio system consisting of 4 antennas with MIMO and 100 MHz channels. We assume Option 7.2 and Option 2 for the functional split [4] between RU-DU and DU-CU, respectively. The flows bit-rates as well as the corresponding burst sizes (i.e., the number of frames forming a burst) for the radio system considered are shown in Table 4. The bit-rates and the PP processing loads are fixed and correspond to a full utilization of radio resources (i.e., the transmission capacity of RUs). We assume the one-way latency limits equal to 100 µs and 1 ms, respectively, for FH and MH flows, in accordance to the values specified in [5] and [36]. To generate candidate routing paths, we applied the k-shortest path algorithm. Numerical results were obtained using a dual-processor 2.2 GHz 10-core Xeonclass machine (40 logical cores) with 128 GB RAM. We used CPLEX v.12.9 [40] to solve the MIP model.

B. TUNING OF MaSCA-RA
According to the algorithm description presented in Section VI, MaSCA contains two parameters: a) MULT -a multiplier used to calculate the maximum number of iterations; b) SWAP -a multiplier used to calculate the condition when to switch between used operators.
For the tuning, we are using MESH-20 and MESH-38 topologies with the number of RU nodes equal to 1-6 times the number of the switching nodes in the network and assuming the C [1,3] PP processing capacity scenario. Hence, there are 12 different topologies used in the tuning, where the biggest one is a MESH-38 with 6 · 38 = 228 RU nodes.
MaSCA-RA is a single-thread algorithm, and we are calling it on 40 threads simultaneously, with the time limit of one hour (the same as for MIP). The final result for each scenario is the best solution from all results from all threads.
We are using two different metrics to evaluate parameter sets for every topology. The first one is dense ranking (''1223'' ranking) -the parameter set with the lowest (best) result is marked as ''1'', second lowest ''2'' and so on. If multiple parameter sets gave the same results, they are marked with the same number and the next one is marked with the immediately following number. The second metric is Gap -we are calculating a percentage gap from the best known solution from the ranking (the parameter set with the lowest result).
Tuning results are presented in Table 5. We tested all  TABLE 5. Results of tuning for two metrics (dense ranking and percentage gap from the best known solution) -the lowest value is the best parameter set. machine (MaSCA-RA is called on 40 threads simultaneously) with the same time limit (one hour), and with one candidate path. We test the MESH-20 and MESH-38 topologies with the number of RU nodes equals 2-5 times the number of the switching nodes in the network with C [1,3] and C [1,5] PP processing capacity scenarios. The results are presented in Table 6, where all values are an average of both C [1,3] and C [1,5] PP capacity scenarios. MIP shows how much better MIP is comparing to MaSCA-RA -negative percentage implies the advantage of MaSCA-RA. We can notice that for all tested topologies, MIP was not able to give an optimal solution. For the smallest network (MESH-20 with 40 RU nodes), it is 3.23% better than MaSCA-RA. In all other cases MaSCA-RA gave better results, up to 82.87% for the smallest MESH-20 topology. Also, MIP could not give any result for the biggest MESH-20 topology, nor for every MESH-38 topology except the smallest one.
Results show that MIP does not scale well. For bigger topologies it is inevitable to use alternative algorithms, such as MaSCA-RA.

D. THE IMPACT OF THE NUMBER OF CANDIDATE PATHS
We also test how the number of candidate paths impacts MaSCA-RA's results. For this experiment, we use the MESH-38 topology with 76, 152, and 228 RU nodes for both C [1,3] and C [1,5] PP processing capacity scenarios (six scenarios in total). We test 1-4 candidate paths between each pair of nodes. For each of the six scenarios, we identify the best number of candidate paths and calculate the percentage GAP of the remaining three path options. Values presented in Figure 5 are the average of the percentage GAP from all six tested scenarios. We can see, that MaSCA-RA gives the best results with two candidate paths. For that reason, we use that number in the following analysis.

E. THE IMPACT OF PP PROCESSING CAPACITY
In this paragraph, we test how the capacity of all PPs in the network affects optimization objective and number of active PPs. For this experiment, we use the MESH-38 topology with 76, 152 and 228 RU nodes for C [1,1] PP processing capacity scenario. All PP nodes in the network have same processing capacity, and it will be multiplied by ψ ∈ {1, 1.25, 1.5, 1.75, 2, ∞}. Results are presented in Figure 6.
We can notice, that the both optimization objective and number of active PP nodes decrease when the processing capacity increases. The profit is the most noticeable with ψ = 1.25 and ψ = 1.5, although for the smallest topology, both tested values decrease linearly. However, we cannot infinitely lower the optimization objective and the number of active PPs, because of the time limit for the demands themselves (especially fronthaul flow). Less active PPs, implies that more VOLUME 11, 2023 FIGURE 6. Results of testing how PP processing capacity multiplier affects optimization objective and number of active PPs. demands will be transferred to the same place, hence the queuing latency will increase.
We can conclude that in a real-life scenario, a small number of very powerful servers will not be able to serve all demands in the big topology. For those, it might be better to place less powerful servers in more localizations.

F. ANALYSIS OF VARIOUS PP COST SCENARIOS
Up to this point, both the activation and the processing cost of PP nodes of z were in balance (Equation 2). We define α to decide whether κ activ or κ proc should have higher impact on the optimization objective. This is consistent with the discussion in Section III-B, where we describe the diversity of cost factors in the network. The new objective (z α ) is calculated as follows: In this paragraph, we use the MESH-38 topology with the number of RU nodes equal to 1-6 times the number of the switching nodes in the network. For this experiment, we ensure that all PP nodes in every topology have the same processing capacity. We use C [1,1] PP processing capacity scenario, with the same ρ max value calculated for the biggest topology (MESH-38 with 228 RUs). We standardize the costs themselves. We assume an overall budget 10000, for both types of costs. We define a base scenario, in which the costs are calculated evenly, based on MESH-38 with 152 RUs.
Moreover, we consider a number of cases in which the costs may differ randomly up or down by some percentage φ in relation to the base scenario (with the assumption that the given budged is maintained). For example, for φ = 80%, we are choosing a random number φ roll ∈ [0%, 80%] to calculate κ activ for two random PPs, one of which will have κ activ = (1 + φ roll ) · κ activ base , and the other κ activ = (1 − φ roll ) · κ activ base . We repeat the process for both κ activ and κ proc separately until all PPs will have assigned costs.
We analyse φ ∈ {0%, 20%, 40%, 60%, 80%}, where φ = 0% represents the base scenario, and α ∈ {0.25, 0.5, 0.75}, where α = 0.5 represents the balance of the costs in z α . We test how the dispersion of the costs, with assumption that the given budget will not be exceeded, affects z α . The results are presented in Figure 7. As we can notice, in every load case, more dispersed costs, mean lower optimization objective. It meets our expectations, since higher costs difference in PPs allows the MaSCA-RA algorithm to select cheaper PPs, even if they are more distant. The biggest profits are in networks with the biggest load (190, 228 RUs).
We can also notice, that z α is higher when the processing cost has higher impact (α = 0.25), and lower when the activation cost is more important (α = 0.75). This is because during the network planning process we need to allocate 100% of demands, but not 100% of possible PPs are activated (we activate from 5 to 25 out of 38 PPs, with the average of 15), hence lowering the impact of the bigger part (processing costs) gives lower results.

G. CASE STUDY
Eventually, we validated an optimized solution by analysing the latencies of data flows in an event-driven simulator of a packet-switched xHaul network implemented in OMNET++ v.5.6.1 environment [43]. Namely, we applied MaSCA-RA for planning the xHaul network, i.e., to optimize the DU placement and routing of flows, and next we simulated the transmission and routing of the packet flows between the network elements. The simulator imitated the operation of packet switches, in particular, queuing of packets in output buffers and prioritized transmission of fronthaul flows. The bursts of packets from particular flow sources were transmitted in periodic transmission windows, according to the traffic model presented in [39]. To avoid the repeatability of results in consecutive transmission windows, we assumed random bursts transmitting (departure) times in particular windows. The latency of a flow represented the maximum transmission latency experienced by a burst belonging to the flow among all transmission windows. The transmission of 10 8 bursts was simulated, at which stable results were achieved.
The analysis was performed in a 17-node transport network (WRO-17) shown in Figure 8. Topology WRO-17 was developed for evaluation purposes based on a subset of real antenna locations (79 RUs in total, marked by triangles) in    the center of city Wrocław in Poland, where the switches are placed close to antennas and connected using links driven along streets. The link lengths reflect real physical distances of depicted connections and have been incremented by some random value, between 100 and 200 meters, to account for driving the fiber to the processing and switching equipment.
In Table 7, we show the estimated and simulated latencies of FH and MH data flows for both uplink and downlink directions. We report the maximum and average values of latencies over all flows in the network. Moreover, we present the minimum and average differences between estimated and simulated latencies, both in terms of absolute and relative values.
In Table 7, we can see that maximum latencies of flows obtained using simulations do not exceed the allowable limits, i.e., 100 µs for FH and 1 ms for MH flows. It means that the latency constraint is satisfied for each individual data burst of each flow, which validates the correctness of the solution obtained for the DU placement and flow routing problem. Moreover, the minimum difference between estimated and simulated latencies is not negative. It confirms that the worst-case latency model applied estimates the upper bounds of the actual latencies of flows. The minimum difference for FH flows is equal to 0, which means that there are some FH flows in the network for which the latency estimation is exact. On average, the overestimation of latencies in FH is on the level of 1% for downlink and 19% for uplink. The average overestimation of latencies of MH flows equals about 39% in downlink and 24% in uplink. The differences between calculated and simulated latencies can be explained by the fact that our latency estimation accounts for the worst VOLUME 11, 2023 case scenario, where a data burst has to wait in a buffer for the transmission of all other bursts. In fact, such a situation may not happen as it would require that all interfering bursts arrive at each switch at the same moment. These differences are not very high, especially for latency-sensitive FH flows, which makes the model suitable for optimization tasks in a packet-switched xHaul network.

VIII. CONCLUDING REMARKS
In this paper, we have addressed the problem of DU placement and flow routing in 5G packet-switched xHaul networks. The objective of the optimization has been focused on minimization of processing pool facilities costs defined in a flexible way and including two components, namely, activation cost and processing cost. Moreover, a reliable flow latency model has been incorporated into the problem considered to ensure that the latency limit of given flows is not exceeded. The problem has been formulated in the form of a MIP model, what allowed to use the exact algorithm provided by the CPLEX solver. However, since the MIP model has not provided sufficient scalability, we have also developed an effective heuristic algorithm MaSCA-RA that achieves good results for larger problem instances that are too complex for MIP. We have run extensive numerical experiments using realistic assumptions to verify the efficiency of the optimization approaches proposed as well to examine performance of the analysed network architecture under various scenarios.
The obtained results indicate, among others, that the MIP method is capable of providing solutions for smaller network instances, however, it has a limited scalability and applicability in medium-and large-size network scenarios. In these cases, the heuristic method proposed has shown to be effective in generating optimized solutions to the packet-based xHaul network planning problem addressed in this work. Indeed, MaSCA-RA achieves up to 63% better results than MIP (at the MIP optimality gap equal to 76%) in a medium-size mesh network, in which the MIP problem is unsolvable within an 1-hour runtime limit for higher traffic demands. In larger networks, MIP is able to provide some results only for the PPC-DUP-FR problem instances with very low traffic demands (at the optimality gap equal to 100%), whereas the solutions generated by the heuristic are at least 83% better than the ones achieved with MIP. MaSCA-RA achieves the best results for two candidate paths between each pair of nodes, and the solutions are on average about 3% better than in a single-path scenario. By increasing the processing capacity of PPs, both the number of active PPs and the cost of their usage can be decreased. However, there is some PP capacity limit above which the additional gains are limited, which is related to the excessive buffering delays caused by too large amounts of data flows destined to a smaller number of active PP nodes. The MaSCA-RA method is capable of activating and allocating the DU workloads at the cheapest PP nodes, which has been shown in the experiments focused on diverse differences in the PP costs.
Eventually, the results of event-driven simulations of a packet-switched xHaul network validate the correctness of the improved latency model used in this work.
In future work, we plan to extend the study to a network slicing scenario, in which the transmission and processing resources of a packet-based xHaul network are shared and allocated in accordance to the latency, bandwidth and DU/CU placement requirements of particular network slices, which are related to specific 5G services. Additionally, we plan to include the latency constraints at the service level.