Cost-Aware Optimization of Optical Add-Drop Multiplexers Placement in Packet-Optical xHaul Access Networks

Abstract

This work concentrates on the problem of optimizing the cost of a passive wavelength division multiplexing (WDM) optical network used as a transport network for carrying the xHaul packet traffic between a set of remote radio sites and a central hub in a 5G radio access network (RAN). In this scope, we investigate the flexible use of optical add-drop multiplexers (OADMs) for the aggregation of traffic from a number of remote sites, where the type/capacity of optical devices—OADMs and optical multiplexers (MUXs)—is selected in accordance with the traffic demand. The approach is referred to as Flex-O. To this end, we formulate the xHaul network planning problem consisting in the joint provisioning of transmission paths (TPs) between the remote sites and the hub with optimized selection and placement of OADMs on the paths and proper selection of MUXs at the ends of the TPs. The problem formulation takes into accounts the optical power budget that limits the maximum transmission distance in a function of the amount and type of optical devices installed on the TPs. The network planning problem is modeled and solved as a mixed-integer linear programming (MILP) optimization problem. Several network scenarios are analyzed to evaluate the cost savings from the flexible (optimized) use of OADMs. The scenarios differ in terms of the availability of OADMs and the capacity of the WDM devices applied on the TPs. The numerical experiments performed in three mesh networks of different size show that the cost savings of up to between 35 and 45% can be achieved if the selection of OADMs is optimized comparing to the networks in which either single-type OADMs are used or the OADMs are not applied.

1. Introduction

The fifth generation (5G) mobile radio networks rely on centralized radio access network (RAN) architectures, which disaggregate (split) either some or all of the radio baseband processing functions from the antennas (located at remote sites) and place them at a central site (hub) [1,2]. The densification of the 5G radio networks and the deployment of various functional split options [3] requires efficient solutions for the transport of radio traffic between the remote sites and the hub in a RAN. This task is realized by xHaul networks [4,5,6]. Such networks are responsible for the transport of different types of data flows—related to both the fronthaul/midhaul/backhaul traffic between the remote/distributed/central units (RU/DU/CU) of the 5G RAN [7] as well as the traffic between remote radio heads (RRHs) and baseband units (BBUs) of the legacy 4G/long-term evolution (LTE) networks. In this work, we focus on a convergent xHaul transport network that can accommodate different types of data flows and transport them in the same physical network infrastructure [5].

The WDM optical fiber networks together with packet-switched Ethernet are two key technologies for xHaul networks, as they are capable of assuring low-cost and high-bandwidth connectivity between a large amount of access sites/antennas and the hub in 5G RANs [8,9,10]. WDM enables the aggregation of high-capacity connections established on different wavelengths in a fiber link by means of an optical MUX device. Passive WDM solutions, which are cost effective, as they do not require signal amplification and dispersion compensation, are especially appropriate for limited-distance 5G xHaul networks [9,11]. Concurrently, Ethernet can improve the utilization of optical connections by means of statistical multiplexing of the packets carrying the radio data of the flows aggregated at a remote site [12] and encapsulated using such protocols as the enhanced common public radio interface (eCPRI) [13] and radio over Ethernet (RoE) [14]. For the prioritized transmission of latency-sensitive Ethernet frames, e.g., related to fronthaul flows, time-sensitive networking (TSN) features are defined in [15].

The WDM and TSN Ethernet technologies reduce the demand for direct fiber connections between the remote sites and the hub, which decreases the xHaul network deployment cost [16,17,18]. The further reduction in the demand for optical fiber resources can be achieved by the application of passive OADM devices. The OADMs allow to aggregate the wavelengths from a number of remote sites in a single optical TP [19,20], as shown in Figure 1, instead of using several direct fiber connections between each of the remote sites and the hub. The flexiHaul system [21], which includes a passive WDM system called xWave 400G [18] and a TSN Ethernet switch [22], is an example of a commercial solution supporting the above-discussed functionalities.

The application of OADMs increases the complexity of the xHaul network planning problem since the decisions concerning the routing of TPs between the remote sites and the hub should be handled jointly with a proper choice of intermediate remote nodes at which the OADMs are placed. An important factor constraining the routing decisions is the maximum transmission distance, which, in a passive optical system such as flexiHaul, depends on the optical power budget, particularly on the attenuation of optical components belonging to a TP. The attenuation as well as the cost of OADMs increases with the number of channels (wavelengths) added to (dropped from) the aggregated WDM optical signal [23]. Therefore, a reasonable approach is to apply the OADMs in a flexible way, namely, according to the wavelength demands of particular remote sites to optimize the path length and reduce the network cost.

The main goal of this work is to investigate the cost savings achieved by the flexible (optimized) application of OADMs for wavelength aggregation at remote sites in a packet-optical xHaul network. To this end, we formulate a novel MILP optimization model that accounts for different types of OADMs, applied flexibly according to the demands, and incorporates the power–budget calculations into the model. The model focuses on the optimization of the network cost and embraces the trade-off between the use of OADMs, which involves some costs, and the savings due to the reduced demand for optical fibers. The optimization model is applicable for xHaul access network deployment scenarios, in which the WDM optical transport network makes use of passive optical elements and the aggregation of traffic (wavelengths) is realized in the optical domain by means of OADMs. The major contributions of this study are as follows:

• Development of an MILP model for physical layer-aware and cost-oriented optimization of OADM placement in packet-optical xHaul networks realized using passive WDM devices.
• Evaluation of cost saving due to the optimized application of OADMs for network scenarios with realistic cost and transmission system parameters.
• Assessment of the complexity of solving the MILP model by means of numerical experiments performed in different network scenarios.

It should be stressed that in our previous studies [19,20], we assumed the application of a single type of OADM/MUX devices, which simplifies the MILP formulation by getting rid of the power budget constraints from the model, but it does not allow for the flexible use of OADMs. Our focus was on the minimization of the number of TPs instead of the optimization of the network cost [19]. To our best knowledge, the problem of the physical layer-aware and cost-oriented optimization of OADM placement in packet-optical xHaul networks implemented using passive WDM devices has not been studied in the literature so far. Additionally, the MILP model presented in this work was not considered in prior studies.

The remainder of the article is structured as following. Section 2 reviews related works. Section 3 presents the network model and main assumptions of the network scenario. In Section 4, the considered xHaul network planning problem is formulated as an MILP optimization problem. In Section 5, the numerical results are presented and discussed. Finally, Section 6 concludes the work.

2. Related Works

Most of the research studies concerning the optimization of optical transport networks in centralized RANs is related to the problem of radio processing functions (BBU/DU/CU) placement. The authors of [16,17] formulated MILP models for the BBU placement problem in WDM optical networks with the goals to minimize the number of BBU sites and the amount of fiber connections. In [24], an MILP formulation was proposed for the dimensioning of BBU resources and optical transponders in active WDM optical networks with direct connections and without traffic aggregation between remote sites and the BBUs. Heuristic approaches for planning survivable fiber connections in WDM optical transport networks based on ring topologies were proposed in [25]. The DU/CU placement problem in a ring WDM optical aggregation network was modeled as an MILP optimization problem in [26]. The authors of [27,28] proposed reinforcement learning algorithms for the DU/CU placement and optical path (lightpath) provisioning problem in optical xHaul networks, where the goal was to minimize the number of DU/CU sites and the bandwidth usage. The flexible splitting of the BBU functions and placing them in a RAN connected by means of an optical transport network was studied in [29]. The dynamic allocation of transmission resources for the transport of xHaul traffic in a passive optical network (PON) was studied in [30,31]. Other related works have focused on the problem of connection provisioning with the optimization of transmission resources [32,33], network survivability [34,35], and energy efficiency [36,37] in optical fronthaul networks.

In the above discussed works, the main focus was on planning lightpath connections in generic scenarios in which either the underlying WDM optical network was pre-deployed, usually assuming the use of active WDM devices, which are expensive, or the network design process did not account for transmission constraints in the optical layer. Additionally, point-to-point lightpath/fiber connections were considered without traffic aggregation at intermediate nodes. Eventually, the optimization objectives were related to the usage of radio processing and transmission resources, whereas the optimization of network cost was neglected.

In our recent works [19,20], in which we analyzed the application of a passive WDM solution in a 5G packet-optical xHaul network, we took into account the impact of a meaningful physical-layer constraint, related to the optical power budget, on the transmission distance during the xHaul network planning process. In these studies, we considered the use of a MUX device, also for the realization of OADMs, of specific capacity corresponding to the WDM system capacity. This assumption simplified the problem modeling, but it did not allow for the optimized deployment of MUX and OADM devices on designed TPs. Therefore, to fill this research gap, in this work, we address the problem of optimized OADM placement with proper MUX selection, taking into account the availability of different types of MUX/OADM devices, with the optimization goal related to the deployment cost of the optical transport network. To the best of our knowledge, both the problem studied and the MILP optimization model proposed have not been considered in the literature so far.

3. Network Model

We model the xHaul access network by means of graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, where $\mathcal{V}$ represents the set of remote and hub nodes, and $\mathcal{E}$ is the set of links between the nodes. We assume that each link consists of a number of optical fibers, and the fiber resources are sufficient to establish the connections between the remote sites and the hub. Let $\mathcal{W}$ be the set of WDM channels (wavelengths) that can be carried in an optical fiber. $W=\left|\mathcal{W}\right|$ denotes the capacity of the WDM transmission system.

The set of traffic demands is denoted by $\mathcal{D}$, where demand $d\in \mathcal{D}$ represents a remote node requesting a certain number of wavelength connections, denoted by $W\left(d\right)$, to be established between the remote node and the hub. The connections are realized by means of optical TPs, where each connection has assigned a wavelength on its TP. We distinguish two types of TPs, namely the following:

• A direct TP—where the remote node is connected with the hub by means of a direct (dedicated) fiber connection (i.e., without any OADM introduced on the TP) that carries only the wavelengths originated at the node and aggregated by means of a MUX.
• A traversing TP—where the optical fiber connection between the end remote site and the hub goes through some intermediate remote nodes at which the aggregation of wavelengths originated at these nodes is realized by means of OADMs (e.g., as illustrated in Figure 1); in this case, the TP serves the wavelength requests both of the end node, for which the TP is established, and of the intermediate nodes.

Let set $\mathcal{P}\left(d\right)$ comprise candidate TPs of demand $d\in \mathcal{D}$. Path $p\in \mathcal{P}\left(d\right)$ is a fiber route going through a subset of network links ($p\subseteq \mathcal{E}$), which connects the remote node of demand d with the hub. Let $D\left(p\right)$ denote the length of TP p. Let $\mathcal{Q}(d,\overline{d})$ be the set of candidate TPs of demand $\overline{d}$ that go through the remote node associated with demand d and which may serve (aggregate) the wavelength connections of d by means of an OADM.

Let $\mathcal{M}$ and $\mathcal{O}$ be the sets of available types of MUXs and OADMs, respectively. Set $\mathcal{M}$ includes also a fictitious type of the MUX supporting one channel, which facilitates the modeling of direct fiber connections in the MILP formulation. This fictitious MUX does not induce any cost and has no attenuation. Let $W\left(m\right)$ denote the number of wavelength channels multiplexied/demultiplexed by MUX $m\in \mathcal{M}$ and let $W\left(o\right)$ be the number of wavelengths added/dropped by OADM $o\in \mathcal{O}$. Eventually, let $o\left(d\right)$ denote the type of OADM selected for demand d.

3.1. Network Deployment Scenarios

In the network deployment scenario proposed, referred to as Flex-O, the aggregation of wavelengths by means of OADM devices is allowed at the intermediate nodes traversed by the TPs, as shown in Figure 2a. Moreover, the type of an OADM is selected flexibly according to the number of wavelength connections requested in the intermediate node at which the traffic aggregation is realized. Namely, $o\left(d\right)$ represents the OADM of the lowest number of added/dropped wavelengths that can support $W\left(d\right)$ wavelengths, i.e., $o\left(d\right)=arg{min}_{o\in \mathcal{O}}W\left(o\right)$ such that $W\left(o\right)\ge W\left(d\right)$.

In the evaluation of the Flex-O approach, we consider the following reference scenarios:

• Fix-O—Similarly as in Flex-O, the aggregation of wavelengths is allowed; however, the OADMs have a fixed capacity corresponding to the capacity of the WDM transmission systems. This scenario was considered in our previous work [19] and is shown in Figure 2b.
• Flex-D—Here, the end nodes (i.e., a remote site and the hub) are connected using direct TPs and the aggregation of wavelengths is realized only at the end nodes by means of MUXs; the MUXs have the capacity selected flexibly according to the number of aggregated wavelengths, as shown in Figure 2c.
• Fix-D—As in Flex-D, the end nodes are connected using direct TPs (i.e., without wavelength aggregation at intermediate nodes) and the MUX capacities reflect the WDM system capacity, which is illustrated in Figure 2d.

3.2. Cost Model

The network deployment cost model assumed in this study includes three basic elements:

–

The cost of leasing optical fibers for the realization of TPs;

–

The cost of the MUXs used for wavelength aggregation and signal filtering purposes at the ends of TPs;

–

The cost of the OADMs applied for wavelength aggregation at intermediate nodes of TPs.

The calculation of the above cost elements is achieved by Constraints (21)–(23) in the MILP model, whereas the overall network cost adds up these elements in objective function (2). In the model, ${\kappa }^{\mathrm{F}}$ denotes the leasing price of a km of dark fiber, ${\kappa }^{\mathrm{M}}\left(m\right)$ is the cost of a MUX of type $m\in \mathcal{M}$, and ${\kappa }^{\mathrm{O}}\left(o\right)$ is the cost of an OADM of type $o\in \mathcal{O}$.

3.3. Transmission Model

We assume that the transmission distance of a TP is limited by the available optical power budget and the attenuation of the fiber and optical components that are introduced on the TP. Namely, the transmission distance (L) of a TP is estimated as follows:

$$\begin{array}{cc}\hfill L& =\frac{P-\left({\sum }_{m\in \mathcal{M}}{N}_{\mathrm{M}}\left(m\right)A_{\mathrm{M}}\left(m\right)+{\sum }_{o\in \mathcal{O}}{N}_{\mathrm{O}}\left(o\right)A_{\mathrm{O}}\left(o\right)+2A_{\mathrm{C}}+A_{\mathrm{MM}}\right)}{\alpha }.\hfill \end{array}$$

(1)

where P is the power budget, $N_{\mathrm{M}}\left(m\right)$ and $A_{\mathrm{M}}\left(m\right)$ are, respectively, the number of MUXs and the attenuation of a MUX of type $m\in \mathcal{M}$, $N_{\mathrm{O}}\left(o\right)$ and $A_{\mathrm{O}}\left(o\right)$ are, respectively, the number of OADMs and the attenuation of an OADM of type $o\in \mathcal{O}$, $2A_{\mathrm{C}}$ represents the attenuation of end connectors, and $A_{\mathrm{MM}}$ is the maintenance margin. We consider that the attenuation of optical devices (MUXs and OADMs) includes the attenuation of their connectors. The power budget (P) is the difference between the minimal transmitter outer optical modulation amplitude ($P_{\mathrm{TX}}$) and receiver sensitivity ($P_{\mathrm{RX}}$), as shown in Figure 2-1 in [38].

Equation (1) calculates the maximum allowable length of the optical fiber on a TP. The calculation is based on the standard optical power budget model, which accounts for the available power budget (P) and the attenuation of optical components that are present on the TP (see the components parameters in Section 5), as explained in Chapter 4.2 in [39]. Due to the short assumed distances, less than 10 km, factors other than the power budget affecting transmission, such as dispersion, are not considered.

3.4. Latencies

Fronthaul data flows in 5G RANs have stringent latency requirements, which are imposed by low-latency 5G services and the processing requirements of functional split options. The one-way latency budget may be as low as some tens of µs for specific fronthaul traffic profiles and functional split options [12,13]. To account for these requirements, in the study, we assume a 50 µs propagation latency limit, which constrains the allowable length of a TP to 10 km. Consequently, the TPs that are longer than the maximum permissible path length are not included in the sets of candidate paths.

4. MILP Optimization Model

In this section, we focus on formulating the xHaul network planning problem for the Flex-O deployment scenario. The problem concerns the provisioning of optimized optical TPs, which assures the connectivity between a set of remote sites with the hub. In this study, the optimization goal of the network planning problem is to minimize the overall network cost (as discussed in Section 3.2), which is achieved by the proper provisioning and configuration of the TPs in the network. The problem consists in the selection of routes of the TPs as well as in the selection and placement of optical devices (MUXs and OADMs) on the TPs. The problem constraints are the following:

• A single TP (either direct or traversing) is selected for each remote node to realize the (wavelength) connections requests of the node. If a traversing TP is selected for a remote node to serve its connection requests, then it implies that an OADM of the capacity sufficient to add/drop the requested connections is installed on the TP at the node.
• Each connection has assigned a dedicated wavelength on the TP by which it is served. The number of wavelengths assigned on a TP cannot exceed the capacity of the WDM transmission system.
• The MUXs of the capacity sufficient to multiplex/demultiplex the wavelengths carried by the TPs have to be used at the end nodes of the TPs. The MUXs are not needed on the TPs that carry single wavelengths.
• The maximum transmission distance of a TP, limited by the optical power budget and optical components of the TP (see Section 3.3), cannot be lower than the length of the TP.
• The propagation latency of a TP must not exceed the available latency budget (see Section 3.4).

We model the network planning problem as an MILP optimization problem. To this end, we define the following set of variables:

binary

• $x_{dp}$—indicates that TP $p\in \mathcal{P}\left(d\right)$ is established for demand $d\in \mathcal{D}$;
• $x_{dl}$—indicates that wavelength $l\in \mathcal{W}$ is assigned to demand $d\in \mathcal{D}$;
• $x_d$—indicates that the TP established for demand $d\in \mathcal{D}$ serves some other demand;
• $y_d$—indicates that demand $d\in \mathcal{D}$ is served by a TP established for other demand;
• $y_{d\overline{d}}$—indicates that demand $d\in \mathcal{D}$ is served by the TP established for demand $\overline{d}\in \mathcal{D}$;
• $y_{d\overline{d}l}$—indicates that wavelength $l\in \mathcal{W}$ is used to serve demand $d\in \mathcal{D}$ on the TP established for demand $\overline{d}\in \mathcal{D}$;
• $x_{dm}^{\mathrm{H}}$—indicates that the MUX of type $m\in \mathcal{M}$ is used at the hub site on the TP of demand $d\in \mathcal{D}$;
• $x_{dm}^{\mathrm{R}}$—indicates that the MUX of type $m\in \mathcal{M}$ is used at the remote site on the TP of demand $d\in \mathcal{D}$;

integer

• $w_d$—represents the number of wavelengths utilized on the TP established for demand $d\in \mathcal{D}$;

linear

• $u_d^{\mathrm{M}}$— the attenuation of MUXs on the TP established for demand $d\in \mathcal{D}$;
• $u_d^{\mathrm{O}}$—the attenuation of OADMs on the TP established for demand $d\in \mathcal{D}$;
• $z^{\mathrm{F}}$—the overall cost of fibers used;
• $z^{\mathrm{M}}$—the overall cost of MUXs deployed;
• $z^{\mathrm{O}}$—the overall cost of OADMs deployed.

In

Table 1. MILP model of the network planning problem.

Objective	Minimize $\mathit{z}={\mathit{z}}^{\mathbf{F}}+{\mathit{z}}^{\mathbf{M}}+{\mathit{z}}^{\mathbf{O}}$		(2)
Constraints
path selection	${\sum }_{p\in \mathcal{P}\left(d\right)}{x}_{dp}+y_d=1,$	$\forall d\in \mathcal{D},$	(3)
	${\sum }_{\overline{d}\in \mathcal{D},\overline{d}\ne d}{y}_{d\overline{d}}=y_d,$	$\forall d\in \mathcal{D},$	(4)
	${\sum }_{p\in \mathcal{Q}(d,\overline{d})}{x}_{\overline{d}p}\ge y_{d\overline{d}},$	$\forall d,\overline{d}\in \mathcal{D},\overline{d}\ne d,$	(5)
	${\sum }_{\overline{d}\in \mathcal{D},\overline{d}\ne d}{y}_{\overline{d}d}\le (W-1)·x_d,$	$\forall d\in \mathcal{D},$	(6)
wavelength assignment	${\sum }_{l\in \mathcal{W}}{x}_{dl}=W\left(d\right)$	$\forall d\in \mathcal{D},$	(7)
	$x_{dl}+x_{\overline{d}l}+y_{d\overline{d}}\le 2,$	$\forall d,\overline{d}\in \mathcal{D},\overline{d}\ne d,$$l\in \mathcal{W},$	(8)
	$x_{dl}+y_{d\overline{d}}\le 1+y_{d\overline{d}l},$	$\forall d,\overline{d}\in \mathcal{D},\overline{d}\ne d,$$l\in \mathcal{W},$	(9)
	${\sum }_{d\in \mathcal{D},d\ne \overline{d}}{y}_{d\overline{d}l}\le 1,$	$\forall \overline{d}\in \mathcal{D},$$l\in \mathcal{W},$	(10)
	$w_d=W\left(d\right)·(1-y_d)+{\sum }_{\overline{d}\in \mathcal{D},\overline{d}\ne d}W\left(\overline{d}\right)·y_{\overline{d}d},$	$\forall d\in \mathcal{D},$	(11)
	$w_d\le W,$	$\forall d\in \mathcal{D},$	(12)
MUX selection	${\sum }_{m\in \mathcal{M}}{x}_{dm}^{\mathrm{H}}=(1-y_d),$	$\forall d\in \mathcal{D},$	(13)
	${\sum }_{m\in \mathcal{M}}{x}_{dm}^{\mathrm{R}}=(1-y_d),$	$\forall d\in \mathcal{D},$	(14)
	${\sum }_{m\in \mathcal{M}}W\left(m\right)·x_{dm}^{\mathrm{H}}\ge w_d,$	$\forall d\in \mathcal{D},$	(15)
	${\sum }_{m\in \mathcal{M}}W\left(m\right)·x_{dm}^{\mathrm{R}}\ge W\left(d\right)·(1-y_d),$	$\forall d\in \mathcal{D},$	(16)
	${\sum }_{m\in \mathcal{M}}W\left(m\right)·x_{dm}^{\mathrm{R}}\ge 2·x_d,$	$\forall d\in \mathcal{D},$	(17)
transmission distance	$u_d^{\mathrm{M}}={\sum }_{m\in \mathcal{M}}{A}_{\mathrm{M}}\left(m\right)·\left(x_{dm}^{\mathrm{H}}+x_{dm}^{\mathrm{R}}\right),$	$\forall d\in \mathcal{D},$	(18)
	$u_d^{\mathrm{O}}={\sum }_{\overline{d}\in \mathcal{D},\overline{d}\ne d}\left(A_{\mathrm{O}}\left(o\left(\overline{d}\right)\right)·y_{\overline{d}d}\right),$	$\forall d\in \mathcal{D},$	(19)
	$\left(P-\left(u_d^{\mathrm{M}}+u_d^{\mathrm{O}}+2·A_{\mathrm{C}}+A_{\mathrm{MM}}\right)\right)·{\alpha }^{-1}\ge {\sum }_{p\in \mathcal{P}\left(d\right)}D\left(p\right)·x_{dp},$	$\forall d\in \mathcal{D},$	(20)
cost	$z^{\mathrm{F}}=2·{\kappa }^{\mathrm{F}}·{\sum }_{d\in \mathcal{D}}{\sum }_{p\in \mathcal{P}\left(d\right)}D\left(p\right)·x_{dp},$		(21)
	$z^{\mathrm{M}}=2·{\sum }_{d\in \mathcal{D}}{\sum }_{m\in \mathcal{M}}{\kappa }^{\mathrm{M}}\left(m\right)·\left(x_{dm}^{\mathrm{H}}+x_{dm}^{\mathrm{R}}\right),$		(22)
	$z^{\mathrm{O}}=2·{\sum }_{d,\overline{d}\in \mathcal{D}:\overline{d}\ne d}\left({\kappa }^{\mathrm{O}}\left(o\left(\overline{d}\right)\right)·y_{\overline{d}d}\right),$		(23)
	$x_{dp},x_{dl},x_d,y_d,y_{d\overline{d}},y_{d\overline{d}l},x_{dm}^{\mathrm{H}},x_{dm}^{\mathrm{R}}\in \{0,1\}$,		(24)
	$w_d\in \mathbb{N}$, $u_d^{\mathrm{M}},u_d^{\mathrm{O}},z^{\mathrm{F}},z^{\mathrm{M}},z^{\mathrm{O}}\in \mathbb{R}$.		(25)

, we present the objective function and the constraints of the MILP optimization model developed for the cost-aware OADM placement problem.

The optimization objective, expressed by (2), is to minimize the WDM optical network deployment cost, according to the cost model defined in Section 3.2.

Constraints (3)–(6) concern the selection of TPs for particular demands. Constraint (3) assures for each demand d that either a TP is selected from the candidate set of paths and established for this demand or the demand is served by means of an OADM by a TP established for some other demand. Constraint (4) assures that the TP established for some demand $\overline{d}$ is used to serve demand d if a direct TP is not established for d (i.e., when $y_d=1$). Constraint (5) imposes that a TP established for demand $\overline{d}$, which also serves demand d, should be routed through the remote site associated with d. Constraint (6) determines variable $x_d$, which indicates if the TP established for demand d is also used to serve some other demand.

Constraints (7)–(12) are responsible for the assignment of wavelengths to particular demands. Namely, Constraint (7) assigns $W\left(d\right)$ wavelengths requested by demand d by setting to one an adequate number of variables $x_{dl}$. Constraint (8) assures that two demands d and $\overline{d}$ may use the same wavelength only if demand d is not served by a TP established for demand $\overline{d}$. Constraint (9) sets variable $y_{d\overline{d}l}$ equal to one if wavelength l is assigned to demand d and demand d is served by the TP established for demand $\overline{d}\in \mathcal{D}$. Constraint (10) assures that at most one demand d may have assigned wavelength l among all demands served be the TP established for demand $\overline{d}$. Whenever a TP is established for demand d (i.e., when $y_d=0$), Constraint (11) determines the number of wavelengths utilized on the TP as the sum of wavelengths requested by d and all other demands served by the TP. Constraint (12) assures that the number of utilized wavelengths does not exceed the WDM transmission capacity (W).

Constraints (13)–(17) are used to determine the type of MUXs deployed at the ends of TPs. The MUXs are installed only for the demands with established TPs ($y_d=0$), which is imposed by Constraints (13) and (14), respectively, for the hub site and the remote site. Constraint (15) assures that the number of channels of the MUX installed at the hub is not lower than the number of wavelengths utilized on the TP. Constraint (16) assures that the number of channels of the MUX installed at the end remote site is sufficient to serve the wavelengths originated at the site. Moreover, Constraint (17) assures the use of a MUX at the end remote site whenever the TP serves also other demands.

Constraints (18)–(20) implement the transmission distance model described in Section 3.3 for each demand that has established a TP. Constraint (18) calculates the attenuation of MUXs used at the ends of the TP, taking into account the type of the MUXs applied. Constraint (19) calculates the attenuation of OADMs installed on the TP at intermediate remote sites. Constraint (20) estimates the optical power budget, accounting for the components of the optical path, to determine the maximum transmission distance allowable for the TP selected.

Constraints (21)–(23) determine the cost elements. Constraint (21) estimates the cost of the optical fiber leased, taking into account the overall length of TPs. Constraint (22) calculates the cost of MUXs deployed at the ends of the TPs, namely, at the hub site and the remote sites. Constraint (22) calculates the cost of OADMs installed at the remote sites that are served by the TPs established for other demands. To reflect both transmission directions, coefficient 2 appears in Constraints (21)–(23).

Finally, Constraints (24) and (25) determine the type of variables.

MILP model (2)–(25) corresponds to the Flex-O network deployment scenario, in which different types of OADM and MUX devices are available and can be applied in a flexible way on the TRs, according to the wavelength demands of particular remote sites. The reference scenarios described in Section 3 can be implemented by introducing the following modifications in the MILP model.

• In scenario Fix-O, sets $\mathcal{M}$ and $\mathcal{O}$ are limited to the single types of MUX and OADM devices, respectively, such that they support the maximum number of channels available in the WDM system; in addition, set $\mathcal{M}$ includes a fictitious type of MUX that supports one channel.
• In scenario Flex-D, all variables $y_d$ are set to 0, which implies that the remote sites are connected with the hub using direct TPs and the OADMs are not applied.
• In scenario Fix-D, as in Flex-D, variables $y_d$ are set to 0 and, moreover, set $\mathcal{M}$ includes only two types of MUXs, namely, the one corresponding to the WDM system capacity and the fictitious one supporting one channel.

5. Evaluation Results and Discussion

The analysis of the Flex-O network deployment scenario is performed in mesh network topologies MESH-9, MESH-20, and MESH-38, also studied in [20,35], which are presented in Figure 3. In the networks, the link lengths are distributed uniformly between 1 and 3 km. A k-shortest path algorithm was used to generate candidate TPs and the paths of the length exceeding 10 km were excluded (according to the assumption in Section 3.4).

Two scenarios with the WDM capacity being equal to 4 and 8 wavelengths (channels) are studied. These capacities reflect the limited number of wavelengths available in the passive WDM solutions considered for low-cost 5G xHaul networks [9] and correspond to the number of wavelengths supported by system xWave 400G [18]. The fiber loss coefficient accounts on both the value of 0.40 dB/km reported in [40] and additional margin of 0.10 dB/km due to splices losses and environmental factors. The connector loss and the maintenance margin are 0.3 dB and 2.0 dB, respectively. The values of $P_{\mathrm{TX}}$ and $P_{\mathrm{RX}}$ are based on the specification [18]. The system parameters are summarized in

Table 2. Assumed values of the transmission system parameters.

WDM capacity (W)	$\{4,8\}$
Fiber loss coefficient ($\alpha$) [dB/km]	$0.5$
Connector loss ($A_{\mathrm{C}}$) [dB]	$0.3$
Maintenance margin ($A_{\mathrm{MM}}$) [dB]	$2.0$
Minimal transmitter outer optical modulation amplitude ($P_{\mathrm{TXoma}}$) [dBm]	$3.0$
Sensitivity of receiver ($P_{\mathrm{RXoma}}$) [dBm]	$-14.0$
Power budget ($P=P_{\mathrm{TXoma}}-P_{\mathrm{RXoma}}$) [dBm]	$17.0$

.

The attenuation of OADMs [23] and MUXs [41,42], presented in

Table 3. Attenuation of OADMs and MUXs; the values do not comprise connector losses.

	Number of Channels
	1	2	3	4	8
OADM attenuation [dB]	0.8	1.4	2.1	2.8	-
MUX attenuation [dB]	0.0	0.9	–	1.2	1.6

, corresponds to typical values of commercial products. In scenario Fix-O, the OADM is composed of a pair of MUX modules, similar to [19,20], where one MUX operates as a de-multiplexer and the ports of bypassed channels are connected directly by means of patchcords. Accordingly, the OADM attenuation in Fix-O is 3.0 dB and 3.8 dB for OADM-4 and OADM-8, respectively, and it includes the losses of a patchcord.

The lease price of a km of dark fiber (${\kappa }^{\mathrm{F}}$) is assumed to be equal to $250 [43,44]. A linear cost model is considered for the optical devices, where one channel is estimated at the cost of $15 for a MUX and $30 for an OADM [45].

For each remote site, the number of requested wavelengths was generated randomly between $W^{\min }$ and $W^{\max }$ such that $1\le W^{\min }\le W^{\max }\le 4$. The traffic load (denoted as $\rho$) represents the average number of wavelengths requested by a remote site; in particular, $\rho =(W^{\min }+W^{\max })/2$. In the analysis, we consider $1.0\le \rho \le 4.0$, where $\rho =1$ corresponds to $W^{\min }=W^{\max }=1$, $\rho =2.0$ to $W^{\min }=1,W^{\max }=3$, etc.

Solver CPLEX v.12.9 [46] was used to solve the MILP model. The solver was run in a parallel mode and with default settings on a dual-processor 2.2 GHz 10-core Xeon workstation (40 logical cores in total) with 128 GB RAM. We report that all the results obtained were optimal.

5.1. Analysis of the Impact of Candidate Paths

In the first set of experiments concerning the Flex-O scenario, we analyzed the overall network cost (z) and the complexity of solving the MILP model in a function of the number of candidate paths (k) in the networks considered.

Figure 4a shows the values of z, obtained and averaged for traffic loads $\rho \in \{1.0,1.5,2.0\}$ and WDM capacity $W\in \{4,8\}$, as a function of k. Moreover, Figure 4b presents the cost savings, defined as a relative difference in z, with respect to the single-path case ($k=1$). The results indicate that the availability of a larger set of candidates routing paths allows to decrease the network cost, which is achieved due to increased opportunities for the aggregation of wavelengths at remote sites. The cost savings are between 9 and 10% in MESH-9/MESH-20, and above $13\%$ in MESH-38, and they stabilize for $k\ge 4$, $k\ge 10$, and $k\ge 12$ in the respective networks.

Figure 5 presents the CPLEX computation times of solving the MILP model (2)–(25) as a function of k in the largest MESH-38 network for different traffic loads ($\rho$) and assuming $W\in \{4,8\}$. We can see that the MILP model is scalable, and optimal solutions are found within less than 40 s, even for the largest problem instance ($k=16$, $\rho =1.5$, $W=8$). In general, the computation times increase with k and W, which translates into a larger set of problem variables and constraints. The impact of $\rho$ on the MILP solving times is related to the amount of available options for aggregation of wavelengths in the network, which are considered by the solver during the search for an optimal solution. Namely, for lower values of $\rho$ at which the remote sites have smaller connection (wavelength) requests, it is possible to aggregate the wavelengths from a larger number of sites on a single TP, and the amount of possible combinations of such sites is high. On the other hand, for higher $\rho$, the remote sites either cannot be served by other TPs since they request numbers of wavelength connections that are too large, or the aggregation of wavelengths is possible just for a few sites, whereas direct TPs are established for the others. It leads to the reduction in the solution space and smaller CPLEX runtimes.

In the remainder, we assume $k=4$ in MESH-9, $k=10$ in MESH-20, and $k=12$ in MESH-38.

5.2. Comparison of Network Deployment Scenarios

Next, we evaluate relative gains (savings) in the overall network cost (denoted as $\Delta$) achieved in the Flex-O network deployment scenario in comparison to the reference scenarios described in Section 3, namely, Fix-O, Flex-D, and Fix-D.

Figure 6, Figure 7 and Figure 8 show the optimized network deployment costs (z) and the values of $\Delta$ as a function of traffic load ($\rho$), assuming different WDM capacities (W) in the three networks. We can see that the application of OADMs (in scenarios Flex-O and Fix-O) allows to reduce the network deployment costs in all networks when compared to the scenarios with direct TPs (i.e., Flex-D and Fix-D). For instance, the cost gains of Flex-O can reach up to above $45\%$ in network MESH-38. Moreover, the optimized application of OADMs and MUXs in Flex-O brings significant cost savings when compared to the Fix-O scenario, in which the optical devices of a fixed capacity are considered. In particular, the cost gains can reach up to $25\%$ in MESH-9, $30\%$ in MESH-20, and $35\%$ in MESH-38 for $W=8$.

In general, the cost savings are higher in larger networks, which can be explained by the higher possibilities for the aggregation of traffic from remote sites. These savings decrease with the traffic load, which comes from higher amount of requested connections (wavelengths) at remote sites and, hence, lower possibilities for their aggregation on the TPs. Finally, the cost gains increase with the WDM system capacity, which is due to the higher number of wavelengths that a TP can carry.

5.3. Cost Analysis

We perform a detailed analysis of the contribution of individual cost elements, namely, the lease of optical fibers and the cost of installed MUXs and OADMs in the network deployment scenarios considered.

Figure 9 presents the cost of fibers, MUXs, and OADMs (represented on the charts as bars segments in different colours) assuming different traffic loads ($\rho$) and WDM system capacities (W) in network MESH-38. Note that the top of each bar represents the overall network cost (z). As it can be seen, scenarios Flex-D and Fix-D do not derive any costs related to OADMs since they assume the use of direct (dedicated) TPs between the remote sites and the hub, without traffic aggregation at intermediate sites. Still, the overall cost of these scenarios is higher than when using OADMs in Flex-O/Fix-O, which is due to the considerable contribution of the cost of fiber in comparison to the cost of OADMs. Moreover, scenarios Flex-D and Fix-D do not require any MUXs for $\rho =1.0$. In this case, the remote sites request single wavelength connections and, therefore, there is no need for wavelength aggregation (using MUXs) at the ends of TPs. The cost of all four network deployment scenarios is the same only in the case of $\rho =4.0$ and $W=4$. Here, the traffic (wavelength) demands at remote sites are high such that no traffic aggregation at intermediate sites is possible using the available WDM transmission resources, and only direct TPs can be established in the network.

5.4. Illustration of Optimized TPs in Urban Network

Finally, we illustrate the results of the optimization of TPs in the exemplary urban network WRO-17, with traffic demands between 1 and 2 wavelengths per a site, WDM capacity $W=8$, and the Flex-O network deployment scenario applied. Topology WRO-17, shown in Figure 10a, represents remote sites (denoted by circles) placed in proximity of a subset of real antenna locations (denoted by triangles) in the center of the city of Wroclaw. The links connecting the remote nodes and the hub site (denoted by a hexagonal) are driven along streets, and their lengths reflect real physical distances.

Figure 10b shows the optimal routing of TPs (each in a different color) with traffic aggregation at intermediate nodes and assignment of wavelengths. OADM-1 and OADM-2 are used to aggregate 1 and 2 wavelengths, respectively, at the intermediate sites. The optimized use of OADMs allows to decrease the total number of TPs from 17 TPs necessary in the Flex-D/Fix-D scenarios to 4 TPs in Flex-O, in which the paths aggregate traffic from up to 5–6 remote sites. In this example, the network deployment cost can be reduced from about $18,000 (in Flex-D) to about $7000 (in Flex-O), which leads to the cost savings of about 60%. The much lower cost values in network WRO-17, when compared to previously studied networks, are related to the lower overall length of the optical fiber used, which is a dominant cost element as shown in Section 5.3. Finally, we can see that the use of wavelengths is unrepeatable on particular TPs, which validates the correctness of the wavelength assignment constraints in the MILP model.

6. Conclusions

We addressed the problem of cost-aware planning of 5G packet-optical xHaul access networks, in which traffic (wavelengths) from a number of remote sites can be aggregated on the TPs. The main focus was on the optimized selection and placement of optical devices—OADMs and MUXs—on the TPs with the aim to minimize the overall network cost. To this end, an MILP optimization model for the network planning problem was formulated. Using the model, four different network deployment scenarios were investigated. The scenarios differed in the wavelength aggregation capabilities and in the flexibility of the use of different types of OADM/MUX devices.

The obtained results indicate that the MIP optimization model proposed is scalable. Additionally, it is beneficial from the network cost perspective to consider larger sets of candidate routing paths. Regarding the cost savings from the flexible (optimized) application of OADMs, they can reach up to $35\%$ when compared to the scenario with fixed-capacity OADMs, and up to above $45\%$ with respect to the network using direct TPs (i.e., without OADMs). In general, the cost savings are higher in larger networks and in the networks with higher WDM capacity, whereas they decrease with the traffic load. Eventually, the cost of OADMs is relatively low with respect to the cost of optical fiber lease, which justifies the aggregation of wavelengths from intermediate remote sites on the TPs.

Our future research will concern the optimized placement of OADMs in xHaul network protection scenarios, which will require a proper extension of the optimization model. Expecting a higher complexity of the optimization problem, we will focus as well on developing heuristics for the optimized planning of protected TPs in such networks.