Slicing Resource Allocation for eMBB and URLLC in 5G RAN

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Introduction
With the increase of the demand for mobile phones and networks, the new Internet of things (IoT) for consumers and vertical industries has developed rapidly. e mobile Internet and the IoT tend to be the main forces to drive the development of mobile communication in the future network. In particular, the equipment of massive IoT that connected to sensors such as humidity sensors and remote industrial robots needs to provide divergent services [1]. For the multiservice requirement of vertical industries in the 5th generation (5G), the one-size-fits-all design concept is not viable anymore, and it is a promising approach to meet the requirement that slicing one physical network into several logical networks according to different demands [2]. Currently, network slicing is one of the most cost-effective latency. Network orchestration architecture for dynamic network slicing is considered in [7], demonstrating how to provide dynamic network slicing for enterprise-networking services and mobile metro-core networks. Rayani et al. in [8] proposed virtualized EPC-based 5G architecture and considered the resource allocation problem, which aims at minimizing the cost of network slicing while ensuring QoS requirement.
In terms of the RAN, some researchers have studied the problem of network slicing resource allocation. One of the main challenges of RAN slicing is to provide different levels of resource isolation through resource abstraction, virtualization, and separation of services [9]. Many papers have already studied the main challenges. e network slicing could be allocated resources for each service to provide performance guarantees and isolate it from other services [10].
ree typical network slices focused on service-oriented deployment by providing different deployment strategies, which can effectively improve the utilization rate of resources [11]. e development of technology focuses on the CN slicing, but it is essential to study the network slicing of the RAN, especially the resource allocation problem with RAN slicing. In addition, the pivotal problem of the RAN slicing algorithm is that the mathematical formula is the NPhard problem [12]. Most scholars focus on the architecture of RAN slicing, and the research on resource allocation optimization of RAN slicing is insufficient. One of the principal research projects is resource allocation among different slices in the RAN [13]. ese issues motivate our paper.
Different from these papers, we pay more attention to the multiservice virtual resource allocation and management of the RAN slicing. Our interest in this article focuses on the methods and mathematical models of resource allocation algorithms for 5G network slicing eMBB and URLLC. e purpose of our research is to improve the resource utilization of the overall system and the reliability of the URLLC service. Our contribution in this paper can be summarized as follows: (i) We propose a network architecture with slice eMBB and slice URLLC in Figure 1 and aim to maximize the spectral efficiency of the overall network system.
(ii) To efficiently allocate the slice resources, we formulate the spectral efficiency maximization problem with the high capacity of eMBB slices and the low delay of URLLC slices.
(iii) e original mixed-integer nonlinear programming problem is approximately transformed into a nonlinear problem by relaxing integer variables, and we prove that the nonlinear problem is a convex optimization problem.
(iv) Finally, we propose a slice resource allocation algorithm by applying the Powell-Hestenes-Rockafellar (PHR) and the branch and bound method. e simulation results show that the proposed algorithm can ensure the users' requirement of the eMBB slice and the users' requirement of the URLLC slice with a high probability and improve the spectral efficiency of the overall system. e remainder of this paper is organized as follows: Section 3 introduces the system model and the problem formulation. In Section 4, we determine the optimal power and the subcarrier allocation spectral efficiency design with network slicing. e simulation results are shown in Section 5. Section 6 concludes this paper.

Related Work
e main idea of RAN slicing resource allocation research is optimizing the performance of the entire network system while ensuring the various users' requirements. In this section, we analyze the resource allocation of RAN slicing from the perspective of single service and multiservice. Regarding the single service of RAN slicing, the researchers focused on the price of slice resources [3,8,[14][15][16] and the throughput [17,18]. In [3], wang et al. studied resource pricing as a Stackelberg pricing game, in which network slice customers (NSCs) maximize their profit by adjusting their slice's resource requirement. Lee et al. [18] considered the multitenant cellular network slicing, aiming to achieve a higher network throughput, fairness, and QoS performance.
As to multiservice network resource allocation, throughput [10,19], delay tolerance [20,21], operator revenue [22,23], and the number of network slicing [24] were analyzed with the RAN slicing. Especially, in [19], a joint eMBB and URLLC scheduler was proposed, which can meet the requirement of URLLC while maximizing the utility of eMBB traffic. e radio resource allocation of different network slices was utilized in the downlink fog RAN in [20], where the network was logically divided into high transmission rate slices and low delay slices, and the main objective was to minimize delay tolerance. In [21], Alsenwi et al. proposed proportional fair resource allocation formula that allocates resources to incoming URLLC traffic, while ensuring the reliability of eMBB and URLLC. Wang et al. in [23] studied network slice dimensioning with resource pricing policy, by exploring the relationship between resource efficiency and profit maximization, aiming to maximize the operator's revenue from the perspective of slice price. To solve the multiservice resource allocation problem in the interslice, Smpokos et al. [24] designed a scheduling algorithm that the scheduler schedules a single type of service with their features in each slice. Although the above authors mentioned the multiservice virtual network with network slicing, the design of the spectral efficiency with multiservice network slicing and URLLC network reliability were not considered.

System Model and Problem Formulation
In this section, we first introduce a slice model of a downlink orthogonal frequency division multiple access (OFDMA) network. en, the types of slices are analyzed. Finally, we formulate a spectral-efficient maximization problem with 2 Wireless Communications and Mobile Computing slices design in the constraints of the subcarrier and the power.

System Model.
We consider a wireless virtual network with a single cell downlink OFDMA system. e users K � 1, 2, . . . , K { } are randomly located in the coverage area of the base station (BS). e allocation round is one transmission time interval (TTI) [25]. During each TTI, the total bandwidth of the system is divided into N subbandwidth B on average and its corresponding subcarrier sets are I n � 1, 2, . . . , N { }. ese resource blocks are shared by two slices, i.e., eMBB slice with user set K 1 , |K 1 | � K 1 and URLLC slice with user set K 2 , |K 2 | � K 2 , where K � K 1 ∪ K 2 and K 1 ∩ K 2 � ∅. In this model, we aim to ensure that the two kinds of slices meet different users' requirement when the spectral efficiency of the network is maximized.

Problem Formation.
For OFDMA downlink wireless virtual network, we apply the slicing technology to solve problems with two types of traffic, i.e., eMBB and URLLC slices. Next, we analyze the constraints of the two kinds of traffic slices, respectively.

Slice 1: eMBB ( roughput Priority).
When user k of slice 1 sends a request to a mobile virtual network operator, the corresponding throughput is given by where a n,k � 1, assign subcarrier n to user k, in which r n,k is the data rate of user k with respect to (w.r.t) subcarrier n; N 0 is the noise spectral density; g n,k and p n denote the channel gain and the transmit power between the BS and user k w.r.t subcarrier n, respectively; and σ 0 is the throughput requirement of user k.

Slice 2: URLLC (Delay Priority).
For the users with delay requirement, we assume that the maximum data arrival rate of users in each slice follows a Poisson distribution, and the packet length of each user follows an exponential distribution. From each user's data packet sequence, we infer that the overall system can be regarded as an M/M/1 system. en, the corresponding delay outage probability of user k in slice 2 is given by where D k and D k,max are the delay of user k and the maximum delay that user k tolerates, respectively, and d k,max is the maximum data arrival rate of user k. In addition, we assume the maximum transmit power of BS is P 0 . Combining the above two slices, the system throughput R � K k�1 N n�1 a n,k B log(1 + (g n,k p n /N 0 B)) and total bandwidth NB, the spectral-efficient problem can be formulated as  Wireless Communications and Mobile Computing max p n ,a n,k where (5a) aims to maximize the spectral efficiency of the network system; (5b) ensures that the transmission rate received by user k is no less than the rate requirement; and (5c) guarantees the low outage probability e of user k in slice 2. For (5d)-(5f ), we assume that all users make full use of the subcarriers with the maximal transmit power, and each subcarrier associates one user at most.

Joint Power and Subcarrier Allocation
Since the original problem (5a)-(5f ) is difficult to solve, an approximation method is adopted. From [26], the original problem (5a)-(5f ) can be approximated as where N k is the number of subcarrier assigned to user k, R k � N k B log(1 + (c k p k /N k )), c k is the channel gain-tonoise ratio (CNR) for user k, and p k is transmit power of user k [26]. Equations (6d) and (6e) are to make full use of the radio resource. Unfortunately, the problem in (6a)-(6e) is a mixed-integer programming problem, which is nonconvex. We can rewrite (6a) as where (6a) and (7) are equivalent. e optimization problem in (6a)-(6e) is formulated by combining (7) and (6b)-(6e).
Since the variable N k is discrete, we can see that the nonconvex optimization problem in (6a)-(6e) is a mixed-integer programming problem. e branch and bound method can be applied to solve the problem, combing the relaxed problem. By relaxing the variable N k and enlarging its range: we can obtain the relaxed problem: It can be proved that the problem in (8a)-(8e) is a convex optimization problem, which is exhibited in the following theorem.
Proof. See Appendix.
From eorem 1, the convex optimization problem in (8a)-(8e) can be solved by the PHR augmented Lagrangian algorithm [27,28]. We first relax the inequality constraint by introducing auxiliary variables x k and y k to enable the equality in (8b) and (8c). en, we can get the augmented Lagrangian function L ρ in (9) ; α k , β k , μ, and λ is the Lagrange multiplier; and ρ is the penalty factor. Next, we further eliminate the variables to reduce the complexity of the algorithm. We calculate the partial derivatives with respect to the auxiliary variables, which can be written as By setting (10) to be zero, we can determine the auxiliary variable that minimizes the augmented Lagrange function. en, we obtain Plugging (12) into (9), we get Similarly, when k ∈ K 2 , we can easily obtain us, Based on (13) and (4), the augmented Lagrangian function can be formulated as (16). In order to facilitate the description of the algorithm, we define (16) and the equality function In addition, the gradient of equality function and inequality function are used in the PHR augmented Lagrangian algorithm, which are, respectively, shown as Wireless Communications and Mobile Computing where e relaxed problem is solved by the PHR augmented Lagrangian algorithm, which is shown in Algorithm 1. For the optimal subcarrier and power allocation, we apply Algorithm 1 and the branch and bound method to solve it. By relaxing the integer constraints in the mixed-integer programming problem, each relaxed problem is solved by Algorithm 1. By adopting the joint power and subcarrier allocation (JPSA) algorithm in Algorithm 2, the iteration is carried out with the branch and bound method until the obtained integer solution satisfies the iterative condition. erefore, we can obtain the optimal resource allocation and the spectral efficiency s:

Simulation
In this section, we evaluate the effectiveness of the proposed JPSA algorithm and compare it with the corresponding relaxed problem. e adaptive particle swarm optimization (APSO) [29], the equal power allocation (EPA), and the equal subcarrier allocation (ESA) algorithm are compared with the JPSA algorithm, where in the EPA the transmit power for each user from BS is P 0 /K and in the ESA the assigned subcarrier number for each user is N/K. In order to describe the result of simulation conveniently, we assume that users in the same slice require the same requirement of throughput or delay but different CNRs. e total number of users is 16, the total bandwidth of the network system is 5 MHz, and the number of subcarriers is 20. To show the utility of network slicing, we evaluate the reliability of the network system with a single slice (eMBB slice or URLLC slice) with that of the network system supporting both eMBB slices and URLLC slices. In Figure 2, we evaluate the spectral efficiency design of the proposed algorithm and other algorithms versus the total power. We can see that the proposed joint JPSA algorithm improves the spectral efficiency more effectively. When the total power is small, the APSO Initialize α, β, μ, λ, ρ > 0, i � 0, θ ∈ (0, 1), i max � 500, V i,old � 10, η > 1, δ ∈ [0, 1]. while V i > δ and i < i max do Solve augmented Lagrangian function with fixed ρ, α, β, μ, λ, through BFGS algorithm with (10) to obtain X i , where End while ALGORITHM 1: e Relaxed optimization problem. 6 Wireless Communications and Mobile Computing [29] and our proposed method are close to the optimal relaxed solution. When the total power is large, the spectral efficiency of APSO [29], ESA, and EPA are not as high as that of the JPSA algorithm. It can be seen from Figure 2 that the solution of the APSO is not stable enough and that the greater the total power of the system is, the more effective the JPSA algorithm is to improve the spectral efficiency.
In Figure 3, we evaluate the spectral efficiency of the eMBB slice, the URLLC slice and the overall network system under different user throughput requirements of the eMBB slice. When σ 0 increases, the spectral efficiency of the eMBB slice is almost the same, and the spectral efficiency of the URLLC slice and the whole system decreases. erefore, when we pay more attention to the eMBB slice, we can appropriately increase the throughput requirement of the users.
As can be seen from Figure 4, the network slice of URLLC is more reliable when the delay requirement is Solve the nonlinear programming problem of the relaxed N in (8a)-(8e) by Algorithm 1, we get l the lower bound of (7) and the initial resource allocation N * k , p * k .
Find the upper bound of the problem. Initialize the subcarrier number N i ∈ Z and the power P i , i � 1, 2, . . . , K. We determine the feasible solution, and we obtain u as an upper bound of (7).

End if
Branch the problem in (7) into problems P 1 with N k ≤ ⌈N * k ⌉ and P 2 with N k ≥ ⌈N * k ⌉ + 1 by the branch and bound method. We solve the two problems P 1 and P 2 that are still the convex optimization problem. Combining Algorithm 1, we get u 1 , N (1) k , p (1) k and u 2 , N (2) k , p (2) k . greater than 0.005 sec. When there is a higher delay requirement of D k,max ≤ 0.003 sec, the URLLC slice is more reliable when using the JPSA algorithm, and its overall reliability is higher than the EPA and ESA algorithms. In Figure 5, in order to facilitate the analysis of the part of Figure 4 whose reliability is close to 1, we increase the magnification ratio of the corresponding figure part as the reliability increases. It is obvious that our proposed algorithm makes URLLC slice more reliable, especially when the reliability of the URLLC slice is larger than 90%. e cumulative distribution function of the low delay requirement for URLLC slices with different CNRs is analyzed in Figure 6. It can be seen from the figure that when c k ≥ 10 dB and d max ≥ 0.004 sec, the probability of D ≤ D max is close to 1. From the overall curve, we can infer that when c k ≥ 10 dB, the cumulative distribution probability is relatively high. at is, the slice URLLC has higher reliability.

Conclusion
In this paper, we studied the spectral efficiency with the eMBB slice and the URLLC slice for OFDMA virtual RAN. We proved that the approximately transformed continuous programming problem is a convex optimization problem, which can be solved by applying the PHR. We proposed a JPSA algorithm combined with the PHR and the branch and bound method. e simulation results show that the proposed algorithm improves the spectral efficiency performance of the network system while ensuring the users' requirement of the eMBB slice and the users' requirement of the URLLC slice with a high probability. In the paper, we have solved how to allocate virtual network resources in two types of slices in a single cell to ensure that the admitted users meet the requirement and maximize the spectrum efficiency of the system. In future research, we will also consider the problem of slice admission and resource allocation for slices in multiple cells. Obviously, when K � 2, the Hessian matrix is positive semidefinite. We can determine whether the matrix (A.3) is a positive semidefinite matrix by analyzing its leading principle minor. ere are four leading principle minors, one of order 1 c 11 � (y 2 1 /Nx 3 1 (1 + y 1 /x 1 ) 2 ln 2) > 0, one of order 2 c 11 c 22 − c 12 c 21 � 0, and one of order 3 and one of order 4 are zero. Similarly, K > 2 also holds. Since one of order 1 c 11 � (y 2 1 /Nx 3 1 (1 + y 1 /x 1 ) 2 ln 2) > 0, one of order 2 c 11 c 22 − c 12 c 21 � 0, one of order 3 and one of order 4 are zero, one of order 5, one of order 6, and so on, the leading principle minor whose order is greater than or equal to 2 is 0.
us, when K ≥ 2, the Hessian matrix of the function we proposed is positive semidefinite. (8a) is a convex function. Otherwise, the inequality constraint function (8b) and (8c) are convex by [30] and convexity of ϕ(x, y). e two equality constraints (8d) and (8e) satisfy the affine transformation. Regarding [30], we obtain this problem (8a)-(8e) is a convex optimization problem.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.