Spectrum Resource Management for Multi-Access Edge Computing in Autonomous Vehicular Networks

01/03/2019 ∙ by Haixia Peng, et al. ∙ 0

In this paper, a dynamic spectrum management framework is proposed to improve spectrum resource utilization in a multi-access edge computing (MEC) in autonomous vehicular network (AVNET). To support the increasing data traffic and guarantee quality-of-service (QoS), spectrum slicing, spectrum allocating, and transmit power controlling are jointly considered. Accordingly, three non-convex network utility maximization problems are formulated to slice spectrum among BSs, allocate spectrum among autonomous vehicles (AVs) associated with a BS, and control transmit powers of BSs, respectively. Via linear programming relaxation and first-order Taylor series approximation, these problems are transformed into tractable forms and then are jointly solved through an alternate concave search (ACS) algorithm. As a result, optimal spectrum slicing ratios among BSs, optimal BS-vehicle association patterns, optimal fractions of spectrum resources allocated to AVs, and optimal transmit powers of BSs are obtained. Based on our simulation, a high aggregate network utility is achieved by the proposed spectrum management scheme compared with two existing schemes.

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I Introduction

Recent advances in automobiles and artificial intelligence technology are promoting the developing of autonomous vehicles (AVs), which are becoming a reality

[1] and are expected to be commercialized and appear on the roads in the coming years [2]. However, salient challenges in computing and communication remain to be addressed to support AV applications. From the computing perspective, various computing tasks need to be carried out on board for real-time environment sensing and driving decision making [3]. Moreover, enabling cooperative driving among AVs, such as platoon-based driving [4, 5, 6] and convoy-based driving [3, 7], also requires extra computing tasks. From the communication perspective, the vehicular network enables AVs to support vehicular safety and non-safety related applications [1], share inter-vehicle information, and provide high-definition (HD) maps [8]. Also, cooperative driving requires inter-vehicle communications for sharing position, velocity, acceleration, and other cruise control information among AVs [5]. All these required information exchanges among AVs increase the communication data traffic and are with different quality-of-service (QoS) requirements.

Some achievements have been made to overcome the challenges in computing and communication in vehicular networks. Edge computing has been regarded as an effective technology to enhance computing and storing capabilities in vehicular networks while alleviating traffic load to the core network [9, 10, 11]. Via moving computing and storing resources to servers placed at the edge of the core network, vehicles can offload its computing tasks to edge servers. Another potential method to address the computing issue is collaborative computing among vehicles [12, 13, 3]. In the scenarios with light computing task load, the utilization of computing resources can be improved through offloading computing tasks to the adjacent vehicles with idle computing power [3]. To address the communication issues in vehicular networks, interworking of multiple wireless access technologies has been widely accepted, such as the interworking of cellular network and dedicated short-range communications (DSRC) technologies [14]. To simultaneously address both computing and communication issues in vehicular networks, multi-access edge computing (MEC)111In 2017, mobile edge computing has been renamed to multi-access edge computing by the European Telecommunication Standards Institute (ETSI) to better reflect the growing interest and requirements in edge computing from non-cellular operators. has recently been considered in some existing works [15, 16].

Inspired by existing works, a new architecture combines MEC with network function virtualization (NFV) and addresses the challenges in computing and communication in autonomous vehicular networks (AVNETs) [17]. Via the MEC technology, 1) AVs with limited computing/storing resources can offload the tasks requiring high computing and storing requirements to MEC servers, such that a shorter response delay can be guaranteed through avoiding the data transfer between the core network and MEC servers; 2) multiple types of access technologies are permitted, thus moving AVs can access MEC servers via different base stations (BSs), such as Wi-Fi access points (Wi-Fi APs), road-side units (RSUs), White-Fi infostations, and evolved NodeBs (eNBs). Moreover, enabling NFV control module at each MEC server [18, 19, 20], the computing/storing resources placed at MEC servers can be dynamically managed and various radio spectrum resources can be abstracted and sliced to the BSs and then be allocated to AVs by each BS.

Efficient management for computing, storing, and spectrum resources is of paramount importance for the MEC-based AVNET. However, it is challenging to simultaneously manage the three types of resources while guaranteeing the QoS requirements for different AV applications, especially in the scenario with a high AV density. In this paper, we focus on spectrum resource management which can be extended to multiple resource allocation as our future work. The main contributions of this work are summarized as follows:

  1. By considering the tradeoff between spectrum resource utilization and inter-cell interference, we develop a dynamic two-tier spectrum management framework for the MEC-based AVNET, which can be easily extended to other heterogenous networks.

  2. Leveraging logarithmic and linear utility functions, we formulate three aggregate network-wide utility maximization problems to fairly slice spectrum resources among BSs connected to the same MEC server, optimize BS-vehicle association patterns and resource allocation, and control the transmit power of BS.

  3. Linear programming relaxation and first-order Taylor series approximation are used and an alternate concave search (ACS) algorithm is designed to jointly solve the three formulated optimization problems.

The remainder of this paper is organized as follows. First, the MEC-based AVNET is introduced in Section II, followed by the dynamic spectrum management framework and the communication model. In Section III, we formulate three optimization problems to slice and allocate spectrum resource among BSs and AVs and control transmit powers of BSs. Then, the three problems are transformed to tractable problems in Section IV and an ACS algorithm is proposed to jointly solve them. In Section V, extensive simulation results are presented to demonstrate the performance of the proposed spectrum management framework. Finally, we draw concluding remarks in Section VI.

Ii System Model

In this section, we first present an MEC-based AVNET architecture and a dynamic spectrum management framework, and then describe the communication model under the considered AVNET.

Ii-a MEC-based AVNET architecture

Based on a reference model suggested by the MEC ETSI industry specification group [15], we consider an MEC-based AVNET with one MEC server to support AV applications, as shown in Fig. 1. The MEC server allows AVs to access the edge computing/storing resources through different wireless access technologies.

To improve the cost efficiency of MEC server placement and provide short response delays to the AVs, the MEC server should be placed close to the edge of the core network rather than at each BS [17] and the communication hops between an MEC server and an AV is assumed to be two. Thus, a large number of AVs within the coverages of several neighbored BSs can be served by the same MEC server and the enlarged service area of the MEC server can better overcome the challenges caused by high vehicle mobility. The total coverage area of BSs connected to an MEC server is defined as the service area of this server. To realize the resource virtualization process, including computing, storing, and spectrum resources, we consider a virtual wireless network controller at the MEC server. Through collecting information from the BSs and the AVs in the service area, resource management functions can run at the controller to adjust the virtual computing and storing resources to different AV tasks and to coordinate wireless access over the wide range of spectrum resources for AVs.

Figure 1: An MEC-based AVNET model.

Ii-B Dynamic spectrum management framework

Due to the high vehicle mobility and heterogenous vehicular applications, AVNET topology and QoS requirements change frequently, and therefore, resource allocation should be adjusted accordingly. To improve spectrum resource utilization, a dynamic spectrum management framework is developed for downlink transmission. Taking a one-way straight road with two lanes as an example in Fig. 2, two wireless access technologies, cellular and Wi-Fi/DSRC [21, 22], are available to the AVs. Wi-Fi APs/RSUs and eNBs are uniformly deployed on one side of the road, where the th Wi-Fi AP and the th eNB are denoted by and , respectively. The transmit power of each eNB, , is fixed and high enough to guarantee a wide-area coverage, such that all AVs can receive sufficient strong control signal or information signal from eNBs. Denote as the transmit power of Wi-Fi AP , which is lower than and dynamically adjusted by the controller. For AVs within the overlapping area of two BSs, only one of the BSs is associated for downlink transmission.

Figure 2: A dynamic spectrum management framework.

We divide the eNBs into two groups, denoted by and , where eNBs in the same group are not neighbored to each other. ENBs and shown in Fig. 2 are the two target eNBs from the two different sets, where is adjacent to . Set of Wi-Fi APs under the coverage area of eNB is denoted by . Denote the total available spectrum resource for vehicular applications to be . After collecting the application requests from AVs via BSs, the controller performs dynamic spectrum management for downlink transmission. The dynamic spectrum management procedure can be divided into two tiers as the following.

  1. Spectrum slicing among BSs: The controller slices the spectrum resource, , into three slices with ratio set with , and allocates them to eNBs in , eNBs in , and Wi-Fi APs, respectively.

  2. Spectrum allocating among AVs: Once the spectrum is sliced, each BS allocates its available spectrum resource to AVs associated to it. By allocating an appropriate amount of spectrum resources to each AV, the QoS requirements of various vehicular applications can be satisfied and the sum of transmission rates over the whole AVNET can be maximized.

Spectrum slicing among BSs, spectrum allocating among AVs, and transmit power controlling for Wi-Fi APs are updated once the traffic load of each eNB fluctuates, which is in a relatively large time scale with respect to the dynamic communication environment. The traffic load of an eNB is defined as the average arrival traffic for AVs in the coverage area of the eNB.

Ii-C Communication model

Assume the three slices of spectrum resource are mutually orthogonal, therefore, there is no inter-tier interference. To improve the spectrum resource utilization, two levels of spectrum reusing are considered. The first level is reusing the spectrum resource among all the Wi-Fi APs as long as with an acceptable inter-cell interference. Moreover, we assume that the Wi-Fi APs with no overlapping coverage area with an eNB can reuse the spectrum allocated to that eNB. Thus, the interference to eNBs caused by the Wi-Fi APs can be controlled by adjusting the transmit powers of the Wi-Fi APs while the spectrum resource utilization can be further improved by allowing each Wi-Fi AP to reuse either the spectrum resource or .

According to the dynamic spectrum management framework presented in Section II-C, all the eNBs in reuse the spectrum resource for downlink transmission. Denote as the set/number of AVs within the coverage of eNB . Then AV , under the coverage of eNB , i.e., , experiences two kinds of interference to the corresponding downlink: from transmission of other eNBs in and Wi-Fi APs in the coverage of eNBs in . Then, the spectrum efficiency at AV () from eNB can be expressed as

(1)

where () is the channel power gain between eNB (Wi-Fi AP ) and AV , and is the power spectrum density of the additive white Gaussian noise (AWGN). Similarly, the spectrum efficiency at AV () from eNB , , can be obtained. Let be the amount of spectrum allocated for AV from eNB . Then, the achievable transmission rates of AV associated with eNBs (or ) can be expressed as

(2)

Denote as set/number of AVs within the coverage of Wi-Fi AP . Let and be the amount of spectrum allocated to AV from and , respectively, by Wi-Fi AP under the coverage of eNB (i.e., ). Then the spectrum efficiencies at AV from Wi-Fi AP include the following two parts,

(3)

And the achievable transmission rate of a tagged AV associated with Wi-Fi AP , i.e., , can be expressed as

(4)

Let and be the amount of spectrum allocated for AV from and , respectively, by Wi-Fi AP under the coverage of eNB (i.e., ), and and be the spectrum efficiencies at AV from Wi-Fi AP . Similarly, the achievable transmission rate of a tagged AV associated with Wi-Fi AP , i.e., , can be given by

(5)

Iii Resource Management Scheme

We consider two kinds of traffic for each AV: delay-sensitive traffic and delay-tolerant traffic. Examples of AV’s delay-sensitive traffic include rear-end collision avoidance and platooning/convoying. The delay-tolerant traffic can be HD map information downloading and infotainment services. Denote

as the probability that an AV generates a delay-sensitive request. To accommodate the large amounts of data traffic generated by AVs while guaranteeing different QoS requirements for different applications, efficient resource management schemes are very important.

For downlink transmission to accommodate AVs’ delay-sensitive requests, the transmission delay from eNB or Wi-Fi AP should be guaranteed statically. Let and be the size and the arrival rate of the delay-sensitive packet. From [23], the maximum delay requirement, , can be transformed to a lower bound of the required transmission rate to guarantee that the downlink transmission delay exceeding at most with probability , which can be expressed as

(6)

Iii-a Spectrum Resource Allocation

To address complicated resource allocation, we will introduce a two-tier approach, including spectrum slicing among BSs and spectrum allocating among AVs, as following.

Spectrum slicing among BSs: Based on the dynamic spectrum management framework, the total available spectrum resources are sliced or divided according to the ratio set for different BSs. The main concern for spectrum slicing is fairness among BSs. To this end, a logarithmic utility function, which is concave and with diminishing marginal utility [23], is considered to achieve a certain level of fairness among BSs [24, 25].

For AV

within the coverages of Wi-Fi APs, binary variables

and represent the BS-vehicle association patterns, where (or ) means AV is associated with eNB (or Wi-Fi AP ), (or ) otherwise. Denote as set/number of AVs within the coverage of eNB while outside of Wi-Fi APs. Then, the utility for vehicle associated to eNBs or Wi-Fi APs is

(7)

The aggregated network-wide utility is defined as the summation of utility of each individual AV. Let and be the matrices describing spectrum allocation among AVs by eNBs and by Wi-Fi APs, respectively. For given BS-vehicle association patterns with fixed transmit power of each Wi-Fi AP, the aggregated network-wide utility maximization problem can be given by

(8)
(8a)
(8b)
(8c)
(8d)
(8e)
(8f)

In problem (P1), the objective function is to maximize the aggregated network utility. Since , , and are the only three slicing ratios, constraints (8a) and (8b) are considered in (P1). Constraints (8c), (8d), (8e), and (8f) indicate that spectrum resources allocated to AVs by a BS should be in this BS’s available spectrum resources. According to problem (P1), each BS equally allocates its available spectrum resources to AVs associated to it (will be discussed in detail in the next section). However, the downlink transmission rate required by an AV depends on its application request. For a BS with a fixed amount of available spectrum, equally allocating spectrum to AVs associated to it and simultaneously guaranteeing their heterogeneous QoS requirements will reduce the number of AVs accessed to it. Thus, QoS constraints on each element in R and are not considered in problem (P1) and the optimal is regarded as the only output to determine the amount of spectrum resources reused by each BS.

Spectrum allocating among AVs: To accommodate situations with high density AVs, a linear network utility function is considered in spectrum allocating among AVs associated to the same BS. For given slicing ratios , , and , and transmit power of each Wi-Fi AP, a network throughput maximization problem can be formulated as

(9)
(9a)
(9b)
(9c)
(9d)
(9e)
(9f)
(9g)
(9h)
(9i)
(9j)
(9k)
(9l)
(9m)

where and are the association matrices between eNBs and AVs, and between Wi-Fi APs and AVs, respectively; and are the corresponding packet size and the arrival rate for delay-tolerant service requests; / (or /) are set/number of AVs only within the coverage of eNB and request for delay-sensitive (or delay-tolerant) services; / (or /) are set/number of AVs within the coverage of Wi-Fi AP and request for delay-sensitive (or delay-tolerant) services.

In problem (P2), the first four constraints are same with problem (P1) and used to demonstrate the required spectrum for each vehicle allocated from its associated BS with constraint (9b) together. Constraints (9c)-(9e) indicate that each vehicle is associated with either the eNB or the Wi-Fi AP closed to it. Constraints (9f)-(9i) ensure the service rates from either an eNB and a Wi-Fi AP so that the delay requirement for a vehicle with delay-sensitive services can be guaranteed. For vehicles with delay-tolerant requests, constraints (9j)-(9m) indicate that the service rate from eNBs or Wi-Fi APs should be not less than the periodic data traffic arrival rate at that eNB or Wi-Fi AP. Via solving problem (P2), the optimal association matrices for eNBs and for Wi-Fi APs , and local spectrum allocation matrices for eNBs and for Wi-Fi APs can be obtained, which maximize the network throughput with guaranteed QoS for different AV applications.

Iii-B Transmit Power Control

In addition to spectrum slicing and allocating among BSs and AVs, controlling the transmit power for Wi-Fi APs to adjust the inter-cell interference would further improve the spectrum utilization. Denote as transmit power matrix of Wi-Fi APs. Equations (1) and (3) indicate that the received signal-to-interference-plus-noise (SINR) by vehicles from either an eNB or a Wi-Fi AP change with Wi-Fi APs’ transmit powers, and therefore, impacting achievable transmission rates for the corresponding downlink. To obtain optimal transmit power control, similar to problem (P2), the linear utility function is considered in this part. For a given slicing ratio set , BS-vehicle association pattern matrices X and , and local spectrum allocation matrices R and , the network throughput maximization problem focusing on transmit power control can be formulated as

(10)
(10a)
(10b)

where is the maximum transmit power allowed by each Wi-Fi AP. In problem (P3), the first eight constraints in (10a) are same with problem (P2) and used to ensure the QoS requirements for delay-sensitive and delay-tolerant services. Constraint (10b) indicates that transmit power of each Wi-Fi AP is less than . Then the optimal transmit power for each Wi-Fi AP can be determined by solving problem (P3). From the above discussion, variables considered in problems (P1), (P2), and (P3) are coupled, thus the three problems should be solved jointly.

Iv Problem Analysis and Suboptimal Solution

Due to the binary variable matrices X and , problems (P2) and (P3) are combinatorial and difficult to solve. Thus, in this section, we first analyze each problem and then transform (P2) and (P3) to tractable forms before we jointly solving these three problems for the final optimal solutions.

Iv-a Problem Analysis

Let be the set of AVs within and associated with Wi-Fi AP , i.e., for , and . Then, the objective function of (P1) can be transformed into,

(11)

where mathematical symbol, , describes the relative complement of one set with respect to another set. According to the constraints of (P1), the sets of spectrum allocating variables, , , , , , and , are independent with uncoupled constrains. Thus, similar to proposition 1 in [23], we can decompose problem (P1) into six subproblems and obtain the optimal fractions of spectrum allocated to AVs from the associated BSs as follows,

(12)

Equation (12) indicates that each BS equally allocates spectrum to AVs associating to it. By replacing the spectrum allocating variables with Equation (12), problem (P1) can be transformed into

(13)
(13a)

Due to the binary variable matrices X and , using the brute force algorithm to solve problems (P2) and (P3) is with high complexity. To address this issue, we allow AVs within the overlapping coverage area of a Wi-Fi AP and an eNB to associate to one or both of the Wi-Fi AP and the eNB [24]. Thus, binary matrices X and are relaxed into real-valued matrices and with elements and , respectively. And then, we can transform problem (P2) into

(14)
(14a)
(14b)
(14c)
(14d)
(14e)
(14f)
(14g)
(14h)
(14i)
(14j)
(14k)
(14l)
(14m)
(14n)
(14o)
(14p)

To analyze the concavity property of problems (P1) and (P2), three definitions about concave functions [26, 27] and two concavity-preserving operations [26] are introduced in Appendix A. The following propositions, proved in Appendix B and Appendix C, summarize the concavity property of problems (P1) and (P2), respectively,

Proposition 1.

The objective function of problem (P1) is a concave function on the three optimal variables , , and , and problem (P1) is a concave optimization problem.

Proposition 2.

The objective function of problem (P2) is a biconcave function on variable set , and problem (P2) is a biconcave optimization problem.

Even though the integer-value variables in problem (P3) can be relaxed to real-value ones by replacing constraint (10a) by (14i)-(14p), the non-concave or non-biconcave relations between the objective function and decision variable of problem (P3) makes it difficult to solve directly. Thus, we use the first-order Taylor series approximation, and introduce two new variable matrices, and with elements that are linear-fractional function of , to replace the received SINR on AVs within each BS’s coverage area. Then, the downlink spectrum efficiency on an AV associated to a BS can be re-expressed as a concave function of . For example, using to replace the SINR received on AV associated to eNB , we can rewritten equation (1) as

(15)

Therefore, problem (P3) can be transformed into

(16)
(16a)
(16b)