With the increasing popularity of various smart devices such as smart phones, tablets, Google Glass, Apple Watch, etc., augmented reality (AR) and virtual reality (VR) have the potential to be the next mainstream general computing platform . Based on high-definition (HD) video services/applications, VR is able to mimic the real world by creating a virtual world or by applying various on-spot sensory equipments, such that immersive user experiences can be supported. In comparison, by augmenting more data information to the real world, AR is able to enhance the perception of reality in a manner of reality-plus-data. Then, what is the real difference between VR and AR? For instance, with VR, you can dive and swim with dolphins. However, with AR, you can watch a dolphin pop out of your book. While VR provides an immersive environment for the user to interact with that world by a head-mounted display, AR makes the user see the superimposing content over the real world in mobile devices, such as laptops and smart phones. Since real-time interactions and flows of massive information are involved in AR/VR applications, it will bring new challenges to the designs of future networks  for accommodating online AR/VR applications. To be specific, for future fifth generation (5G) wireless networks, the applications of AR/VR require innovations in the cloud-based network architectures , with an objective of significantly improving the network throughput, delay performance, wireless capacity, etc.
To support the enormous traffic demands involved in AR/VR applications, there have been a great number of research activities in 5G network studies [4, 5, 6, 7]. N. Bhushan et al.  pointed out that the 5G wireless networks could meet the 1000x traffic demands over the next decade, with additional spectrum availability, densification of small-cell deployments, and growth in backhaul infrastructures. Meanwhile, the massive multi-input multi-output (MIMO) technique offers huge advantages in terms of energy efficiency, spectral efficiency, robustness and reliability , which allows for the use of low-cost hardware at both base stations and user terminals. Moreover, the large available bandwidth at millimeter wave (mmWave) frequencies makes mmWave transmission techniques attractive for the future 5G wireless networks [6, 7]. On the other hand, the gigantic data traffics on the next generation of Internet have also been investigated [8, 9, 10]. C. Walravens et al.  studied the high-rate, small packet traffic in an Ethernet controller and used a technique called receive descriptor recycling (RDR) to reduce the small-packet loss by 40%. N. Laoutaris et al.  proposed using this already-paid-for off-peak capacity to perform global delay-tolerant bulk data transfers on the Internet. M. Villari et al. studied the osmotic computing by moving cloud resources closer to the end users, which is regarded as a new paradigm for edge/cloud integration . What’s more, some studies have been investigated for video communications [11, 12], which play a significant role in big data communications. W. Xiang et al.  proposed a light field (LF)-based 3D cloud telemedicine system and extend the standard multi-view video coding (MVC) to LF-MVC, which can achieve a significant 23 percent gain in compression ratio over the standard MVC approach. G. Wang et al.  proposed a new LF-MVC prediction structure by extending the inter-view prediction into a two-directional parallel structure, which can achieve better coding performance and higher encoding efficiency.
To reduce the network latency for high-speed reliable services like AR/VR and surveillance, usage of different chromatic dispersion compensation methods were discussed to reduce the transmission delay in fiber optical networks . Low-delay rate control algorithms have been proposed to address the delay problem in [14, 15]. For instance, for the AR applications considered in , low-delay communications of the encoded video over a Bluetooth wireless personal area network were investigated, by using a combination of the dynamic packetisation of video slices together with the centralized and predictive rate control. Mobile AR and VR have been used and studied recently [16, 17, 18, 19]. A. D. Hartl et al. studied the verification of holograms by using mobile AR, where a re-parametrized user interface is proposed in . The privacy preservation of cloth try-on was studied in , by using mobile AR. In , S. Choi et al. proposed a prediction-based delay compensation system for head mounted display, which compensated delay up to 53 milliseconds with 1.083 degrees of minimum average error. In , T. Langlotz et al. presented an approach for mitigating the effect of color blending in optical see-through head-mounted displays, by introducing a real-time radiometric compensation.
Different from conventional video applications, AR/VR applications impose a strict requirement on the uplink/downlink transmission delays. Take the 360-degree video (an application of VR) as an example, the jitter and visual field delays, i.e., motion-to-photons (MTP) latency should be limited within 20 milliseconds. Otherwise, the users will feel dizzy . Therefore, the transmission delay is one of main challenges for running AR/VR application over future 5G wireless networks. Moreover, few studies have investigated the issue of system energy consumption for the heavy traffic and high-rate transmissions required by AR/VR applications. Motivated by these gaps, it is important to propose a 5G wireless network solution for reducing the transmission delays and system energy consumption in AR/VR applications. The main contributions of this work are summarized in the following.
Based on requirements of AR/VR applications, a solution with software-defined networking (SDN) architecture is proposed for future 5G wireless networks, which is able to significantly reduce the network latency.
To facilitate the AR/VR data provisioning, a multi-path cooperative route (MCR) scheme is proposed for fast wireless transmissions from multiple edge data centers (EDCs) to the desired user. Moreover, the delay model with the MCR scheme is analytically studied. The lower and upper bounds of MCR delay are further obtained.
A service effective energy (SEE) model is proposed to evaluate the energy consumption of MCR scheme in AR/VR applications. Furthermore, a service effective energy optimization (SEEO) algorithm is developed for minimizing the SEE in 5G small cell networks.
Simulation results indicate that the delay and SEE of MCR scheme are better than the delay and SEE of conventional single path route scheme for AR/VR applications in 5G small cell networks.
The remainder of the paper is organized as follows: In Section II, a solution with SDN architecture is proposed for AR/VR applications in 5G small cell networks, where storage strategies of AR/VR data are discussed. Section III describes a comprehensive network latency model. The MCR scheme is proposed and the MCR delay is investigated in Section IV. Moreover, the lower and upper bounds of MCR delay is derived. The optimization problem of SEE is formulated in Section V, where a two-step joint optimization algorithm is proposed for AR/VR applications in 5G small cell networks. Simulation results and discussions are presented in Section VI. Finally, Section VII concludes this paper.
Ii System Model
Ii-a Network Model
We consider a two-tier heterogeneous cellular network, where multiple small cell base stations (SBSs) and EDCs are deployed within the coverage of a macro cell base station (MBS). The MBS and EDCs are connected to the core networks through fiber to the cell (FTTC). An SDN architecture is adopted to support the separation of data and control information in Fig. 1. As the network controller, the SDN controller divides the control information into MBSs and data information into SBSs and EDCs. MBSs are mainly responsible for the delivery of control information and routing decisions. The EDCs are data centers deployed at the edge of core networks, where massive AR/VR data are stored. All EDCs and SBSs, equipped with mmWave transmission techniques, are parts of the 5G small cell network. Utilizing the mmWave multi-hop transmission technique, AR/VR data streams can be transferred between EDCs and SBSs.
It is assumed that the MBSs, denoted by , follow a Poisson Point Process (PPP) with density , the SBSs, denoted by , follow a PPP with density , the user terminals, denoted by , follow a PPP with density , and the EDCs, denoted by , follow a PPP with density , respectively in the two-dimension (2-D) plane. The distributions of MBSs, SBSs, EDCs and user terminals are assumed to be independent of each other. To have a clear focus, only the coverage of a single MBS is analyzed in this paper. For ease of exposition, the SBSs located within the coverage of the MBS are denoted as a set , whose number is expressed as . The set of EDCs located within the coverage of the MBS is denoted as , whose number is expressed as . The set of user terminals within the coverage of the MBS is denoted as , whose number is expressed as .
For a user terminal with AR/VR traffic demands, a request is first sent to an associated MBS by uplinks. Upon receiving a user’s request, the associated MBS searches EDCs that are located close to the requesting user. If however, there is an EDC located outside the macro cell, then the associated MBS sends the request to the MBS to which this EDC belongs, through the SDN controller. Upon receiving the routing information transmitted from the MBS, the close-by EDCs transmit AR/VR data to the destination SBS that is located closest to the requesting user. Finally, the destination SBS delivers the AR/VR data to the requesting user by mmWave transmission links. In above solution, the SDN architecture is adopted to facilitate the request/feedback transmissions from users by control information links. Moreover, the big AR/VR data is promptly transmitted by multiple EDCs to the destination SBS. Utilizing the buffering scheme of the destination SBS, the jitter of multi-path AR/VR transmission between EDCs and the destination is minimized. Furthermore, the requirements of AR/VR applications, e.g. low network latency and massive data transmission, are satisfied by this SDN solution in 5G small cell networks.
Ii-B Storage Strategies of AR/VR Data
Consider a library that consists of AR/VR video contents. We define as the corresponding popularity distributions of these AR/VR video contents that are arranged in a popularity descending order, where ( and ) denotes the popularity of the
popular AR/VR video content, i.e., the probability that an arbitrary user request is for AR/VR video content. Without loss of generality, the distribution of is assumed to be governed by a Zipf distribution ,
is a positive value that characterizes the skewness of the popularity distribution, and.
In general, a subset of the AR/VR video contents are stored in EDCs, whereas the remaining video contents can be fetched from the remote data centers (RDC). For ease of exposition, we let denote the AR/VR video content placement strategy in EDCs, where means that AR/VR video content () is stored at EDC (), whereas means that AR/VR video content is not stored at EDC . Since the storage capacity at each EDC is limited that cannot store all AR/VR video contents, generally there exist three storage strategies in existing studies.
First in first out (FIFO): The contents stored at the EDC form a queue in a chronological order until the storage capacity is reached. In this way, the content at the head of the queue has to be removed for accommodating the newly incoming content at the tail of the queue.
Least recently used (LRU): The contents are stored at the EDC according to how frequently they are requested by users recently. In this way, if the storage capacity of EDC is reached, then the least recently used content will be replaced by the newly incoming content.
Popularity-priority: All contents are stored at the EDC in a popularity descending order until the storage capacity is reached. In this way, the more popular content can be stored by comparing the popularity of the newly incoming content with that of the least popular content stored at EDC.
In our considered network model, the popularity-priority strategy is adopted to store the most popular AR/VR video content data at each EDC. Although the popularity distribution of AR/VR video contents may vary with time, to maintain cache consistency, we consider in this paper a relatively static popularity distribution within a given interval. This assumption is valid in examples including popular short news videos that are updated every 2-3 hours, new movies that are posted every week, new music videos that are posted about every month.
For ease of analysis, it is assumed that each EDC has the same storage capacity, in which () AR/VR video contents of the same size can be stored. Since the popularity-priority strategy is adopted where each EDC stores the most popular contents independently, it ends up with that the same most popular video contents are stored at each EDC, i.e.,
For ease of reference, the notations and symbols with the default values used in this paper and simulations are listed in Table I.
|, ,||Density of MBSs, SBSs, users, respectively||5 , 50 , 200|
|, ,||Transmission power at each SBS, EDC, user, respectively||30 dBm, 30 dBm, 23 dBm|
|Time slot of millimeter wave channels||5 s|
|Noise power spectral density||-174|
|Bandwidth of millimeter wave wireless links||200 MHz|
|Service rate at the MBS|
|Factor of user arrival rate|
Standard variance of shadow fading over wireless channels
|Maximum transmission distance of SBSs and EDCs||100 meters|
|Data packet size||1024 Bytes|
|Buffer size of SBS||1 MB|
|Distance between the macro cell network and the RDC||1000 km|
|Transmission rate in optic fibers|
|Skewness parameter of popularity distributions||0.8|
|Number of video contents in the library||500|
|Maximum distance between the EDC and the destination SBS||500 meters|
|,||The fixed coefficient of MBS||21.45, 354 Watt|
|,||The fixed coefficient of SBS||7.84, 71 Watt|
|,||The fixed coefficient of EDC||7.84, 71 Watt|
|Lifetime of MBS||10 years|
|Lifetime of SBS||5 years|
|Lifetime of EDC||5 years|
|Energy consumption of one video content stored at the EDC||Joule|
Iii Network Latency Model
For the AR/VR service provisioning upon receiving an arbitrary user’s request, the network latency model is formulated as
where denotes the probability that the requesting user can find the desired AR/VR data in the nearby EDCs. If the required AR/VR data can be found in EDCs, then the network latency is a sum of the delays within a macro cell coverage. Otherwise, the transmission delay over the optical networks should also be taken into account.
(1) : The delay incurred when a user terminal sends a request to the MBS through uplinks, which consists of the uplink transmission delay and the queuing delay at the MBS , i.e.,
When a user sends a request to the MBS, the corresponding received signal power at the MBS is given as 
where the same transmission power is adopted at each user , denotes the distance between the user and MBS , denotes the path-loss exponent, denotes the channel gains from the user to the MBS , where we have for each entry (, ), and and denote the number of receive antennas at the MBS and the number of transmission antennas at the user, respectively. Then the probability of successfully delivering the user request to the MBS is expressed as
where denotes the received signal power threshold for successful reception at the MBS. Provided that MBSs are randomly located in a 2-D plane with density , approximation is obtained based on [Eq. (10), 22], where we have by letting . Otherwise if , retransmissions are performed. Then we have the average transmission delay for successfully delivering a user request to the MBS as
where denotes the time for transmitting a user request from a user to the associated MBS, and corresponds to the average number of retransmissions .
Furthermore, an M/M/1 queuing model is adopted for calculating the queuing delay at the MBS upon successfully receiving the user’s request. Then we have
where denotes the average arrival rate of users’ requests at the MBS, which is proportional to the user density in the macro cell, i.e., where is the factor of user arrival rate. denotes the service rate at the MBS.
(2) : The delay incurred when the MBS sends the user request/control information to the EDCs that own the requested AR/VR data through downlinks.
When the MBS sends routing information to the specifical EDC () that owns the AR/VR data requested by user , the corresponding received signal-to-interference-and-noise ratio (SINR) at EDC is given by
where denotes the transmission power at MBS, denotes the distance between MBS and EDC , denotes the distance between MBS and EDC , denotes the noise power, denotes the channel gains between MBS and EDC , where we have for each entry (, ), denotes the channel gains between MBS and EDC , where we have for each entry (, ), and and denote the number of receive antennas at the EDC and the number of transmission antennas at the MBS, respectively. Based on our previous work , the probability of successfully delivering the routing information from the MBS to EDC can be readily expressed as
where denotes the SINR threshold for successful reception at the EDC and denotes the summation of all elements in . For ease of exposition, we let
Then can be expressed by using (13) and (14) as
respectively. Then we have
where denotes the downlink transmission time of a packet from the MBS to the EDC.
(3) : The backhaul delay, i.e., the delay incurred when the EDC delivers the requested AR/VR data to the destination SBS which associates with the requesting user.
In order to reduce the transmission delay of AR/VR data in 5G small cell networks, a multi-path cooperative route (MCR) scheme is proposed in Section IV. A, where the closest EDCs simultaneously transmit the massive AR/VR data to the destination SBS.
(4) : The delay incurred when the destination SBS transmits the requested AR/VR data to the requesting user. Considering the directivity of mmWave transmission, the interference is negligible in 5G small cell networks . Then the corresponding received signal power at user is given by
where the same transmission power is adopted at each SBS, denotes the distance between the destination SBS and the user , denotes the path-loss exponent, denotes the channel gains between the SBS and the user , where we have for each entry (, ), and and denote the number of receive antennas at the user and the number of transmission antennas at the SBS, respectively. The probability of successfully delivering the requested AR/VR data to the requesting user is expressed as
where denotes the received signal power threshold for a successful reception. Then we have
where denotes the downlink transmission time of a data packet from the destination SBS to the user.
(5) : The fiber delay incurred in the uplink/downlink transmissions when the MBS has to fetch AR/VR data from the RDC upon a search failure in local EDCs. Considering that the transmission rate in optic fibers is and the distance between the given macro cell and the RDC is , the fiber delay is expressed as
Iv AR/VR Multi-path Cooperative Transmissions
For AR/VR applications, not only a large network throughput is required for transmitting a massive data, but also a low system delay is needed to support the user interactions. In traditional networks the data is transmitted from a source to a destination through a fixed path. In this case, the maximum network throughput is restricted by the minimum transmission rate of links along the path. It implies that the total network throughput is constrained by the most congested link with the minimum transmission rate in the fixed path. Moreover, the system delay is also limited by the minimum transmission rate in the bottleneck of the fixed path. To solve these issues, a MCR scheme is proposed to meet the requirements of the massive data transmission and low system delay for AR/VR applications.
Iv-a Multi-Path Cooperative Route (MCR) Scheme
Considering the fluctuation of wireless channels, it is very difficult to transmit the massive AR/VR data with the low system delay constraint by a fixed path in 5G small cell networks. On the other hand, the AR/VR data can be repeatedly stored in multiple EDCs according to the content popularity. Therefore, the same AR/VR data can be cooperatively transmitted to a user from adjacent EDCs. The basic multi-path cooperative route scheme is described as follows:
EDCs selection: According to the system model, multiple EDCs are located in a macro cell. When the requested AR/VR data is stored at EDCs, selected EDCs simultaneously transmit the same AR/VR data to a destination SBS that is the closest to the requesting user. In the end, this destination SBS transmits the AR/VR data to the user by mmWave links.
Multi-path transmission strategy: selected EDCs are incrementally ordered by the average distance between the EDC and the destination SBS. The is the selected EDC away from the destination SBS with an average distance . The requested AR/VR data is divided into parts with the proportion . Moreover, the selected EDC only need to transmit the data of . In this case, the closer EDC need to transmit the larger AR/VR data and the distant EDC transmit a smaller amount of AR/VR data.
Relay SBSs selection: Based on the system model, SBSs are densely deployed in the coverage of every MBS. When the maximum transmission distance of SBS with mmWave transmission techniques is configured as , it is assumed that there exist more than two SBSs in the distance . In this case, the requested AR/VR data is transmitted to the destination SBS by wireless relayed SBSs. To minimize the relay delay in SBSs, the relay route algorithm with the minimum hop number is adopted for the transmission path between the requested EDC and the destination SBS. Relay SBSs are selected by the relay routing algorithm with the minimum hop number, e.g., the shortest path based geographical routing algorithm .
Iv-B Delay Theorem of Multi-Path Cooperative Route Scheme
MCR Delay Theorem: When EDCs are deployed in a 5G small cell network, the AR/VR data stored at EDCs are simultaneously transmitted to a destination SBS by the MCR scheme. The system delay of MCR scheme is expressed by
where is the buffer size of SBS, is the data packet size, is the rounding up operation of a number, is the average distance between the destination SBS and the EDC . and are the densities of SBSs and EDCs in the coverage of MBS. In a wireless route between the EDC and the destination SBS, the wireless transmission is time slotted and one packet is transmitted in each time slot . is the maximum transmission distance of SBSs and EDCs, is the transmission power of a SBS, is the threshold of the signal receiver, is the noise power spectral density, is the bandwidth of mmWave links,
is the standard deviation of shadow fading over wireless channels in dB.
Proof: According to the MCR scheme, the destination SBS simultaneously receives the AR/VR data from adjacent EDCs by multi-path wireless routes. is the distance between the destination SBS and the EDC
. Without loss of generality, the probability density function (PDF) of the distanceis assumed to be governed by 
where is Gamma function. When , is the set of positive integers, . The average value of is derived by
where results due to the Gaussian integral, i.e., .
In this paper, the relay routing algorithm with the minimum hop number is adopted for the transmission path between the requested EDC and the destination SBS. Therefore, the relay distance is configured as . When the average transmission distance is , the average hop number of is
where is the rounding up operation of a number.
Considering the distributions of SBSs and EDCs, the number of SBSs in the coverage of a EDC is calculated by . Moreover, the probability that a SBS selected by the EDC for relaying the AR/VR data is . When mmWave links are assumed to be line of sight (LoS) links in this paper, the wireless link fading is expressed by , , where is the shadow fading coefficient and is the standard deviation of shadow fading over wireless channels in dB. The wireless transmission is successful over mmWave links only if is satisfied. Therefore, successful probability of wireless transmission over mmWave links is 
When one packet is transmitted over the distance by the multi-hop relay method in this paper, the transmission delay is expressed by
To reduce the effect of delay jitter caused by MCR scheme, a buffer is adopted at the destination SBS. When the SBS buffer size and the packet size are configured as and , the maximum tolerable buffer delay is for a multi-hop relay route between the EDC and the destination SBS when the AR/VR application is run by users. When the transmission control protocol (TCP) is used for AR/VR data, the EDC can transmit the next packet only if the current packet is successfully accepted at the destination SBS. Hence, the total delay of one packet in the multi-hop relay route is . Based on the MCR scheme, the EDC only need to transmit the data of . The system delay between the EDC and the destination SBS is expressed by
where . Considering that EDCs are utilized for simultaneously transmission in the MCR scheme, the system delay of MCR scheme is derived by
where is obtained under the condition that the system delay does not depend on the route based on the result of (27).
The MCR delay theorem is proved.
Lemma 1: When EDCs are deployed in a 5G small cell network, the AR/VR data stored at EDCs are simultaneously transmitted to a destination SBS by the MCR scheme. The lower and upper bounds of system delay in the MCR scheme are given by
where is the maximum distance between the EDC and the destination SBS.
Proof: Based on the configuration of system model, densities of MBCs, SBSs and EDCs satisfy the following constraint: . The upper bound of system delay in the MCR scheme is derived by
where is obtained under the condition that the number of cooperative transmission EDCs is larger than one, i.e., , is obtained under the condition of .
The average distance between the destination SBS and the EDC is derived by
Based on the result of (31), the lower bound of system delay in the MCR scheme is derived by
where is obtained under the condition of , is obtained under the condition of .
Therefore, the Lemma 1 is proved.
V Service Effective Energy Optimization
V-a Service Effective Energy
For the AR/VR applications, wireless transmissions are premised on the basis of QoS. In this paper, the QoS is defined by
where is an indicator function, which equals to 1 when the condition inside the bracket is satisfied and 0 otherwise; is the maximum delay threshold for AR/VR applications. On the other hand, a massive amount of wireless traffic generated by AR/VR applications is transmitted in 5G small cell networks. Hence, the energy consumption is another important metric for evaluating the performance of the proposed MCR scheme. Considering the requirement of QoS in AR/VR applications, the service effective energy (SEE) is defined by
where is the system energy of MCR scheme.
Based on the system model in Fig. 1
, the system energy of MCR scheme includes the energy consumed at MBSs, SBSs and EDCs. Without loss of generality, the energy consumption of MBSs and SBSs is classified into the embodied energy, i.e., the energy consumed in the manufacturing process of infrastructure equipments from a life-cycle perspective, and the operation energy, i.e., the energy consumed for wireless traffic transmissions. The energy consumption of EDCs is classified into the embodied energy, the operation energy and the storage energy, i.e., the energy consumed for video storage at EDCs. As a consequence, the system energy of MCR scheme is extended as
where , and are the energy consumption at MBS, SBS and EDC, respectively; is the energy consumption of one video content stored at the EDC; , and are the operation power of MBS, SBS and EDC, respectively; , and are the lifetime of MBS, SBS and EDC, respectively; , and are the embodied energy of MBS, SBS and EDC, respectively; and are the fixed coefficients of the operation power at MBSs; and are the fixed coefficient of operation power at SBSs; and are the fixed coefficients of operation power at EDCs.
V-B Algorithm Design
Assumed that AR/VR video contents are stored in local EDCs. To save the energy consumption of MCR scheme, the optimal SEE problem is formulated by
where the minimum SEE is solved by finding the optimal density of EDCs and the optimal number of video contents at EDCs. Considering the popularity distribution of video contents, the total number of video contents is expressed by . To avoid the difficulty caused by an infinite distance between the EDC and the destination SBS on solving the optimization problem, the maximum distance between the EDC and the destination SBS is constrained within a maximum threshold for the optimal SEE. Considering functions of MBSs, SBSs and users, the wireless transmission powers of MBSs, SBSs and users are constrained by .
To solve the optimal SEE problem in (36), a two-step solution is proposed in this paper. In Step 1, the required system delay is solved for the AR/VR MCR scheme. In Step 2, the SEE is optimized for the AR/VR MCR scheme.
Step 1: Based on (36), the required system delay is formulated by
Based on (3), the delays , and are independent of the density of EDCs and the number of video contents . Therefore, in this optimal algorithm the maximum delay threshold of AR/VR applications is replaced by a variable . The condition inside of QoS indication function is expressed by
Based on (20) and (21), the backhaul delay decreases with the increase of the EDC density and the fiber link delay decreases with the increases in the number of video contents . Considering two conditions and , the critical value with the given value of is obtained by traversing all available values in the set of . When a value of is substituted into (38), a corresponding value of is obtained. Therefore, is the critical value for the available value of . Moreover, the available value pair of and is denoted by .
Step 2: Based on the result of Step 1, the minimum system energy of MCR scheme is formulated by
where the available value pairs and are substituted into (35), the optimal SEE is solved by obtaining the minimum system energy of MCR scheme. The detailed SEE optiMization (SEEM) algorithm is shown in Algorithm 1.
Compute equation with value to obtain the critical value ;
Put into the set ;
Vi Simulation Results and Performance Analysis
Based on the proposed system delay model of the MCR scheme, the effect of various system parameters on the system delay of the MCR scheme will be analyzed and compared by numerical simulations in this section. In what follows, the default values of system model are illustrated in Table I. Moreover, the performance of SEEO algorithm is simulated and analyzed in this section.
Fig. 2 shows the fiber link delay with respect to the number of video contents considering different skewness parameters of popularity distributions. When the skewness parameter of popularity distribution is fixed, the fiber link delay decreases with the increase of the number of video content at EDCs. When the number of video content is fixed, the fiber link delay decreases with the increase of the skewness parameter of popularity distribution.
Fig. 3 depicts the backhaul delay with respect to the density of EDCs considering different number of cooperative EDCs. When the number of cooperative EDCs is fixed, the backhaul delay decreases with the increase of the density of EDCs. When the density of EDCs is fixed, the backhaul delay decreases with the increase of the number of cooperative EDCs.
Fig. 4 illustrates the backhaul delay with respect to the density of EDCs under different maximum transmission distances of SBSs and EDCs. When the density of EDCs is fixed, the backhaul delay decreases with the increase of the maximum transmission distances of SBSs and EDCs.
Fig. 5 compares the backhaul delay with respect to the density of EDCs under the MCR scheme and the single path route scheme. Fig. 5(a) shows that the backhaul delay of MCR scheme is less than that of the single path route scheme. Fig. 5(b) describes the gains in terms of backhaul delay achieved by the MCR scheme over the single path route scheme. Results in Fig. 5(b) indicate that the gains in terms of backhaul delay decrease with the increase of the density of EDCs.
In Fig. 6, the impact of buffer size of SBSs on the backhaul delay with different densities of EDCs is investigated. When the density of EDCs is fixed, the backhaul delay increases with the increase of the buffer size of SBSs.
Fig. 7 presents the backhaul delay with respect to the density of SBSs under different maximum distances between the EDC and the destination SBS. When the maximum distance between the EDC and the destination SBS is fixed, the backhaul delay increases with the density of SBSs. When the density of SBSs is fixed, the backhaul delay decreases with the increase of the maximum distance between the EDC and the destination SBS.
Fig. 8 shows the system energy with respect to the density of EDCs under different numbers of video contents stored at EDCs. When the number of video contents is fixed, the system energy increases with the density of EDCs. When the density of EDCs is fixed, the system energy increases with the increase of the number of video contents stored at EDCs.
Fig. 9 depicts the SEE with respect to the density of EDCs under different numbers of video contents stored at EDCs. Based on the SEEO algorithm, the optimal solution of and are solved by and . Fig. 9(a) is a three-dimension figure describing the relationship among the SEE, the density of EDCs and the number of video contents stored at EDCs. Fig. 9(b) provides a two-dimension view of Fig. 9 (a), for a better illustration. Based on the results in Fig. 9, the minimum SEE is achieved when the number of video contents and the density of EDCs are configured as 144 and 9.873 , respectively.
Fig. 10 compares the SEE with respect to the number of video contents under the MCR scheme and the single path route scheme. Based on the curves in Fig. 10, the SEE of MCR scheme is always less than that of single path route scheme in 5G small cell networks. When the number of video contents stored at EDCs is configured as 144, the SEE of MCR scheme achieves the minimum, i.e., . When the number of video contents stored at EDCs is configured as 264, the SEE of single path route scheme achieves the minimum, i.e., . Compared with the SEE minimum of single path route scheme, the SEE minimum of MCR scheme is reduced by 11.5%.
The requirement of lower latency and massive data transmission for AR/VR applications imposes a great challenge on future wireless networks. In this paper a solution based on the SDN architecture is proposed for facilitating the AR/VR service provisionings in 5G small cell networks. To meet the requirements of lower delay and massive data transmission in AR/VR applications, a MCR scheme is proposed with an objective of achieving more efficient AR/VR wireless transmissions in 5G small cell networks, in which, a theorem on the delay of MCR scheme is proposed. Furthermore, both the lower and upper bounds of the delay in the MCR scheme are derived. Since VR technologies enable the user to interact with the virtual world, VR technologies are more sensitive to the latency compared with AR technologies. The SEEM algorithm is designed to minimize the network energy consumption while guaranteeing that the delay is less than a given threshold by adopting the MCR scheme. Therefore, the SEEM algorithm is relatively more suitable for VR applications than for AR applications. Simulation results indicate performance gains on both the delay and the SEE of the proposed MCR scheme compared with that of the conventional single path routing scheme in future 5G small cell networks.
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