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Cacheaided mobile edge computing for B5G wireless communication networks
EURASIP Journal on Wireless Communications and Networking volume 2020, Article number: 15 (2020)
Abstract
This paper investigates a cacheaided mobile edge computing (MEC) network, where the source offloads the computation task to multiple destinations with computation capacity, with the help of a cacheaided relay. For the proposed cacheaided MEC networks, two destination selection criteria have been proposed to maximize the computation capacity of the selected destination, the channel gain of relay link and the channel gain of direct link, respectively. Similarly, three destination selection criteria have been proposed for the cachefree MEC networks based on the computation capacities of destinations and the channel gains of transmission links, respectively. To evaluate the system performance regarding the latency constraint, we provide the outage probability for the proposed network which is defined based on the transmissionpluscomputation time. Our analysis suggests that caching can significantly alleviate the impact of increasing the size of computation task, since only half of the transmission time of cachefree network is required. However, the cacheaided network can not fully exploit the signal from both direct and relay links, thus the improvement by caching is less significant in the high signaltonoise ratio (SNR) region, compared with the cachefree network employing the destination with maximal channel gain of direct link. Numerical results are given to validate our analysis.
Introduction
Mobile edge computing (MEC) has been emerging as a powerful tool to support realtime and highquality services, such as virtual reality and tactile internet applications [1]. Due to the limited computation capacity and storage, mobile devices have to offload the computation tasks to computing access points, e.g., cloud datacenters, which possess powerful computing capability and significantly reduce the computation latency. Therefore, it is of vital importance to accommodate traditional wireless networks to support latencysensitive computation task for the fifthgeneration (5G) wireless networks. Accordingly, the authors in [2–4] have proposed the concept of mobile edge computing (MEC) wireless communications networks, where the computation tasks can be offloaded to the edge nodes with computation capacity through the wireless links.
Cooperative relaying is a promising technique to improve the spectrum efficiency, strengthen the system security, and enhance the network connectivity [5–8]. To improve the performance of MEC networks, cooperative relaying has been proposed to improve the transmission rate, which therefore reduces the latency and the energy efficiency [9–11]. Specifically, Cao et al. in [9] proposed to utilize relay nodes consisting of retransmission and cooperative computation to improve the performance of MEC network, and the authors designed an energyefficient algorithms for the proposed network. In [10], Hu et al. investigated the wireless powered cooperation network, where the access terminals are powered by the radio signal transmitted from the MEC base station, and the authors optimized the transmit power for the proposed system. Based on above works, Wen et al. in [11] further considered the fullduplex relaying scenario and jointly optimized the task offloading and computing scheme.
During the peak traffic, the network transmission confronts a huge challenge of congestion, which causes a severe issue of latency [12, 13]. Therefore, caching was proposed to effectively alleviate the congestion of traffic in wireless networks [14–16]. To mitigate the congestion of communications traffic and improve the network performance, the convergency of caching and MEC has become a major topic in the field of wireless communications [17–20]. With the aid of caching, the stressing burden of offloading can be alleviated; thus, the throughput and energy efficiency of MEC networks can be enhanced. In particular, the authors in [9] proposed to jointly optimize the cache placement and computation task offloading. Moreover, Tan et al. in [21] investigated the cacheenabled MEC network and designed a virtual resource allocation scheme for the network with heterogeneous services. Further, Zhou et al. in [22] optimized the cache placement and computation task offloading strategy from an informationcentric perspective. Besides the above research, there have been some researches on the newly developed materials [23–26], which can be used in wireless networks for both transmission and improving the environments.
In this paper, we study the cacheaided MEC networks, where the task offloading from the source to the destinations with computation capacities is assisted by a cacheenabled relay. Also, we compare the performance of cacheaided relay network with that of cachefree network. In particular, we propose several destination selection criteria with the purposes of maximizing the computation capacity of destination, the channel gain of direct and relaying links, respectively. As we consider the latencyconstraint MEC networks, the outage probabilities based on maximal transmissionpluscomputation time for the proposed criteria are derived under Rayleigh fading channels. Our analysis suggests that caching can significantly alleviate the impact of the increasing size of computation task, as only half of the transmission time of cachefree network is required. However, the cacheaided network can not fully exploit both direct and relaying links, and the enhancement by caching is less significant in the high signaltonoise ratio (SNR) region. Simulation results are given to validate the analysis.
The key contributions of this paper are summarized as follows:
We study the cacheaided MEC networks, where the task offloading from the source to the destinations with computation capacities is assisted by a cacheenabled relay.
Several destination selection criteria are utilized to choose one best destination, in order to enhance the network performance.
For each selection criterion, we present the analytical outage probability analysis in order to evaluate the network performance in the whole range of SNR.
Methods/experimental
As depicted in Fig. 1, we consider a MEC network, where the source S aims to offload a computation task with size of L bits to the destination D_{n} (n∈[1,N]) with the assistance of a cacheaided relay R. Specifically, D_{n} is equipped with a CPU of cycle frequency of δ_{n}, and we assumes that each bit of computation task requires K CPU cycles to complete the computation. For the sake of convenience, we assume that each node in the considered networks is equipped with a single antenna, and the flat fading Rayleigh channels are considered as well. Based on the latency constraint for transmission and computation time, we define the outage event for the proposed system. To enhance the system performance, we propose two destination selection criteria for the cacheaided network and three destination selection criteria for the cachefree network, aiming to select the destination with maximal computation capacity and maximal channel gain form direct or relay link, respectively.
System model
For a cacheaided network where the relay is equipped with cache, the computation task can be transmitted from the relay; thus, the sourcetorelay and sourcetodestination can be reduced. Therefore, the computation time and transmission time for D_{n} are respectively given by
where B is the dedicated bandwidth for the transmission of computation task, \(\phantom {\dot {i}\!}v_{n}\sim \ \mathbf {E}(\beta)\) is the channel gain of the Rto D_{n} link [27–29], P is the transmit power at the source and relay, and σ^{2} is the variance of the additive Gaussian noise \(n\sim \mathcal {C}\mathcal {N}\left (0,\sigma ^{2}\right)\) [30, 31]. Note that we consider a latencyconstraint scenario, in which the maximal transmission plus computation time is fixed to T, where \(T>\frac {KL}{\min _{n\in [1,N]}(\delta _{n})}\) is assumed to ensure the implementation of task computing for arbitrary D_{n}. Therefore, we adjust the traditional definition of outage event and further define that the outage at destination D_{n} occurs when the required transmission plus computation time is greater than T, i.e.,
which is equivalent to
where \(\gamma _{th,n}^{(1)}\) denotes the outage threshold for the received SNR at D_{n} for the cacheaided network, and \(\gamma _{th,n}^{(1)}\) is defined as
For the cachefree network where there is no cache equipped at the relay, two transmission time slots are required. In detail, the source conveys the computation task to both relay and D_{n} during the first phase, and the relay decodes and transmits the computation task to D_{n} during the next phase. The selection combining receiver is employed at the destination to combine the twobranches signal. Accordingly, the computation time and transmission time for D_{n} are respectively given by
where u∼ E(α) is the channel gain of the StoR link and w_{n}∼ E(ε) is the channel gain of the Sto D_{n} link. Similarly, the outage event occurs when
where \(\gamma _{th,n}^{(2)}\) is the outage threshold for the received SNR at D_{n} for the cacheaided network, and \(\gamma _{th,n}^{(2)}\) is defined as
Destination selection criterion
In this section, we aim to design the destination selection ^{Footnote 1} criteria to enhance the performance for the cacheaided network and the cachefree network, respectively. Different from the traditional wireless communications networks, MEC wireless networks consider the computation capacities of destinations, in which the traditional selection criteria may not be suitable. Note that the optimal destination selection criterion is very complicated and unrealistic in practice, we thus propose the following suboptimal criteria for the considered networks. The details of the selection criteria are illustrated as follows.
For the cacheaided network, we propose two destination selection criteria, which aim to achieve maximal computation capacity at the destination and maximal channel gain for the relaytodestination link, respectively. The destination n^{∗} is selected based on the following criteria.
Criterion CacheAidedI
$$\begin{array}{*{20}l} n^{*}=\arg \max_{n\in[1,N]}(\delta_{n}) \end{array} $$(10)Criterion CacheAidedII
$$\begin{array}{*{20}l} n^{*}=\arg \max_{n\in[1,N]}(v_{n}) \end{array} $$(11)
For the cachefree network, we propose three destination selection criteria. The destination n^{∗} is chosen according to the following criteria.
Criterion CachefreeI
$$\begin{array}{*{20}l} n^{*}=\arg \max_{n\in[1,N]}(\delta_{n}) \end{array} $$(12)Criterion CachefreeII
$$\begin{array}{*{20}l} n^{*}=\arg \max_{n\in[1,N]}(v_{n}) \end{array} $$(13)Criterion CachefreeIII
$$\begin{array}{*{20}l} n^{*}=\arg \max_{n\in[1,N]}(w_{n}) \end{array} $$(14)
We see that for criterion CachefreeI, the destination with maximal computation capacity is selected. For criterion CachefreeII, the destination with maximal channel gain of relayto destination link is selected. For criterion CachefreeIII, the destination with maximal channel gain of sourceto destination link is selected.
Outage performance analysis
In this section, the exact outage probabilities for the proposed networks are derived. Moreover, some insights on the system are given to better analyze the proposed system.
Cacheaided network
For the cacheaided network, from criterion CacheAidedI, we see that the destination with maximal computation capacity \(\delta _{n^{*}}=\max _{n\in [1,N]} (\delta _{n})\phantom {\dot {i}\!}\) is selected. Therefore, the outage event happens when the Rto\(\delta _{n^{*}}\phantom {\dot {i}\!}\) link cannot support the transmission of computation task, and the outage probability for criterion CacheAidedI is given by
where \(v_{n}^{*}\) can be replaced by v_{n} since the selection of destination does not affect the relaytodestination link. Using the probability density function (PDF) of random variable (RV) v_{n}, \(f_{v_{n}}(x)=\frac {1}{\beta }e^{\frac {x}{\beta }}\), we can obtain Pout,I(1) as [32]
From criterion CacheAidedII, we see that the destination with maximal channel gain of relaytodestination link \(v_{n^{*}}=\max _{n\in [1,N]} (v_{n})\) is selected. Also, the computation capacity of the selected destination varies with identical probability of using computation capacity δ_{n}. Note that the channel gains of D_{n} vary with different time slot and the selected destinations \(D_{n}^{*}\)s are of different computation capacities. Thus, the outage threshold for each transmissions varies. However, for criterion CacheAidedII, the probabilities of selecting D_{n} are identical, i.e., \(\Pr \left (\gamma _{th,n^{*}}^{(1)}=\gamma _{th,n}^{(1)}\right)=1/N\). Therefore, the outage probability for criterion CacheAidedI is given by
Using the PDF of RV v_{n}, \(f_{v_{n}^{*}}(y)=\frac {1}{\beta }e^{\frac {yN}{\beta }}\), we can obtain Pout,II(1) as
Cachefree network
For the cachefree network, from criterion CachefreeI, we see that the destination with maximal computation capacity \(\delta _{n^{*}}=\max _{n\in [1,N]} (\delta _{n})\) is selected. Therefore, the outage probability for criterion CachefreeI is given by
where step (a) follows the law of total probability. We see that the first term denotes the outage probability of direct link and the second terms denotes the outage probability of relay link, which means that the cachefree relay network can fully exploit signals from both direct and relay branches. However, the cacheaided network can only exploit the relaybranch signal. Further, we can rewrite Pout,I(2) as
Similarly, w_{n} and \(v_{n}^{*}\) can be replaced by w_{n} and v_{n}, respectively. Substituting the PDFs of RV u, v_{n}, and w_{n}, i.e., \(f_{u}(x)=\frac {1}{\alpha }e^{\frac {x}{\alpha }}\), \(f_{v_{n}}(y)=\frac {1}{\beta }e^{\frac {y}{\beta }}\), and \(f_{w_{n}}(z)=\frac {1}{\varepsilon }e^{\frac {z}{\varepsilon }}\), we can compute Pout,I(1) as
From criterion CachefreeII, we see that the destination with maximal channel gain of relaytodestination link \(v_{n^{*}}=\max _{n\in [1,N]} (v_{n})\) is selected. However, for criterion CacheFreeII, the probabilities of selecting D_{n} are identical, i.e., \(\Pr \left (\gamma _{th,n^{*}}^{(2)}=\gamma _{th,n}^{(2)}\right)=1/N\). Therefore, the outage probability for criterion CachefreeII is given by
Using the PDFs of RVs u, v_{n} and w_{n}, i.e., \(f_{u}(x)=\frac {1}{\alpha }e^{\frac {x}{\alpha }}\), \(f_{v_{n}^{*}}(y)=\frac {1}{\beta }e^{\frac {yN}{\beta }}\) and \(f_{w_{n}}(z)=\frac {1}{\varepsilon }e^{\frac {z}{\varepsilon }}\), we can obtain Pout,II(2) as
From criterion CachefreeIII, we see that the destination with maximal channel gain of relaytodestination link \(w_{n^{*}}=\max _{n\in [1,N]} (w_{n})\) is selected. Similarly, for criterion CacheFreeIII, the probabilities of selecting D_{n} are identical, i.e., \(Pr\left (\gamma _{th,n^{*}}^{(1)}=\gamma _{th,n}^{(1)}\right)=1/N\). Therefore, the outage probability for criterion CachefreeIII is given by
Applying the PDFs of RVs u, v_{n}, and w_{n}, i.e., \(f_{u}(x)=\frac {1}{\alpha }e^{\frac {x}{\alpha }}\), \(f_{v_{n}^{*}}(y)=\frac {1}{\beta }e^{\frac {y}{\beta }}\), and \(f_{w_{n}}(z)=\frac {1}{\varepsilon }e^{\frac {zN}{\varepsilon }}\), we can obtain Pout,III(2) as
From the above analysis on the outage performance, we can draw the following insights on the proposed networks.
Remarks 1
From (15), we see that for criteria CacheAidedI and CacheFreeI, the increase of the number of destination N cannot guarantee the improvement of the network, unless the added destination is of higher computation capacity. This is is because the destination with highest computation capacity is selected, which leads to the loss of diversity on transmission channel.
Remarks 2
From (16)–(18) and (23)–(30), we see that the increase of the number of destination N may results in performance loss of network for criteria CacheAidedII, CacheFreeII and CacheFreeIII. This is due to the fact that the overall outage probability is obtained by averaging the outage probabilities of each destinations with different computation capacities. The involvement of destination with low computation capacity causes the degradation of outage performance.
Remarks 3
Cacheaided networks can effectively improve the system performance by reducing half of the transmission time than the cachefree network. Therefore, criteria CacheAidedI and CacheAidedII outperform the criteria CacheFreeI and CacheFreeII, respectively, in the low SNR region.
Remarks 4
From the outage results, we see that criterion CacheFreeIII can achieve full diversity by exploiting both relay and direct links. However, criterion CacheAidedII can only exploiting the multidestination diversity. Therefore, criterion CacheFreeIII outperform criterion CacheAidedII in the high SNR region.
Results and discussion
In this section, we give the numerical and simulation results regarding the proposed criteria CacheAidedI, CacheAidedII, CacheFreeI, CacheFreeII and CacheFreeIII, denoted as “CAI," “CAII,” “CFI,” “CFII,” and “CFIII,” respectively, for convenience sake. Also, we assume the considered nodes are each equipped with one antenna since the limitation of size. The pathloss model is adopted, and we assume the average channel gain of StoR link α=8, the average channel gain of Rto D_{n} link β=5 and the average channel gain of Sto D_{n} link ε=1. If not specified, we set the number of destination N=2, the size of computation task L=50 Mbits, the allocated bandwidth B=100 MHz, the transmission plus computation latency threshold T=0.5 s, transmit SNR P/σ^{2}=15 dB and K=10 [33].
Figure 2 illustrates how outage varies with transmit SNR P/σ^{2}, where P/σ^{2} changes from 0 to 30 dB, when N=2, L=50 Mbits, K=10, B=100 MHz and T=0.5 s. From Fig. 2, we see that the simulation outage probabilities match the analytical outage probabilities, which confirms our analysis. Moreover, we see that in the low SNR region, the cacheaided relay network can achieve better performance as cacheaided relay network requires half of the transmission time than cachefree relay network. However, in the high SNR region, for the criteria with the same destination selection purpose, e.g„ CAI and CFI, or CAII and CFII, the criterion for the cachefree relay network outperforms the criterion for cacheaided relay network. This is due to the fact that the cachefree network can exploit one more branch signal than cacheaided relay network, including both the direct and relaying links. However, for the cacheaided relay network, the maximal diversity order is equal to N and no directlink signal can be exploited.
Figure 3 shows the variations of outage probability with latency threshold T, where the values T falls in the range of [0.1,1], when N=2, L=50 Mbits, K=10, B=100 MHz and P/σ^{2}=15 dB. From Fig. 3, we confirm the correctness of our analysis by comparing the simulation and analytical outage probabilities. Also, we see that for criteria CAI and CFI, the network cannot exploit the diversity of transmission channel, thus the improvement of these two criteria is limited. Moreover, we see that, with the increase of T, the outage probabilities for all criteria decrease. This is because for larger value of T, the computation task is can be easier to achieve. Also, Eq. (4) suggests that when T is large enough, the outage threshold can barely increase, thus decrease of outage probability with the increase of T decelerates.
Figure 5 depicts how the outage probability changes with different numbers of destinations Nwhen L=50 Mbits, K=10, B=100 MHz, P/σ^{2}=15 dB and T=0.5 s. Specifically, N varies from 1 to 8, and the capacity of destination D_{n}, i.e., δ_{n}, is equal to (11−n) GHz, in a descending order. This is reasonable since the destination with higher computation capacity is considered first to achieve lower latency (Fig. 4). From Fig. 5, we see that for criteria CAI and CFI, the outage probabilities remain the same, since the δ_{1}= maxn∈[1,N]δ_{n} and D_{1} is always selected. However, for criterion CFII, the outage probability increases when N is large. This is due to the fact that the diversity order for CFII is two and the augment of destination can only improve the second hop of relaying link. Moreover, we assume the later included destinations are of weaker computation capacity, which might cause higher outage probability; thus, from Eq. (30), the overall outage probabilities increase. However, for criteria CAII and CFIII, the increase of N significantly improves the network performance; thus, the difference of computation capacity of destination can be neglected.
Figure 4 illustrates the effect of the size of computation task L on the outage performance of system. In specific, L varies from 10 to 100 Mbits, and we set N=2, K=10, B=100 MHz, P/σ^{2}=15 dB and T=0.5 s. From Fig. 4, we see that the increase of L greatly increases the outage probability, since the burdens of transmission is proportional to the size of computation task. Also, the results shows that with the increase of L, the cachefree relay networks are more vulnerable than cacheaided networks, since the increase of L doubles the burdens of twophase transmission for cachefree networks. As a result, with small values of L, CFI outperforms CAI, yet different phenomenon occurs when the values of L is large.
Figure 6 demonstrates how the outage probability changes with various values of dedicated bandwidth B, when N=2, L=50 Mbits, K=10, P/σ^{2}=15 dB, and T=0.5 s. Additionally, B varies from 10 to 100 MHz. Also, we see that for criteria CAI and CFI, the network only exploits the diversity of computation capacity of destination, which barely affects the network performance as the computation capacity of destination is fixed. Thus, the improvement of these two criteria is not significant. Moreover, we see that, with the increase of B, the outage probabilities for all criteria decrease. This is because for larger value of B, the computation task can be easier to achieve. Furthermore, from Eq. (4), we see that when B is large enough, the outage threshold tends to a fixed values, thus decrease of outage probability with the increase of B decelerates.
Conclusions
This paper studied the cacheaided MEC networks, for which we proposed five destination selection criteria. To evaluate the effectiveness of the proposed criteria, the outage probabilities based on the transmission plus computation time for the propose criteria have been derived. Our results show that the proposed criteria aiming to maximize the channel gain of direct or relaying links can significantly improve the system performance. However, the criteria with purpose of maximizing the computation capacity of destination enjoys very limited benefits of signal diversity. Moreover, analysis suggests that caching can significantly alleviate the impact of increasing the size of computation task as only half of the transmission time of cachefree network is required. Numerical results have been given to validate our analysis. In future works, we will consider the application of this work for IoT networks, such as urban environment improvement [34–36] and environmental monitoring [37–40]. Moreover, we will incorporate the intelligent algorithms such as learningbased algorithms [41, 42], deep learning [43, 44], and reinforcement learning [45–47] into the considered system, in order to further enhance the network performance.
Availability of data and materials
The authors state the data availability in this manuscript through the email to the corresponding author.
Notes
 1.
Note that in literatures [14], user selection is used instead of destination selection. However, both of them represent the same meaning in practice.
Abbreviations
 CAI:

CacheAidedI
 CAII:

CacheAidedII
 CFI:

CacheFreeI
 CFII:

CacheFreeII
 CFIII:

CacheFreeIII
 MEC:

Mobile edge computing
 PDF:

Probability density function
 RV:

Random variable
 SNR:

Signaltonoise ratio
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Acknowledgements
This work was supported in part by the NSFC under grant 61871139, in part by the Innovation Team Project of Guangdong Province University under grant 2016KCXTD017, and in part by the Science and Technology Program of Guangzhou under grant 201807010103.
Funding
This work is supported by the National Natural Science Foundation of China (no. 61871139), by the Natural Science Foundation of Guangdong Province (no. 2018A030313736), by the Scientific Research Project of Education Department of Guangdong, China (no. 2017GKTSCX045), by the Science and Technology Program of Guangzhou, China (no. 201707010389), and by the Project of Technology Development Foundation of Guangdong (no. 706049150203).
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JX gave the main ideas in this work, LC made the simulation experiments, XL derived the formulas, and SL helped write the main manuscript of this work. FZ has helped check the latest reference, rewritten the part of the introduction, and provided some insights from the work in this paper. DD has helped improve the language of this manuscript, corrected the grammar errors and clarified some unclear sentences in the manuscript. LF has helped improve the presentation of figures style in this work and helped enhance the novelty of this paper. All authors have read and approved the final manuscript.
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Xia, J., Li, C., Lai, X. et al. Cacheaided mobile edge computing for B5G wireless communication networks. J Wireless Com Network 2020, 15 (2020). https://doi.org/10.1186/s1363801916120
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Keywords
 Cache
 MEC
 B5G
 Outage probability
 Relay