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arxiv: 1907.01523 · v1 · pith:PSG7WP7Snew · submitted 2019-06-30 · 📡 eess.SP · cs.IT· cs.LG· math.IT

Deep Learning for Hybrid 5G Services in Mobile Edge Computing Systems: Learn from a Digital Twin

Pith reviewed 2026-05-25 12:54 UTC · model grok-4.3

classification 📡 eess.SP cs.ITcs.LGmath.IT
keywords mobile edge computingdeep learningdigital twinenergy consumptionuser associationresource allocation5G servicesultra-reliable low-latency communications
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The pith

A digital twin trains a deep neural network offline to determine real-time user association that minimizes normalized energy consumption per bit in mobile edge computing systems handling both ultra-reliable low-latency and delay-tolerant 5G

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper considers a mobile edge computing setup that mixes ultra-reliable low-latency communications with delay-tolerant services and seeks to cut normalized energy consumption by jointly choosing user association, resource blocks, and offloading probabilities while respecting quality-of-service constraints. User association is decided centrally at the mobility management entity, while each access point solves its own resource and offloading sub-problem. A digital twin simulates the live network at a central server to train a deep neural network offline; the trained network then supplies association decisions instantly, and the twin later monitors real-network drift to retrain the model. The resulting scheme reports lower energy per bit and lower complexity than a prior benchmark while staying close to the performance of a globally optimal solver.

Core claim

By training a deep neural network on data generated by a digital twin of the real network, the mobility management entity obtains near-optimal user association decisions in real time; for any fixed association an optimization routine then sets resource allocation and offloading probabilities at each access point, yielding lower normalized energy consumption and lower computation time than an existing method while approaching the global optimum.

What carries the argument

Digital-twin-trained deep neural network for user association, paired with per-access-point optimization of resource allocation and offloading probabilities.

If this is right

  • Normalized energy consumption per bit falls below that of the compared existing method.
  • Computation time required to obtain a feasible solution is lower than the benchmark method.
  • Achieved performance remains close to that of a globally optimal solver.
  • The model can be retrained periodically by monitoring drift between the digital twin and the live network.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the twin remains faithful, the same offline-training pattern could be reused for other joint association-and-allocation problems whose constraints change on similar time scales.
  • The separation of slow association decisions from fast local optimization suggests a natural division of labor between a central digital twin and edge nodes.
  • Testing on hardware-in-the-loop platforms would reveal how sensitive the energy savings are to model mismatch that the twin cannot fully capture.

Load-bearing premise

The digital twin must accurately reproduce the statistics and time-varying behavior of the real network so that the offline-trained network stays effective after deployment and can be updated without large performance loss.

What would settle it

Measure normalized energy consumption when the deployed system runs on a live network whose traffic statistics or mobility patterns deviate measurably from those reproduced by the digital twin; a statistically significant rise above the reported simulation gap would falsify the claim.

Figures

Figures reproduced from arXiv: 1907.01523 by Branka Vucetic, Changyang She, Rui Dong, Wibowo Hardjawana, Yonghui Li.

Figure 1
Figure 1. Figure 1: System model. single-AP problem, the AP optimizes resource allocation and task offloading for users that are associated with it. Each AP is equipped with a MEC server and each user has a local server. Time is discretized into slots. The duration of each slot is Ts . The service rates of the mth MEC server and the kth July 3, 2019 DRAFT [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Queueing model. The queueing models of the local servers and the MEC servers are illustrated in [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Digital twin enabled DL algorithm. The framework of the digital twin enabled DL algorithm is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Network topologies in our simulation. The DNN consists of one input layer, four hidden layers, and one output layer, where each hidden layer has 100 neurons. To achieve a better performance of the DL algorithm, we do not use α and λ as the input of the DNN. Instead, the vector [10 log( e λ ξ 1−1 α ξ 1,1 + 1), ..., 10 log( e λ ξ 1−1 α ξ M,1 + 1), ..., 10 log( e λ ξ K −1 α ξ 1,K + 1), ..., 10 log( e λ ξ K −1… view at source ↗
Figure 5
Figure 5. Figure 5: Normalized energy consumption v.s. total number of u [PITH_FULL_IMAGE:figures/full_fig_p025_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Training loss function v.s. number of learning epoch [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Normalized energy consumption v.s. user distributi [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Normalized energy consumption with uncertain user d [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
read the original abstract

In this work, we consider a mobile edge computing system with both ultra-reliable and low-latency communications services and delay tolerant services. We aim to minimize the normalized energy consumption, defined as the energy consumption per bit, by optimizing user association, resource allocation, and offloading probabilities subject to the quality-of-service requirements. The user association is managed by the mobility management entity (MME), while resource allocation and offloading probabilities are determined by each access point (AP). We propose a deep learning (DL) architecture, where a digital twin of the real network environment is used to train the DL algorithm off-line at a central server. From the pre-trained deep neural network (DNN), the MME can obtain user association scheme in a real-time manner. Considering that real networks are not static, the digital twin monitors the variation of real networks and updates the DNN accordingly. For a given user association scheme, we propose an optimization algorithm to find the optimal resource allocation and offloading probabilities at each AP. Simulation results show that our method can achieve lower normalized energy consumption with less computation complexity compared with an existing method and approach to the performance of the global optimal solution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper considers a mobile edge computing system supporting both ultra-reliable low-latency and delay-tolerant services. It minimizes normalized energy consumption (energy per bit) by jointly optimizing user association (via MME), resource allocation, and offloading probabilities (via APs) subject to QoS constraints. A digital twin of the network is used to train a DNN offline at a central server for real-time user association; an optimization algorithm then solves the per-AP subproblem. The twin monitors network variations and updates the DNN. Simulation results claim the approach yields lower normalized energy consumption and complexity than an existing method while approaching the global optimum.

Significance. If the digital-twin fidelity assumption holds, the decomposition (DNN for association + per-AP optimization) plus the monitoring/update loop offers a practical route to low-complexity real-time control in dynamic hybrid 5G MEC systems. The offline-training-plus-online-update pattern is a timely contribution to ML-for-communications work and could reduce online overhead while preserving QoS. The paper does not, however, supply machine-checked proofs, reproducible code, or parameter-free derivations, so the significance remains conditional on the simulation assumptions being representative of real deployments.

major comments (2)
  1. [Simulation Results] Simulation Results section: the reported gains in normalized energy consumption and complexity are obtained entirely by training and testing inside the same digital-twin model. No experiments on model mismatch, unmonitored dynamics, or transfer to a physically distinct environment are presented, so the central deployment claim rests on the unvalidated assumption that the twin exactly captures real-network statistics and dynamics.
  2. [Proposed Architecture] Digital-twin update mechanism (described in the Proposed Architecture section): the claim that the twin 'monitors the variation of real networks and updates the DNN accordingly' is load-bearing for handling non-static networks, yet no quantitative results on update frequency, triggering criteria, or performance loss after updates are supplied.
minor comments (2)
  1. [Abstract] The abstract refers to 'an existing method' without a citation; the comparison baseline should be explicitly identified.
  2. [System Model] Notation for normalized energy consumption and the precise definition of the global optimum benchmark should be stated earlier and used consistently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate where revisions will be made.

read point-by-point responses
  1. Referee: [Simulation Results] Simulation Results section: the reported gains in normalized energy consumption and complexity are obtained entirely by training and testing inside the same digital-twin model. No experiments on model mismatch, unmonitored dynamics, or transfer to a physically distinct environment are presented, so the central deployment claim rests on the unvalidated assumption that the twin exactly captures real-network statistics and dynamics.

    Authors: We agree that all numerical results are generated inside the digital-twin model. This is by design: the twin serves as a high-fidelity surrogate that enables offline training and controlled evaluation of the joint DNN-plus-optimization scheme. The reported gains therefore demonstrate performance under the modeling assumptions stated in the paper. We acknowledge that explicit mismatch or transfer experiments are absent. In the revised manuscript we will add a short subsection in Simulation Results that states this modeling assumption explicitly, quantifies the twin fidelity parameters used, and notes the need for future real-world validation. revision: partial

  2. Referee: [Proposed Architecture] Digital-twin update mechanism (described in the Proposed Architecture section): the claim that the twin 'monitors the variation of real networks and updates the DNN accordingly' is load-bearing for handling non-static networks, yet no quantitative results on update frequency, triggering criteria, or performance loss after updates are supplied.

    Authors: The referee correctly notes that the update loop is central to the non-stationary claim. The manuscript currently describes the mechanism at a conceptual level only. We will revise the Proposed Architecture section to include a new set of simulation results that illustrate (i) a concrete triggering criterion based on measured variation in user density and channel statistics, (ii) the resulting update interval, and (iii) the normalized-energy-consumption recovery after each update. These results will be added to the revised version. revision: yes

Circularity Check

0 steps flagged

No circularity; simulation claims are independent of any self-referential derivation

full rationale

The paper's central performance claims rest on simulation results obtained by training a DNN inside a digital-twin model of the network and then evaluating normalized energy consumption and complexity within the same model. No equations, parameter-fitting steps, or uniqueness theorems are presented that reduce a claimed prediction back to its own inputs by construction. The digital-twin training procedure is described as an offline process whose outputs are then deployed; this is a standard simulation-based workflow rather than a self-definitional loop. No self-citations are invoked as load-bearing premises for the optimization or DL architecture. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a digital twin can be maintained in sufficient fidelity to train a DNN whose outputs remain near-optimal when transferred to the live network; no free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption A digital twin can be kept sufficiently accurate to train a DNN that transfers to the real system without large performance degradation.
    Invoked when the paper states that the twin monitors variation and updates the DNN accordingly.

pith-pipeline@v0.9.0 · 5762 in / 1259 out tokens · 20794 ms · 2026-05-25T12:54:38.693425+00:00 · methodology

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · 4 internal anchors

  1. [1]

    The number of subcarriers allocated to the kth user is denoted as N ξ m,k

    Achievable Rate for URLLC: We consider orthogonal frequency division multiple access (OFDMA) systems. The number of subcarriers allocated to the kth user is denoted as N ξ m,k . Since the packet size of URLLC services is small, it is reason able to assume that the bandwidth of N u m,k subcarriers is smaller than the coherence bandwidth and the transmissio...

  2. [2]

    Data Rate for Delay Tolerant Services: For delay tolerant services, the packet size is long, and Shannon’s capacity is a good approximation of the achiev able rate. If the kth user is accessed to the mth AP , the ergodic capacity of the kth user, k ∈ K b, can be expressed as Egb m,k ( Rb k ) = Egb m,k [ N b m,k W log2 ( 1 + α b m,k gb m,k P t, b k N b m,k...

  3. [3]

    If the small-scale channel gain is above the threshold, the n the packets are offloaded to the MEC with probability one

    Offloading Policy of URLLC Services: Considering that feedback from receivers to trans- mitters may cause large overhead and extra delay, we assume t hat only 1 bit CSI is available at each transmitter, which indicates whether the small-sca le channel gain is above a certain threshold, gth, u k . If the small-scale channel gain is above the threshold, the ...

  4. [4]

    We consider an offloading policy that does not depend on the current small-scale channel gain

    Offloading Policy of Delay Tolerant Services: For each long packet, the transmission duration may exceed the channel coherence time. We consider an offloading policy that does not depend on the current small-scale channel gain. When the kth user, k ∈ K b, has a packet to process, the packet is offloaded to the MEC server with prob ability xb k ∈ [0, 1] and p...

  5. [5]

    QoS Constraints on Local Servers: If a packet is executed locally, the processing delay is Dlc, u k = cu k C u k (slots). (5) When the channel is in deep fading, i.e., gu m,k < g th, u k , all the packets of a user is served by the local server and the arrival process is a Bernoulli proce ss with average arrival rate λ u k. Given a constant service rate, ...

  6. [6]

    The E2E delay of a packet when offloading to the MEC s erver should satisfy the following constraint, 1 + Dmc, u k ≤ Dmax, u, (11) where data transmission occupies one slot

    QoS Constraints When Offloading to a MEC Server: When there are long and short packets in a PS server, an accurate approximation of the CCDF of the pr ocessing delay of short packets is given by [25], ǫmc, u k = (ρmc m ) ( SmDmc,u k cu k −1 ) , (9) where ρmc m is the workload of the mth MEC server, defined as follows, ρmc m = ∑ k∈Ku xu kλ u kcu k + ∑ k∈Kb x...

  7. [7]

    (14) Besides, the processing rate should not exceed the maximal c omputing capacity of the server, C b k ≤ C max, b k

    Rate Constraint of Local Servers: To ensure the stability of the queueing system on local servers, we need to guarantee that the processing rate is hig her than the average data arrival rate, C b k ≥ (1 − xb k)λ b k¯cb k, (cycles/slot). (14) Besides, the processing rate should not exceed the maximal c omputing capacity of the server, C b k ≤ C max, b k

  8. [8]

    Rate Constraint of Wireless Link: To ensure the stability of the communication queue in Fig. 2, we need to guarantee that the average transmission ra te of the wireless link is equal to or higher than the average data arrival rate, i.e., Egb m,k ( Rb k ) ≥ xb k¯bb kλ b k/T s, (15) where ¯bb k is the average number of bits in a long packet

  9. [9]

    (16) Otherwise, constraint (13) should be satisfied

    Workload Constraint on the MEC Server: In the case that only delay tolerant services offload packets to the mth MEC server, xu k = 0, ∀k ∈ K u, the stability of the PS server can be satisfied if the workload meets the following constraint, ρmc m = ∑ k∈Kb xb kλ b k¯cb k Sm ≤ 1. (16) Otherwise, constraint (13) should be satisfied. C. Objective Function: Normal...

  10. [10]

    URLLC Services: For URLLC services, the circuit power at the local server and the average transmit power for packets offloading are λ u kEloc, u k and λ u kP t, u k Ts (J/slot), respectively. Since the average data arrival rate is λ u kbu k (bits/slot), the normalized energy consumption is ηu k = (1 − xu k)λ u kEloc, u k + xu kλ u kP t, u k Ts λ u kbu k = ...

  11. [11]

    Then, the energy consumption per bit is ηloc, b k = Eloc, b k / ¯bb k

    Delay Tolerant Services: If a packet is processed at the local server, the average ener gy consumption is Eloc, b k = k0(C b k )2¯cb k, which is obtained from (4). Then, the energy consumption per bit is ηloc, b k = Eloc, b k / ¯bb k. If the packet is offloaded to a MEC server, the energy consump tion and the average amount of data transmitted in each slot...

  12. [12]

    To find the optimal offloading probability, we optimize gth, u k by the following three steps to meet all the constraints in pr oblem (23)

    URLLC Services: For URLLC services, the offloading probability is determine d by the threshold of small-scale channel gain gth, u k . To find the optimal offloading probability, we optimize gth, u k by the following three steps to meet all the constraints in pr oblem (23). In the first step, we find the minimal energy consumption per pa cket at the local serve...

  13. [13]

    Delay Tolerant Services: We apply the binary search to find the optimal offloading prob- abilities of delay tolerant services that meet the constrai nts of problem (23). Given N th, b k , the upper bound of the offloading probability that satisfies the c onstraints on average data rate and maximal transmit power in (15) and (19f) can be obtained by su bstitut...

  14. [14]

    We denote the index of the AP with the highest output as m∗ k = arg maxm∈M ˆβ ξ m,k

    Highest V alue (Exploitation): For the kth user, a direct way to map the continuous variables ˆβ ξ k to discrete a user association scheme is to access to the AP wi th the highest output. We denote the index of the AP with the highest output as m∗ k = arg maxm∈M ˆβ ξ m,k . Then, β ξ m∗ k,k (0) = 1 and ˆβ ξ m,k (0) = 0 , ∀m ̸= m∗ k. The user association sc...

  15. [15]

    Since only one user changes the scheme, this method is referr ed to as one step exploration

    One Step Exploration: Based on β(0), we change the association scheme of one of the K u + K b users, while the association scheme of the other users remai ns the same as β(0). Since only one user changes the scheme, this method is referr ed to as one step exploration. With this exploration policy, each user may access to M − 1 APs, and hence there are µ O...

  16. [16]

    The user association schemes generated with this method ar e denoted as β(µ OS + 1), ..., β(µ OS + µ RE), where µ RE is the number of schemes generated with the method

    Random Exploration: With the random exploration policy, each user randomly sele cts one of M APs with probability 1/M . The user association schemes generated with this method ar e denoted as β(µ OS + 1), ..., β(µ OS + µ RE), where µ RE is the number of schemes generated with the method. B. The DNN Training From the 1 + µ OS + µ RE user association scheme...

  17. [17]

    Study on scenarios and requir ements for next generation access technologies,

    3GPP TSG RAN TR38.913 R14, “Study on scenarios and requir ements for next generation access technologies,” Jun. 2017

  18. [18]

    Latency critical IoT applications in 5G: Perspective on t he design of radio interface and network architecture,

    P . Schulz, M. Matth´ e, H. Klessig, et al. , “Latency critical IoT applications in 5G: Perspective on t he design of radio interface and network architecture,” IEEE Commun. Mag. , vol. 55, no. 2, pp. 70–78, Feb. 2017

  19. [19]

    A sur vey on mobile edge computing: The communication perspective,

    Y . Mao, C. Y ou, J. Zhang, K. Huang, and K. B. Letaief, “A sur vey on mobile edge computing: The communication perspective,” IEEE Commun. Surveys Tuts. , vol. 19, no. 4, pp. 2322–2358, 2017

  20. [20]

    Cross-layer optimizat ion for ultra-reliable and low-latency radio access networ ks,

    C. She, C. Yang, and T. Q. S. Quek, “Cross-layer optimizat ion for ultra-reliable and low-latency radio access networ ks,” IEEE Trans. Wireless Commun. , vol. 17, no. 1, pp. 127–141, Jan. 2018

  21. [21]

    Quasi-st atic multiple-antenna fading channels at finite blocklengt h,

    W. Yang, G. Durisi, T. Koch, and Y . Polyanskiy, “Quasi-st atic multiple-antenna fading channels at finite blocklengt h,” IEEE Trans. Inf. Theory , vol. 60, no. 7, pp. 4232–4264, Jul. 2014

  22. [22]

    Energy-Efficient Joint Offloading and Wireless Resource Allocation Strategy in Multi-MEC Server Systems

    K. Cheng, Y . Teng, W. Sun, A. Liu, and X. Wang, “Energy-effi cient joint offloading and wireless resource allocation strategy in multi-MEC server systems,” 2018. [Online]. Ava ilable: https://arxiv.org/pdf/1803.07243v1.pdf

  23. [23]

    Energy-latency tradeoff for energy-aware offloading in mobile edge computing networks,

    J. Zhang, X. Hu, Z. Ning, E. C. . Ngai, L. Zhou, J. Wei, J. Che ng, and B. Hu, “Energy-latency tradeoff for energy-aware offloading in mobile edge computing networks,” IEEE Internet Things J. , vol. 5, no. 4, pp. 2633–2645, Aug. 2018

  24. [24]

    Asynchronous Mobile-Edge Computation Offloading: Energy-Efficient Resource Management

    C. Y ou, Y . Zeng, R. Zhang, and K. Huang, “Asynchronous mob ile-edge computation offloading: energy-efficient resourc e management,” 2018. [Online]. Available: https://arxiv.o rg/abs/1801.03668

  25. [25]

    Exploiting future radio res ources with end-to-end prediction by deep learning,

    J. Guo, C. Yang, and C.-L. I, “Exploiting future radio res ources with end-to-end prediction by deep learning,” IEEE Access, vol. 6, pp. 75 729–75 747, Nov. 2018

  26. [26]

    Applications of deep reinforcement learning in communic ations and networking: A survey,

    N. C. Luong, D. T. Hoang, S. Gong et al., “Applications of deep reinforcement learning in communic ations and networking: A survey,” submitted to IEEE Commun. Surveys Tuts. , 2018. [Online]. Available: https://arxiv.org/pdf/1810 .07862.pdf

  27. [27]

    APM: Driving value with the digital twin,

    M. Wise, “APM: Driving value with the digital twin,” in GE Digital , 2017

  28. [28]

    Energy-ef ficient joint offloading and wireless resource allocation strategy in multi-MEC server systems,

    K. Cheng, Y . Teng, W. Sun, A. Liu, and X. Wang, “Energy-ef ficient joint offloading and wireless resource allocation strategy in multi-MEC server systems,” in Proc. IEEE ICC , 2018

  29. [29]

    Wireless networks for mo bile edge computing: Spatial modelling and latency analysi s,

    S.-W. Ko, K. Han, and K. Huang, “Wireless networks for mo bile edge computing: Spatial modelling and latency analysi s,” IEEE Trans. on Wireless Commun. , vol. 17, no. 8, pp. 5225–5240, Aug. 2018

  30. [30]

    Joint resource allocati on and user association for heterogeneous services in multi -access edge computing networks,

    J. Zhou, X. Zhang, and W. Wang, “Joint resource allocati on and user association for heterogeneous services in multi -access edge computing networks,” IEEE Access , vol. 7, pp. 12 272–12 282, Jan. 2019. July 3, 2019 DRAFT 32

  31. [31]

    Performance Optimization in Mobile-Edge Computing via Deep Reinforcement Learning

    X. Chen, H. Zhang, C. Wu, S. Mao, Y . Ji, and M. Bennis, “Per formance optimization in mobile-edge computing via deep reinforcement learning,” 2018. [Online]. Available: https://arxiv.org/abs/1804.00514v1

  32. [32]

    Learning-Based Computation Offloading for IoT Devices with Energy Harvesting

    M. Min, D. Xu, L. Xiao, Y . Tang, and D. Wu, “Learning-base d computation offloading for iot devices with energy harvesting,” 2017. [Online]. Available: https://arxiv.o rg/abs/1712.08768v1

  33. [33]

    Online learning for offloadin g and autoscaling in energy harvesting mobile edge computin g,

    J. Xu, L. Chen, and S. Ren, “Online learning for offloadin g and autoscaling in energy harvesting mobile edge computin g,” IEEE Trans. Cogn. Commun. Netw. , vol. 3, no. 3, pp. 361–373, Sept. 2017

  34. [34]

    Deep reinforcement learning for online offloading in wireless powered mobile-e dge computing networks,

    L. Huang, S. Bi, and Y .-J. A. Zhang, “Deep reinforcement learning for online offloading in wireless powered mobile-e dge computing networks,” Sept. 2018. [Online]. Available: htt p://arxiv.org/abs/1808.01977

  35. [35]

    Latency and reliab ility-aware task offloading and resource allocation for mob ile edge computing,

    C.-F. Liu, M. Bennis, and H. V . Poor, “Latency and reliab ility-aware task offloading and resource allocation for mob ile edge computing,” in Proc. IEEE Globecom , 2017

  36. [36]

    Offloading schemes in mobile edge co mputing for ultra-reliable low latency communications,

    J. Liu and Q. Zhang, “Offloading schemes in mobile edge co mputing for ultra-reliable low latency communications,” IEEE Access, vol. 6, pp. 12 825–12 837, 2018

  37. [37]

    Energy efficiency of mobile clients in cloud computing

    A. P . Miettinen and J. K. Nurminen, “Energy efficiency of mobile clients in cloud computing.” HotCloud, vol. 10, pp. 4–4, 2010

  38. [38]

    Optimizati on of radio and computational resources for energy efficienc y in latency-constrained application offloading,

    O. Munoz, A. Pascual-Iserte, and J. Vidal, “Optimizati on of radio and computational resources for energy efficienc y in latency-constrained application offloading,” IEEE Trans. V eh. Technol., vol. 64, no. 10, pp. 4738–4755, Oct. 2015

  39. [39]

    Mobile-ed ge computing: Partial computation offloading using dynamic voltage scaling,

    Y . Wang, M. Sheng, X. Wang, L. Wang, and J. Li, “Mobile-ed ge computing: Partial computation offloading using dynamic voltage scaling,” IEEE Trans. Commun. , vol. 64, no. 10, pp. 4268–4282, Oct. 2016

  40. [40]

    Harchol-Balter, Performance Modeling and Design of Computer Systems: Queue ing Theory in Action

    M. Harchol-Balter, Performance Modeling and Design of Computer Systems: Queue ing Theory in Action . Cambridge University Press, 2013

  41. [41]

    Delay analysi s and computing offloading of URLLC in mobile edge computing systems,

    Y . Duan, C. She, G. Zhao, and T. Q. S. Quek, “Delay analysi s and computing offloading of URLLC in mobile edge computing systems,” in Proc. WCSP , 2018

  42. [42]

    Energy-optimal mobile cloud computing under stochastic wireless channel,

    W. Zhang, Y . Wen, K. Guan, D. Kilper, H. Luo, and D. O. Wu, “ Energy-optimal mobile cloud computing under stochastic wireless channel,” IEEE Trans. Wireless Commun. , vol. 12, no. 9, pp. 4569–4581, Sept. 2013

  43. [43]

    On the Geo/D/1 a nd Geo/D/1/N queues,

    A. Gravey, J.-R. Louvion, and P . Boyer, “On the Geo/D/1 a nd Geo/D/1/N queues,” Perform. Eval. , vol. 11, no. 2, pp. 117–125, Jul. 1990. [Online]. Available: http://dx.doi.o rg/10.1016/0166-5316(90)90018-E

  44. [44]

    Delay analys is for wireless fading channels with finite blocklength chan nel coding,

    S. Schiessl, J. Gross, and H. Al-Zubaidy, “Delay analys is for wireless fading channels with finite blocklength chan nel coding,” in Proc. ACM MSWiM , 2015

  45. [45]

    Optimizing resource allocation in the short blocklength regime for ultra-reliable and low-latency communications ,

    C. Sun, C. She, C. Yang, T. Q. Quek, Y . Li, and B. Vucetic, “ Optimizing resource allocation in the short blocklength regime for ultra-reliable and low-latency communications ,” IEEE Trans. Wireless Commun. , 2018

  46. [46]

    Human-level control through deep reinforcement learnin g,

    V . Mnih, K. Kavukcuoglu, D. Silver et al. , “Human-level control through deep reinforcement learnin g,” Nature, vol. 518, no. 7540, pp. 529–533, Feb. 2015

  47. [47]

    Adam: A method for stochastic opt imization,

    D. P . Kingma and J. Ba, “Adam: A method for stochastic opt imization,” 2014. [Online]. Available: http://dblp.uni-trier.de/db/journals/corr/corr1412.htmlKingmaB14

  48. [48]

    Evolved universal ter restrial radio access

    3GPP , LTE ETSI TR 36.931 v9.0.0, “Evolved universal ter restrial radio access.” May 2011

  49. [49]

    Burst iness aware bandwidth reservation for ultra-reliable and low-latency communications (URLLC) in tactile internet,

    Z. Hou, C. She, Y . Li, T. Q. S. Quek, and B. Vucetic, “Burst iness aware bandwidth reservation for ultra-reliable and low-latency communications (URLLC) in tactile internet,” IEEE J. Sel. Areas Commun. , vol. 36, no. 11, pp. 1–10, Nov. 2018

  50. [50]

    Boyd and L

    S. Boyd and L. V andenberghe, Convex Optimization. New Y ork, NY , USA: Cambridge University Press, 2004. July 3, 2019 DRAFT