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Communications, Caching and Computing for Mobile Virtual Reality: Modeling and Tradeoff

Yaping Sun, Zhiyong Chen, Meixia Tao, Hui Liu

arXiv:1806.08928v1cs.IT

TL;DR

Mobile VR requires massive data delivery at ultra-low latency, motivating resource allocation that reduces wireless transmission requirements. The paper combines MEC caching with local caching and projection computing, deriving an optimal homogeneous-FOV policy and a CCCP-based local solution for heterogeneous FOVs. Numerical results show bandwidth-saving potential while meeting low-latency requirements.

  • Problem

    Mobile VR must deliver gigabyte-scale data within less than 20 ms, while the paper seeks to minimize bandwidth using MEC caching and computing under stringent latency constraints.

  • Method

    The paper jointly optimizes mobile-device caching and projection computing, using a closed-form policy for homogeneous FOVs and IQP transformation with CCCP for heterogeneous FOVs.

  • Results

    CCCP shows promising communication-bandwidth savings in the heterogeneous scenario, while the homogeneous analysis reveals communications-caching-computing tradeoffs.

  • Takeaways & Limitations

    Caching selected FOVs and computing projection at the mobile device provide a framework for reducing transmission requirements while satisfying latency constraints.

Abstract

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Virtual reality (VR) over wireless is emerging as an important use case of 5G networks. Immersive VR experience requires the delivery of huge data at ultra-low latency, thus demanding ultra-high transmission rate. This challenge can be largely addressed by the recent network architecture known as mobile edge computing (MEC), which enables caching and computing capabilities at the edge of wireless networks. This paper presents a novel MEC-based mobile VR delivery framework that is able to cache parts of the field of views (FOVs) in advance and run certain post-processing procedures at the mobile VR device. To optimize resource allocation at the mobile VR device, we formulate a joint caching and computing decision problem to minimize the average required transmission rate while meeting a given latency constraint. When FOVs are homogeneous, we obtain a closed-form expression for the optimal joint policy which reveals interesting communications-caching-computing tradeoffs. When FOVs are heterogeneous, we obtain a local optima of the problem by transforming it into a linearly constrained indefinite quadratic problem then applying concave convex procedure. Numerical results demonstrate great promises of the proposed mobile VR delivery framework in saving communication bandwidth while meeting low latency requirement.

I. INTRODUCTION

The paper addresses wireless mobile VR’s massive-data, ultra-low-latency demands by combining MEC caching with computing at the mobile VR device. It develops a joint resource-allocation framework and optimization methods to reduce transmission requirements.

  • I. INTRODUCTION: Mobile VR must deliver gigabyte-scale data within less than 20 ms, creating an ultra-high-rate wireless bandwidth bottleneck.
  • I. INTRODUCTION: MEC provides edge caching and computing to reduce traffic load and response time for mobile VR delivery.
  • I. INTRODUCTION: The proposed framework computes preprocessing in the cloud and projection at the MEC server or mobile VR device, reducing wireless transmission data and latency.
  • I. INTRODUCTION: Offloading projection to the mobile device can reduce wireless traffic by at least half, because 3D FOV data are at least twice the size of 2D FOV data.
  • I. INTRODUCTION: For homogeneous FOVs, the paper derives a closed-form optimal joint caching-and-computing policy and characterizes communications-caching-computing tradeoffs.
  • I. INTRODUCTION: For heterogeneous FOVs, the NP-hard optimization is transformed into an IQP and solved for a local optimum using CCCP, with numerical evidence of bandwidth savings under low latency.

II. SYSTEM MODEL

The system models on-demand 360° VR delivery from an MEC server to a mobile VR device, with both sides providing caching and computing resources. The device chooses which 2D or 3D FOVs to cache and which projections to compute locally under cache, latency, and energy constraints.

  • II. SYSTEM MODEL: The system serves only the requested viewpoint FOV rather than the entire 360° video through one MEC server and one mobile VR device.
  • II. SYSTEM MODEL: Each viewpoint’s 2D-to-3D projection is characterized by 2D size DI, 3D size DO, and computation cost w; typically, α = DO/DI ≥ 2.
  • II. SYSTEM MODEL: Requests follow an independent reference model over N viewpoints, with uniform probability Pi = 1/N and deadline τ for every request.
  • II. SYSTEM MODEL: The mobile device cache stores selected 2D and 3D FOVs, while the larger MEC cache stores both FOV types for all viewpoints.
  • II. SYSTEM MODEL: The device selects local projection through di, subject to CPU frequency fV and average energy budget Ē; its computing capability is the maximum number of projections supported under that budget.
  • II. SYSTEM MODEL: The joint decision (cO, cI, d) combines 3D-caching, 2D-caching, and local-computing decisions under cache-size and average-energy constraints.

D. Service Mechanism and Transmission Rate Requirement

Each joint caching-and-computing decision determines a service route for the requested FOV and its minimum transmission rate under the latency deadline. The resulting average rate is minimized subject to resource constraints, exposing tradeoffs among caching, computing, energy, and bandwidth.

  • D. Service Mechanism and Transmission Rate Requirement: A joint decision (cO, cI, d) enables four service routes, each with a distinct minimum transmission rate Ri under the latency constraint.
  • D. Service Mechanism and Transmission Rate Requirement: Local 3D caching serves a requested 3D FOV directly, requiring negligible latency and Ri = 0.
  • D. Service Mechanism and Transmission Rate Requirement: Local computing with local 2D caching projects the cached 2D FOV on the device without transmission, provided DIw/fV < τ.
  • D. Service Mechanism and Transmission Rate Requirement: Local computing without local caching downloads the 2D FOV from the MEC server and projects it locally, combining wireless transmission and computation latency.
  • D. Service Mechanism and Transmission Rate Requirement: MEC computing downloads the 3D FOV from the MEC server, with the required rate determined by the transmission latency under the deadline.
  • D. Service Mechanism and Transmission Rate Requirement: The optimization minimizes average required transmission rate, equivalently bandwidth for fixed spectral efficiency, under cache-size and average-energy constraints.
  • D. Service Mechanism and Transmission Rate Requirement: Local 2D caching with computing matches local 3D caching’s rate gain while using at least half the cache, but adds energy consumption; other routes exchange cache, energy, and rate costs.

B. Optimal Properties and Equivalent Formulation

The paper derives structural properties of joint caching and computing, then reduces the original optimization to an equivalent formulation. The resulting policy avoids redundant caching or computing and decomposes transmission-rate gains by service route.

  • Equivalent formulation: The optimization is reformulated using counts of locally cached 3D FOVs, locally cached 2D FOVs, and locally computed projections.These quantities parameterize the equivalent joint-policy optimization.
  • Equivalent formulation: For homogeneous viewpoints, the optimal policy can be represented by assigning contiguous viewpoint groups to 3D caching, 2D caching, and local computation.The assignments preserve optimality under identical projection tuples and simplify structural analysis.
  • Optimal properties: Caching a 3D FOV makes local 2D caching unnecessary because the request can be served directly from the local cache.This follows from the optimality property between local 2D and 3D FOV caching.
  • Optimal properties: When a 3D FOV is locally cached, local computing provides no additional gain; when a 2D FOV is cached, not using it for projection wastes caching resources.Both conclusions follow from comparing policies with unchanged transmission rate and lower resource cost.
  • Equivalent formulation: The objective separates the baseline MEC-computing rate from gains due to local 3D caching, local computing with 2D caching, and local computing without caching.The final gain can be negative when fV < F, defining the local computing limited region; fV ≥ F is the MEC computing limited region.

IV. OPTIMAL POLICY AND TRADEOFF ANALYSIS

The paper characterizes the optimal joint policy and the communications-caching-computing tradeoff in the local computing limited region, where caching and computing interact to reduce transmission rate. The analysis shows that caching can enable local computing, while power-efficient local computation further lowers the required rate.

  • Optimal policy: The optimal policy in the local computing limited region yields the minimum transmission rate and defines the 3C tradeoff.This region is characterized by fV < F.
  • Tradeoff analysis: When fV < F, performance gains come from local 3D caching and local computing with local 2D caching, while computing without local caching has negative gain.The optimal number of locally computed projections is jointly limited by local caching and computing capabilities.
  • Tradeoff analysis: Local computing with 2D caching is selected before local 3D caching because 2D caching costs less per FOV, with DO = αDI.Remaining storage is allocated to 3D caching only after the computing-plus-2D-caching opportunity is used.
  • Numerical analysis: R∗ first decreases with local computing capability and then remains unchanged once computing capability exceeds caching capability.This behavior indicates that caching facilitates utilization of local computing in the local computing limited region.
  • Numerical analysis: R∗ increases with fV and k but decreases with Ē in the local computing limited region.Higher Ē enables more projections to be computed locally, while larger k reduces the number of locally computable projections.

B. MEC Computing Limited Region

In the MEC computing limited region, local computing can provide gains even without local 2D caching, changing the balance among caching, computing, and transmission rate. The numerical analysis identifies complementary effects between caching and computing and a nonmonotonic dependence on computation frequency.

  • Optimal policy: Theorem 2 gives the optimal joint policy and minimum transmission rate when F ≤ fV.This is the MEC computing limited region.
  • Tradeoff analysis: When F ≤ fV, gains come from local 3D caching, local computing with local 2D caching, and local computing without local caching.Because computing without 2D caching is beneficial, the optimal number of computed projections is limited only by computing capability.
  • Numerical analysis: R∗ decreases monotonically with local caching capability, and its decreasing rate increases with local computing capability, reaching 50% in the reported case.The result likewise indicates that local computing facilitates utilization of caching capability.
  • Numerical analysis: R∗ first decreases and then increases with fV, while it decreases with Ē and increases with k.The nonmonotonic frequency effect reflects a tradeoff between reduced computation latency and fewer computable projections.
  • Numerical analysis: The computation frequency minimizing R∗ depends on projection parameters (DI, DO, w, τ) but not on Ē or k.This dependence is stated for the optimal computation frequency in Equation (20).

V. PROBLEM FORMULATION IN HETEROGENEOUS SCENARIO

For heterogeneous viewpoints, the paper generalizes the joint caching-and-computing optimization to viewpoint-specific parameters and costs. It then characterizes the problem as strongly NP-hard and transforms it into an indefinite quadratic program solvable by CCCP.

  • Problem formulation: The heterogeneous scenario allows each viewpoint to have different parameters, including DIi, wi, τi, and Pi.The optimization is formulated over these viewpoint-specific characteristics.
  • Problem formulation: The objective uses the minimum transmission rates required under MEC-server versus mobile-device projection while satisfying the latency constraint.C′ denotes the mobile VR device cache size.
  • Problem formulation: For each viewpoint, the formulation accounts for transmission-rate gains and caching and computing costs for each service route.These quantities are organized in Table III.
  • Optimization approach: Problem 3 is strongly NP-hard and is transformed into an equivalent indefinite quadratic program solved efficiently via concave-convex procedure.The transformation provides the stated solution approach for heterogeneous viewpoints.

A. Computational Intractability

The heterogeneous joint policy problem is reformulated as a multiple-choice, multidimensional knapsack problem, establishing strong NP-hardness.

  • Problem formulation: Each viewpoint selects one of four service routes through a binary variable x_i,j.x_i,j = 1 indicates that viewpoint i is served via route j; otherwise, x_i,j = 0.
  • Computational complexity: Problem 4 is a 4-choice, 2-dimensional knapsack problem equivalent to the joint policy optimization.
  • Problem formulation: The reformulation assigns each route choice a profit value, caching cost, and energy cost.
  • Computational complexity: Because MMKP is strongly NP-hard, the original joint policy optimization problem is also strongly NP-hard.

B. Equivalent IQP and CCCP

The paper converts the discrete joint policy into an equivalent penalized linearly constrained IQP and applies CCCP to obtain local optima through repeated linearized solves.

  • Equivalent optimization: Problem 4 is transformed equivalently into Problem 5, a continuous joint policy optimization problem with the original linear constraints and an added constraint.
  • Equivalent optimization: Problem 5 has lower computational complexity than directly solving Problem 4, but its concave constraint prevents straightforward efficient optimization.
  • Penalized formulation: The concave constraint is penalized in the objective to produce Problem 6 with penalty parameter µ > 0.
  • CCCP solution: Problem 6 is a linearly constrained IQP whose objective is a linear function minus a differentiable quadratic convex function.
  • CCCP solution: CCCP iteratively solves a sequence of linear problems after initializing with a feasible point.
  • Equivalence and initialization: For sufficiently large µ, Problems 5 and 6 share the same optimal solution, while multiple CCCP initializations are used to select the lowest-rate local solution.

C. Numerical Results

The heterogeneous-scenario evaluation compares CCCP with three baselines while varying local cache size and computation frequency, and reports substantial transmission-rate savings.

  • Evaluation setup: CCCP is run 100 times with δ = 0.001 from random feasible initial points, retaining the local optimum with the lowest average transmission rate.
  • Baselines: The evaluation compares CCCP against MEC computing, greedy 3D caching, and greedy caching and computing.
  • Heterogeneous scenario: Figure 7 evaluates how local cache size C′ and local computation frequency fV affect the optimal average transmission rate in the heterogeneous scenario.
  • Results: CCCP exhibits promise in saving communication bandwidth compared with the baselines.
  • Results: At the reported cache setting, CCCP provides a 63% transmission-rate gain over MEC computing, compared with 45% for greedy 3D caching and 48% for greedy caching and computing.

VI. CONCLUSION

The paper characterizes communications-caching-computing tradeoffs for homogeneous FOVs and uses CCCP to obtain a local optimum for heterogeneous FOVs.

  • Homogeneous scenario: When fV < F, R∗ increases with fV under one caching condition and otherwise decreases with C at the rate of RS.The supplied conclusion states the condition in partially fragmented notation.
  • Homogeneous scenario: When F ≤ fV, R∗ first decreases and then increases with fV under one caching condition, while otherwise it increases with fV.The conclusion also reports that R∗ decreases with C at the rate of RS.
  • Heterogeneous scenario: In the heterogeneous scenario, the NP-hard joint policy problem is transformed into an equivalent IQP and solved via CCCP to obtain a local optimum.Numerical results are reported to show good performance for this approach.

APPENDIX A: PROOF OF LEMMA 1

The appendix analyzes optimal variables by examining how the transformed objective changes with caching and computing decisions, then substitutes the resulting choices into the objective.

  • Case analysis: For fV < F, the transformed objective increases with d − min{cI, d}, so an optimum satisfies d ≤ cI.The proof then replaces cO using the cache constraint.
  • Problem transformation: The appendix analyzes Problem 7 through separate aspects and rewrites its constraints before deriving optimal choices for d and cI.Several supplied passages contain only equation fragments surrounding these rewrites.
  • Problem transformation: When the objective decreases with d, the proof sets d = cI without loss of optimality and rewrites the problem accordingly.This step reduces the number of independent decision variables in the transformed problem.
  • Optimality conditions: When α > 1, the objective decreases with cI, so the optimal cI is set to its feasible minimum.The supplied passage truncates the explicit minimum expression.
  • Optimality conditions: For F ≤ fV, the proof uses the relation RV ≤ RS < αRV to determine whether the objective increases or decreases with cI and d.The resulting cases set cI and d at boundary values such as cI∗ = min{d∗, C} or cI∗ = d∗.
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