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Optimization of Radio and Computational Resources for Energy Efficiency in Latency-Constrained Application Offloading

Olga Muñoz, Antonio Pascual-Iserte, Josep Vidal

arXiv:1405.4487v2cs.IT

TL;DR

The paper addresses how to optimize computation offloading between mobile terminals and femto-access points under latency constraints. It jointly optimizes radio and computational resources over MIMO channels, deriving offloading and communication solutions together with special-case conditions. The framework also identifies boundaries such as minimum latency and minimum energy, while leaving mobility-related extensions outside the presented analysis.

  • Problem

    The problem is to determine when total, partial, or no application offloading best balances communication and computation under latency constraints.

  • Method

    The paper formulates and solves a joint radio-computational resource-allocation problem for MIMO offloading, including communication strategy and computation-load distribution.

  • Results

    The analysis establishes optimal offloading conditions, minimum required latency, and minimum energy when latency is unconstrained.

  • Takeaways & Limitations

    The framework provides closed-form expressions and optimization results for analyzing the energy-latency trade-off in radio-cloud application offloading.

  • Takeaways & Limitations

    The paper's analysis assumes a setting in which the stated mobility assumption is valid; alternative approaches for users whose mobility violates it are left outside the paper's scope.

Abstract

from arXiv · show

Providing femto-access points (FAPs) with computational capabilities will allow (either total or partial) offloading of highly demanding applications from smart-phones to the so called femto-cloud. Such offloading promises to be beneficial in terms of battery saving at the mobile terminal (MT) and/or latency reduction in the execution of applications, whenever the energy and/or time required for the communication process are compensated by the energy and/or time savings that result from the remote computation at the FAPs. For this problem, we provide in this paper a framework for the joint optimization of the radio and computational resource usage exploiting the tradeoff between energy consumption and latency, and assuming that multiple antennas are available at the MT and the serving FAP. As a result of the optimization, the optimal communication strategy (e.g., transmission power, rate, precoder) is obtained, as well as the optimal distribution of the computational load between the handset and the serving FAP. The paper also establishes the conditions under which total or no offloading are optimal, determines which is the minimum affordable latency in the execution of the application, and analyzes as a particular case the minimization of the total consumed energy without latency constraints.

I. INTRODUCTION

The paper develops a framework for jointly optimizing radio and computational resources for latency-constrained application offloading over MIMO links. It determines communication strategies, computation-load distributions, and conditions favoring partial, total, or no offloading.

  • I. INTRODUCTION: The framework jointly optimizes computational and radio resource usage while considering energy consumption and total execution time.The setting assumes multiple antennas at both the mobile terminal and serving femto-access point.
  • I. INTRODUCTION: The optimization selects transmission power, precoder, rate, and computational-load distribution between the mobile terminal and femto-access point.The transmission strategy covers both uplink and downlink data transfer.
  • I. INTRODUCTION: The model makes the offloading amount an optimization variable, allowing parallel processing at the mobile terminal and femto-access point when optimal.This extends approaches that restrict execution to either the cloud or the handset.
  • I. INTRODUCTION: The transmission strategy adapts to current uplink and downlink channel conditions and includes maximum radiated-power and supported-rate constraints.The analysis targets an offloading-specific MIMO strategy rather than only mutual-information maximization or transmission-power minimization.
  • I. INTRODUCTION: The analysis derives conditions for optimal total or no offloading, minimum affordable latency, and minimum energy without latency constraints.It also provides partial closed-form expressions and a one-dimensional convex numerical optimization technique for the resource-allocation problem.
  • I. INTRODUCTION: The paper focuses on theoretical radio-cloud interaction and does not address business, economic, or cloud-pricing aspects.Combining multiuser scheduling with the energy-latency optimization is left for future research.

II. TYPES OF APPLICATIONS AND COMPUTATIONAL MODELS

The paper classifies applications by how their data or code can be partitioned and focuses on parallelizable, data-partitioned applications. It models execution using dataset size, deadline, output size, and CPU cycles, then chooses local, total, or partial offloading to the MT and serving FAP.

  • Applications are grouped as data-partitioned, code-partitioned, or continuous-execution applications.
  • Data partitioned oriented applications: Data-partitioned applications divide input files or images into subsets processed in parallel.
  • Code partitioned oriented applications: Code-partitioned applications divide programs into methods that may be parallel or sequential because outputs can feed later methods.
  • Continuous execution applications: Continuous-execution applications, including gaming and interactive software, have unknown execution durations and distinct real-time requirements.
  • The paper focuses on data-partitioned applications with known input size and parallel execution, characterized by dataset size, deadline, and output size.
  • The offloading problem selects local, total-cloud, or partial execution and divides the workload between the MT and serving FAP under time, computation, channel, and energy constraints.

FEMTO-CLOUD

The femto-cloud scenario studies a mobile terminal connected to a serving FAP with computational resources, using radio and computation decisions to balance energy and latency. The analysis assumes a nearly static, channel-known, single-user or per-user setting and models MT energy only.

  • The channel is assumed not to change during the application's maximum latency, with channel knowledge available at transmitter and receiver.
  • The analysis excludes FAP energy because FAPs are normally grid-powered, but their consumption could be added to the models.
  • The multiuser case is handled only per user; jointly allocating bandwidth and processor rate across users remains future work.
  • The framework adapts transmission rate, power, and precoder to optimize the energy-latency trade-off jointly with computation.

1) UL Transmission (MT Acting as Transmitter):

The uplink model relates MT power consumption to radiated power, rate, and baseline circuitry costs, then minimizes communication energy for a given transmission time and data amount. With multiple antennas, optimal transmission uses channel eigenmodes with water-filling power allocation.

  • The uplink rate is rUL = sUL/tUL, while a baseline power is consumed whenever the transmission circuitry remains switched on.
  • The MT uplink power model includes extra RF/BB circuit power and a linear transmitter-power term governed by ktx,1 and ktx,2.
  • The model is calibrated using practical LTE-MT measurements, with numerical parameters obtained through regression.
  • The model also specifies MT downlink power through reception-circuit and decoding-rate terms, although the section's optimization focuses on uplink transmission.
  • For any tUL and sUL, eUL(tUL, sUL) is defined as the minimum MT uplink energy under the transmission optimization constraints.
  • In a MIMO channel, energy-minimizing transmission uses channel eigenmodes with power water-filling, where the active-mode count depends on tUL and sUL.

2) Characterization:

The characterization establishes convexity and generic energy-versus-latency behavior for uplink transmission. Baseline circuit power can create a unique finite energy-minimizing duration or rate, whereas with zero baseline power the normalized energy decreases as rate decreases.

  • eUL(tUL, sUL) is jointly convex with respect to transmission time and transmitted data size.
  • For fixed sUL, the energy-versus-time function is convex, so any local minimum is also global.
  • Regardless of model-parameter values, the energy-versus-time curve is either single-minimum or monotonically decreasing.
  • With ktx,1 = 0.4 W, the energy curves have finite minima; for 1.5 MBytes and 0.75 MBytes, these occur at 1.24 s and 0.62 s, respectively.
  • With ktx,1 = 0, energy decreases monotonically with transmission time, so longer transmission remains energetically favorable in the model.
  • For ktx,1 = 0.4 W, normalized uplink energy is minimized at ŘUL = 0.97 b/s/Hz; with ktx,1 = 0, it increases monotonically and ŘUL = 0.

C. Trade-off between Latency and Energy in the DL Transmission

The downlink energy–latency trade-off is characterized through the relationship among received energy, transmitted bits, and transmission time. The optimal downlink strategy uses the highest feasible rate, found through a convex maximum-rate problem and eigenmode water-filling.

  • The DL transmission relationship between energy, received bits, and transmission time is jointly convex in time and bits.
  • The maximum supported DL rate is obtained from a convex optimization problem under a positive semidefinite transmit-power covariance constraint.
  • The optimal DL transmission uses the channel eigenmodes with water-filling over the corresponding eigenvalues.

D. Main Conclusions

The conclusions characterize energy-efficient uplink and downlink transmission and formulate joint communication–computation offloading as a constrained resource-allocation problem. The resulting optimization distributes application processing between the MT and FAP while accounting for latency, communication overhead, power limits, and local-processing energy.

  • Uplink energy minimization uses channel eigenvectors, with the number of active eigenmodes increasing with the UL data rate.
  • Uplink energy per transmitted bit has a global minimum even when normalized energy is nonconvex.
  • When ktx,1 = 0, uplink energy per bit increases with the UL data rate, so minimizing energy favors lowering that rate.
  • Application latency is the maximum of local-computation time and offloading time, which includes uplink transmission, FAP execution, and downlink reception.
  • The optimization minimizes MT energy from uplink transmission, downlink reception, and local processing subject to a maximum latency and radio-power constraints.
  • The offloading model partitions Sapp bits between local MT processing and remote FAP processing, with both computations performed in parallel and no partitioning overhead.

B. Simplification of the Global Resource Allocation Problem

The global resource-allocation problem is simplified by exploiting tight rate and latency constraints and reducing the optimization to the offloaded workload and uplink rate. Convexity then enables efficient numerical calculation of the optimal partition and transmission rate, while infeasibility identifies the need for a larger latency budget.

  • The downlink rate constraint is tight at optimum, allowing tDL to be eliminated from the optimization variables.Reducing downlink time lowers the objective while preserving feasibility until the maximum-rate constraint is met.
  • The original allocation problem is reduced to two variables: the remotely processed bits SP1 and the UL transmission rate rUL.
  • The reduced objective fo(SP1) is convex because it is numerically equivalent to minimizing the original convex problem over all variables except SP1.
  • If the feasibility condition requiring SminP1 is not met, the only solution is to increase the maximum allowed latency Lmax.
  • For each possible partition, the optimal UL rate is determined by the unique minimum of the UL energy function over the feasible rate interval.
  • The remaining one-dimensional partition problem can be solved numerically using gradient-based algorithms or nested intervals.
  • The method calculates the optimal partition at the stationary point of the convex reduced objective, when boundary values are not optimal.

VI. ANALYSIS OF PARTICULAR CASES

The particular-case analysis provides insight into the general resource-allocation problem and offers practical guidelines for applying the proposed solution.

  • The particular cases analyze the previously defined resource-allocation problem to provide insight into its formulation and solution.
  • The analysis is intended to give practical guidelines for applying the proposed resource-allocation approach.

A. Optimality of No Offloading

The paper derives necessary and sufficient conditions for no offloading and total offloading, and identifies the latency threshold below which the optimization is infeasible.

  • A. Optimality of No Offloading: No offloading is optimal when processing the entire application locally is feasible and the local solution satisfies the associated optimality condition.Local feasibility requires Lmax ≥ SappτP0, meaning local execution does not violate the latency constraint.
  • B. Optimality of Total Offloading: Total offloading is optimal when processing all application bits remotely is feasible and its corresponding optimality condition holds.Remote feasibility requires that uplink transmission, remote processing, and downlink output transmission fit within Lmax.
  • C. Feasibility and Minimum Affordable Latency: The optimization becomes infeasible below a minimum affordable latency Lo, which can be obtained analytically from the crossing of the feasibility bounds.Lo is lower than both the all-local processing time and the all-remote execution time.
  • C. Feasibility and Minimum Affordable Latency: At the minimum affordable latency Lo, partial offloading is required, with the bit distribution determined by the latency-dependent feasibility bounds.The feasible values of SP1 are represented by vertical segments between the bounds shown in Fig. 7.

D. Minimum Energy without Latency Constraints

Without an effective latency constraint, the energy-minimizing solution uses either entirely local or entirely remote processing. When offloading is selected, the uplink rate minimizes communication energy per bit.

  • D. Minimum Energy without Latency Constraints: Without latency constraints, partial offloading is never energy-optimal; all data are processed either locally at the MT or remotely at the FAP.The unconstrained case is modeled by Lmax →∞, or equivalently by removing the latency constraint.
  • D. Minimum Energy without Latency Constraints: The energy-optimal choice between local and remote processing follows from comparing the energy required to process one bit locally with the corresponding remote-processing energy.The comparison includes uplink transmission, remote computation, and downlink reception for the remotely processed bit.
  • D. Minimum Energy without Latency Constraints: When offloading is optimal without latency constraints, the uplink data rate minimizes energy consumption per bit.With a binding latency constraint, the optimal uplink rate instead depends on the selected local–remote partition.
  • D. Minimum Energy without Latency Constraints: With a latency constraint, total offloading or no offloading can still be optimal, whereas latency minimization requires partial offloading.For latency minimization, the optimal partition depends on the maximum uplink rate.

VII. SIMULATION RESULTS

Simulations evaluate the proposed strategy across antenna configurations, channel gains, latency budgets, and a representative channel realization. Energy savings and remote processing generally increase with channel quality and antenna count, while latency constraints shape the required partition.

  • Simulation setup: The simulations use MIMO 4x4, MIMO 4x2, MISO 4x1, and SISO 1x1 configurations, averaging most curves over 1000 random channels.Unless stated otherwise, the maximum allowed latency is Lmax = 4 s.
  • Energy and latency: Energy savings increase as both the number of antennas and the mean channel gain increase, relative to no offloading.The no-offloading reference energy is εP0Sapp.
  • Offloading behavior: At low channel gains all files are processed locally, whereas higher gains increase remote processing until total offloading is reached; more antennas further increase remote processing.Fig. 10 reports the percentage of files processed remotely as a function of mean channel gain γ.
  • Communication behavior: As channel quality improves, the optimal uplink rate increases, while practical maximum-rate constraints cause the attainable and optimal rates to saturate.The simulations impose a maximum rate of 5.5 bit/s/Hz per allowed LTE modulation and coding scheme.
  • Latency effects: Tight latency constraints require partial offloading, whereas very high tolerated latency can make all-local or all-remote processing optimal.For the representative channel realization, total offloading is optimal at very high tolerated latencies.
  • Latency effects: Relaxing the latency constraint improves energy savings until the savings saturate beyond a certain latency value.At higher channel gains, the minimum-energy solution can use less than the available latency budget because of the uplink transmission power model.

VIII. CONCLUSIONS AND FUTURE WORK

The paper presents a joint communication–computation offloading framework with closed-form results that clarify the energy–latency tradeoff. Its current scope assumes partitionable data and a single, constant-channel offloading setting, motivating extensions to more general applications, channels, and users.

  • Conclusions: The framework jointly optimizes communication and computational resources for an energy-limited MT running a computationally demanding application.It addresses whether the application should be partially offloaded to the serving FAP.
  • Conclusions: Closed-form expressions simplify the optimization and clarify the inherent energy–latency tradeoff in communication and computation.The analysis also derives conditions for total or no offloading and examines particular design cases.
  • Scope and future work: The solution applies to data-partitioned applications with a predefined amount of data whose bits can be divided between local and remote processing without size constraints.Applications with modularity constraints or a predefined execution structure require further extension.
  • Scope and future work: The present work considers one FAP and leaves multi-FAP parallel execution, cooperative transmission, and multiuser resource allocation for future research.These extensions would require allocating shared radio and computational resources across users or execution sites.
  • Scope and future work: The proposed strategy assumes the channel remains constant throughout offloading, so mobility requires causal time-varying-channel adaptations or statistical reformulation.The statistical formulation may avoid dependence on instantaneous channel state, but obtaining a simple optimal solution is described as complicated.
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