Energy efficient and delay-constrained sleep period optimization for green radio communication

Abstract

Green communication technology research deals with the methods to achieve efficient energy utilization by radio communication devices. Recent advances in this area include radio resource optimization, radio resource management, and optimal sleep control. In this paper, we focus on the problem of optimizing mean cost subject to a constraint on sleep period. We solve this problem and find the optimal solution to the sleep period and investigate the behavior of the optimum sleep period and the standard deviation of the cost function. We then present numerical results for optimum sleep period, and statistical parameters, namely, standard deviation, and deviation figure. This work not only models mean cost optimally but also compares with ad hoc average costs, which do not account both energy consumption and delay.

Introduction

Green or energy efficient wireless communications can broadly be seen in three points of view. The first one is the traditional view point, that is, energy efficient wireless communication. The second view point is ecological, which means that a green wireless communication system should reduce green house gas emissions. Finally, the third view point is related to reduced operational (OPEX) costs [1].

In this work, we focus on the traditional view point of green communication, that is energy efficient mobile wireless terminals. Mobile terminal, such as, user equipment (UE) is compact in size and has limited battery power. To enable power saving, wireless standards facilitate two modes of operation, namely, sleep mode and idle mode. Mobile terminals, when not in use, can operate in those modes. However, the UE can come back to normal mode of operation whenever required. While in sleep mode the UE remains absent from the eNodeB,¹ in the idle mode the UE listens to broadcast messages in regular intervals.

Sleep mode: To get into the sleep mode, the UE and access point or eNodeB exchange the sleep request and response messages, which include the following. (i). sleep mode transition time (ii). duration of maximum sleep period and minimum sleep period (iii). duration of listen period. During the listen period, the eNodeB sends a message on the indication of incoming traffic to the UE. Based on the message, the UE gets into to either normal mode or sleep mode [2].

Idle mode: In this mode, scanning operation is performed for a short period, which helps the UE to save power and other useful resources. When the eNodeB receives packets to forward to a particular UE in the idle mode it broadcasts a paging message to access the UE [2].

The total energy consumption by mobile or wireless terminals due to different transmissions can be reduced significantly by allowing the terminal to sleep for fixed durations of time. However, this leads to a time delay in the response of the wireless terminal to activity request. Therefore, there exists an inherent trade-off between total energy consumed and response delay incurred. This motivates us to introduce a cost function which strikes the balance between both the energy consumption and the response delay as a weighted function of the above two quantities.

Literature review, comparison and comments: In the past works, authors investigated on energy efficient protocols, sleep control and management policies that optimize energy consumption costs. In [3], authors designed sleep control policies that minimize the mean value of a cost function. In it, the cost function represents costs due to energy consumption and costs for backlogged packets. Packet queuing delay and wireless terminals’ energy efficiency was analyzed in [4] wherein authors derived size of an optimal sleep window that achieves superior power performance while satisfying delay constraints. Different sleep modes of fixed or mobile terminals have been investigated by queuing-theoretic modeling [5]. For energy efficiency of wireless terminals, a transceiver duty cycle management strategy is developed and investigated in [6].

Energy efficiency as a performance measure, has been analyzed in [[7], [8]]. In [7], authors considered a multi-hop vehicular ad hoc network (VANET) and analyze its end-to-end reliability and energy efficiency of safety message broadcast. In [8], authors addressed the problem of energy efficient data offloading by adopting cooperative two-hop device-to-device (D2D)-vehicle-to-vehicle (V2V) transmission mode. In it, authors proposed a two-stage resource allocation algorithm for realizing energy-efficient vehicular heterogeneous networks. However, these works do not model sleep period and hence different from our cost modeling and its analysis.

In [9], authors studied optimum sleep period control and derived optimal sleep policy for different distributions using dynamic programming. In it, authors assumed arrival process in which activity duration is independent of response delay. Our problem formulation is different from [9]. We formulate a stochastic convex optimization problem to obtain the sleep period which optimizes the expectation of cost function as there should be a constraint on the maximum limit on the sleep period. We analytically optimize the expected value of the cost function and simulate it for exponential distributions for inter-arrival times of activity requests.²

Optimal sleep control is a well-investigated research topic. However, due to its importance in next generation wireless communication standards, for example, the third generation partnership project (3GPP) long-term evolution (LTE) [[12], [13]], we revisited the conceptual idea and came up with novel cost function model and sleep period optimization problem. Note that our modeling of cost function and optimization analysis and results are analytically rich, insightful, and useful for the next generation green radios and systems.

In this paper, we make the following contributions.

• Average cost function modeling: We present a model for average cost function and formulate sleep period optimization problem. In it, we put a constraint on sleep period. The problem formulation is novel in the sense that it is independent of probability distributions.

• Average number of sleep periods: We derive closed form expression for the average number of sleep periods by assuming exponential distribution for time of arrival of the first activity request. To gain more analytical insights, we also derive a simple upper bound for the mean number of sleep periods and also present some useful remarks on the result.

• Stochastic, constrained optimization problem, and its solution: We derive the optimal solution to the delay-constrained optimization problem which minimizes mean cost function. However, the optimal solution is for a specific distribution, that is, exponential distribution. The analysis we provide can be easily extended to other distributions as well. We numerically compute the optimal solution by solving a transcendental equation.

• Characterization of optimal sleep duration and analysis: We investigate the behavior of the optimum sleep period and gain more insights. We extend our analysis and present an insightful closed form expression on the standard deviation of the instantaneous cost function, which is a function of continuous and discrete random variables. Furthermore, we define a new statistical measure, deviation figure and study its behavior.

• Numerical results and interpretation: We present simulation results for optimum sleep period to validate the analysis. Furthermore, we present plots to qualitatively study the variation of standard deviation and a new statistical parameter deviation figure.³ Finally, we compare proposed average cost with ad hoc and suboptimal benchmark costs.

The paper is organized as follows. Section 2 provides details of the system model. Section 3 formally states the optimization problem and derives its solution. Numerical results and conclusions follow in Sections 4 Simulation results, 5 Conclusions and future directions, respectively.

The rest of the paper uses the following notation. The probability of an event $\mathcal{E}$ is denoted by $Pr\left(\mathcal{E}\right)$. For a continuous random variable (CRV) $T$, its probability density function (PDF), cumulative distribution function (CDF), expectation, and variance are denoted by $f_T\left(t\right)$, ${\mathcal{P}}_T\left(t\right)$, $\mathbf{E}\left[T\right]$, and $\mathbf{var}\left[T\right]$, respectively. $\mathcal{P}(N=k)$ denotes probability mass function (PMF) of a discrete random variable (DRV) $N$.