## Journal of Green Engineering

Vol: 5    Issue: 1

Published In:   October 2014

### THIS ARTICLE HAS BEEN RETRACTED: Cross Layer Design based Green Cellular Architecture Using Stochastic Optimization

Article No: 2    Page: 23-58    doi: 10.13052/jge1904-4720.512

 1 2 3 4

Cross Layer Design based Green Cellular Architecture Using Stochastic Optimization

Received 2 Feb 2015; Accepted 5 March 2015; Publication 29 May 2015

L. Senthil Kumar1, J. Vasantha Kumar2 and M. Meenakshi3

• 1Research Scholar, CEG, Anna University, Tamil Nadu, India
• 3Professor, CEG, Anna University, Tamil Nadu, India
• Corresponding Authors: senthilkumarl@live.com; j.vasanth489@gmail.com; meena68@annauniv.edu

## Abstract

Cross layer techniques are in general used to enhance a network’s performance. Various cross layer models have been proposed by researchers for energy efficient scenarios, but most of these models do not consider all the fundamental Quality of service requirements along with energy efficiency. Quality of Service and Queue Stability affect the energy consumption and network performance in each time slot of a network. So an adaptive model is necessary to guarantee the Quality of service and Queue stability along with reduced energy consumption. The model proposed in this paper uses the stochastic drift plus penalty method to improve energy efficiency along with Quality of Service and Queue stability constraints. The optimization technique in the proposed model does not require channel density function. The energy efficiency improvement under Quality of Service and Queue Stability constraint is demonstrated by simulation studies in the paper.

## Keywords

• Cross layer
• Quality of Service
• stochastic drift plus penalty method
• Energy efficiency
• Queue Stability

## 1 Introduction

Cross layer design based network performance improvement has been an evolving strategy in recent times. Though many adaptation schemes are deployed in different OSI layers, the lack of coordination among them makes the overall performance of the system non-optimal. Only proper coordination across layers can benefit the system to achieve Quality of Service (QoS) with optimized goals across layers. For some applications, the packet arrival rate at the transmission buffer is continuous, while for some other applications, the packet arrival is quite bursty in nature. Therefore, if the packet scheduler at the lower layer does not utilize the traffic information of the application it is dealing with, it may cause excessive delay (and buffer overflow when the buffering capacity is limited) and/or excessive power consumption. An intelligent packet scheduler should be able to adjust the transmission rate at the physical layer depending not only on the channel gain, but also on the buffer while satisfying the QoS requirements on delay, overflow and packet error rate. For example, when packet delay is relatively less important than transmission power, the scheduler should not hurry up transmission by using a higher power level in bad channel conditions when the buffer has relatively fewer packets. It can wait for a better channel condition.

This approach achieves two goals: it satisfies the packet error rate, delay and buffer overflow requirements and it does so with the lowest possible transmission power. In future green radio networks, the scheduler will have to apply similar techniques to save energy. In this paper, we show how joint optimization can be used in an intelligent scheduler to reduce energy consumption.

Among all the cross-layer adaptation techniques, the rate and power adaptation techniques at the physical layer are the most important ones for green radio network design, since they minimize transmission power based on upper layer information. Therefore, without loss of generality, in this paper, we concentrate on the power minimization issue that is of particular importance for green radio networks. We show how the transmitter power can be saved using cross-layer optimal policies, where the rate and power at the physical layer are adjusted to minimize power with specific QoS requirements, thereby striking a balance between “green needs” and service requirements.

The objective of this work is to design a cross-layer scheduler that determines the number of packets to be transmitted in each time slot. In order to determine number of packets, the scheduler utilizes both the physical layer information (e.g., channel gain) and the data-link layer information (e.g., buffer occupancy and nature of traffic). Also, scheduler objectives are to minimize average transmission power under the constraints on the average delay and average overflow. Therefore, in a particular time-slot n, the scheduler first determines the states of the traffic, buffer and channel, and then chooses action dynamically to optimize average transmission power, delay and overflow. Since the nature of the problem is dynamic, it falls into the general category of stochastic dynamic programming problems. To solve this dynamic problem, we use Lyaponuv drift plus penalty algorithm where in the number of packets to be transmitted in each time slot is determined for transmission over fading channels considering both the physical layer and the data-link layer optimization goals. At the physical layer, our goal is to optimize the transmission power while satisfying a particular bit error rate (BER) requirement. On the other hand, at the data-link layer, our goal is to optimize the delay and packet loss due to overflow. Overall, the cross-layer approach is shown to be effective in conserving the energy of the system while satisfying the QoS requirements.

### 1.1 Related Works

Energy-efficient cross-layer optimized techniques and designs have been a major research attention in the last decade among wireless researchers working in different networks and protocol stacks.

In [1], the authors have presented a cross-layer design technique that determine the optimal policy based on both the physical layer and the data-link layer information with cross-layer dynamic adaptation policy, thereby delay, overflow rate and BER also be guaranteed precisely for all traffic arrival rates. Also significant system-level throughput gain has been achieved using cross-layer adaptation policy compared with single-layer channel-dependent policy.

A study of energy efficiency of emerging rural-area networks based on flexible wireless communication is presented in [5]. Authors have given clear approaches to energy efficient PHY parameter adjustment and also added into consideration the notion of physically achievable modulation and coding schemes. In [11], a cross-layer adaptation scheme based on neural network is proposed that improves QoS by online adapting media access control (MAC) layer parameters depending on the application layer QoS requirements and physical layer channel conditions.

The problem of optimal rate control in wireless networks with Rayleigh fading channel is studied in [12], Dynamic programming based optimization technique is used to obtain the optimal rate control policy. Energy-efficient transmission techniques for Rayleigh fading networks are studied in [7], where the authors show how to map the wireless fading channel to the upper layer parameters for cross-layer design. An energy-efficient cross-layer design for a MIMO downlink SVD channel is given in [14]. In [4], authors has related the error vector magnitude (EVM), bit error rate (BER) and signal to noise ratio (SNR). They also present the fact that with such relationship it would be possible to predict or in cases substitute EVM in places of BER or even SNR.

Energy-efficient operation modes in wireless sensor networks are studied in [13] based on cross layer design techniques over Rayleigh fading channels using a discrete-time queuing model and a three-dimensional nonlinear integer programming technique. The authors in [10] have carried out joint optimization of the physical layer and data link layer parameters (e.g. modulation order, packet size, and retransmission limit). The problem of optimal trade-off between average power and average delay for a single user communicating over a memoryless block fading channel using information-theoretic concepts is investigated in [9].

### 1.2 Paper Organization

The paper is organized as follows. Section 2 describes system model including traffic and buffer models. Section 3 describes computation of transition matrix in WARP test-bed. In Section 4, we formulate the cross-layer design problem and discuss cost functions and constraints. Section 5 provides methodology of finding optimal policies and optimal costs for different objectives or QoS requirements using Lyapunov drift penalty algorithm. We discuss the results in Section 6 and conclude in Section 7.

## 2 System Model

Figure 1 System model.

Let TB denotes the duration of each time-slot. Therefore, the physical layer time-slot rate is RB = 1/TB time-slots per second. We assume that the packets transmitted in one time-slot experience the same channel gain. Let b(n) denote the number of packets taken from the buffer for transmission and a(n) the number of packets arriving into the transmitter buffer from the upper layer application. Assume that the duration of a block is equal to N number of discrete time-slots and ‘n’ denotes the index of a particular. For example, a(n) denotes the number of packets arriving from higher layer at time-slot n.

The status of the system at any instant is described by one of the S possible system states. The job of a PHY-layer scheduler is to find the control action μ ∈ {S1, S2, S3, S4, S5, S6,} for all the time-slot. Sn = 1, 2, …, N, where μ is the set of available actions and N (in number of slots) is the duration of communications. Our goal is to find an optimal stationary policy μ so that it translates the state into a corresponding optimal action, μ (s), We will discuss later how the action, which corresponds to transmission rate and/or power of the problem, can be selected when adaptation is made with only the physical layer, and also with cross-layer variables.

### 2.1 Buffer Modeling

Since in practical wireless transmitter, packets are stored in a buffer of finitecapacity, unlike most of the adaptive transmission methods in the literature, we assume that the size of the transmission buffer is finite and it can hold a maximum of B packets. Note that since the traffic is random in nature, the buffer may be empty sometimes and it may be full at some other times. If the buffer does not have enough space for all incoming packets, some packets will be dropped. Therefore, in this paper our goal is to bound both the queuing delay and the packet overflow. Particular value of these bounds depend on the QoS requirement of the application being considered. Let Q(n) denote the number of packets in the buffer at time slot n, therefore, the state space of the buffer’s packet occupancy can be expressed as Q(n) = {0, 1, 2, …, B}. Higher layer traffic produce arrival rate a(n), departing packets rate b(n) which is the function of channel, power.

### 2.2 Traffic Modeling

Usually, wireless network traffic is bursty, correlated and randomly varying. The Markov modulated Poisson process (MMPP) model, wherein, at any state, the incoming traffic is Poisson distributed A packets may arrive according to the Poisson distribution with average arrival rate λi packets per time-slot. In each time-slot, the transmitter selects b(n) packets for transmission over the wireless channel. In each time slot modulation schemes are chosen based on the cost function of the algorithm. Since the number of arrived packets a(n) and the number of packets chosen for transmission b(n) are randomly varying, the buffer occupancy fluctuates between 0 to B, where B is the storage capacity of the buffer. The buffer state at time-slot n can be given as

$Q(n)=Q(n−1)+a(n)−b(n) (1)$

## 3 Warp Testbed

In this work, realistic Channel State information is obtained by using the WARP [16] test-bed. Total received signal strength is dependent both on distance and fading. We have assumed that the distance remains unaltered during the time period of interest, and hence we can just rely on fading to capture the variations in signal strength. However in situations where the above premise does not hold true one can combine this fading-based Markov chain model with mobility to model signal strength fluctuations.

The channel state partitioning can be done in different ways, but the equal probability method, where all the channel states have the same stationary probability, is the most popular in literature, because it offers a good trade-off between the simplicity and the accuracy for modeling a wireless fading channel. We denote the channel states by Ck = {C1, C2, C3, C4, C5, C6}, where the state is said to be in Ck when the gain lies between γk-1 and γk as shown in Table 1.

Table 1 Channel states

Channel State SNR (dB)
C1 3.0–5.0
C2 5.0–8.0
C3 8.0–10.5
C4 10.5–14.0
C5 14.0–18.0
C6 Greater than 18.0

### 3.1 Transition Matrix

The Markov chain transition matrix is obtained via an empirical approach, in which the Markov chain transition matrix is calculated by directly measuring the changes in signal strength. The transition matrix depicting SNR variation can be determined by collecting received signal strength measurements using the WARP test-bed and calculating the EVM values and then determining the transitions from one state to the other.

The transition probabilities Pci,cj, ci, cj ∀ Ck were determined based on SNR variations which are obtained directly from EVM. The state of the channel can be estimated at the receiver and the information can be fed back to the tansmitter. When the perfect channel state information is available at the transmitter befre the transmission decision is taken, we usually refer to the channel as fully observable.

Figure 2 Flow chart for determining transition matrix.

The transition matrix is determined in this work by performing signal strength measurements at the receiver for experiments conducted over fading channel. The first step in framing transition matrix is to calculate EVM values for each block with assumption that each block consist N samples. EVM can be calculated by using following expression [4],

$EVM=[ 1T∑t=1T|It−I0,n|2+|Qt−Q0,n|21N∑n=1N[ Io,n2+Qo,n2 ] ]​​​12 (2)$

$SNR=[ 1T∑n=1T|It2+Qt2|21N∑n=1T[ nI,t2+nQ,t2 ] ] (3)$

where

It, Qt – Received symbol at t’th instant

I0,t, Q0,t – Transmitted symbol at t’th instant

I0,n, Q0,n – N Unique ideal Constellation Points

From above equations it is clear that, SNR is inversely proportional to square of EVM.

$SNR≈1/EVM2 (4)$

Therefore, we have the sequence of SNR values from which we can obtain SNR transition matrix using hidden Markov model.

The subsequent step is to determine the number of transitions from each state to the others by observing the sequence of states. For example, suppose there are 6 states in all and that the sequence of states is {…… 2, 4, 6, 2, 4 ……}. The subsequence {2, 4} means that we increment the number of transitions from state 2 to state 4 by one. The next transitions are from states 4 to 6, 6 to 2 followed by another transition from 2 to 4. Once all the transitions have been considered, we use the relative values of the number of transitions from state i to state j for all states j, to determine the empirical transition probabilities from state i to all states j, Pij

A stochastic matrix (also termed transition matrix), is a matrix used to describe the transition of SNR between various states, in the present case SNR variation in a Rayleigh Channel. The transition matrix derived based on our experiment is as follows:

$Pij = S1S2S3S4S5S6[ S1S2S3S4S5S60.36510.22620.17100.14780.08170.00820.22860.23880.21050.17290.12890.02040.13900.25480.22210.18300.16170.03950.05920.23390.22940.22440.18930.06380.00920.15640.26690.23680.22150.10920.00010.05270.21090.30180.24910.1855 ]$

We observe from the above that the total variation is small, which implies that the distributions are close to each other. i.e., probability of SNR being in same state for next slot is higher than probability of changing to adjacent state in next time slot.

Based on the system state the corresponding cost functions are calculated and actions are taken accordingly. The possible actions are shown in Table 2.

Table 2 Possible actions based on channel states

Actions MCS
S1 BPSK,(1/2)
S2 QPSK,(1/2)
S3 QPSK,(3/4)
S4 16QAM,(1/2)
S5 16QAM,(3/4)
S6 64QAM,(2/3)

These typical values have been used directly as possible action for traditional adaptive scheme. In our paper, we are taking Queue State information along with channel states to take optimum action.

## 4 Proposed Problem Formulation

### 4.1 Energy Considerations

In digital communications, as a general rule, energy consumption is lowered by either shortening transmission time or lowering transmission power. Higher bitrates lower the transmission time, but are sustainable only when the power is high enough to result in sufficient SNR. Thus, unless we allow for data to be dropped, a tradeoff between the time and the power exists. The theoretical relationship between bit rate and transmission power is given by Shannon’s formula, which defines the boundary for the channel capacity. Since the formula does not provide a means to achieve the boundary bitrates, a theoretical solution can be practically infeasible. Moreover, in theory, the transmitter power is usually analyzed in isolation, while in reality the transmitter needs supporting hardware, which has non-zero power consumption.

### 4.2 Energy Efficiency

Considering an OFDM kind of multi-carrier transmission scheme in the physical layer, with some approximation (discarding the guard intervals), we can consider the subcarriers individually, and for each of them Shannon’s formula defines the maximum achievable bitrate as:

$Ri=Wlog2(1+γiΓ)=Wlog2(1+pTx,igiNoWΓ) (5)$

where,

W represents the bandwidth occupied by a single subcarrier

γi represents signal-to-noise ratio

gi channel gain

PTx,i transmission power at the ith subcarrier

N0 represents power spectral density of white Gaussian noise

Γ SNR gap

Total maximum data rate for k sub carriers is

$R=∑i=0kRi (6)$

Total energy consumed by a bit is

$ETxb=PTotR (7)$

where, PTot – Total Power

In data transmission significant part of the energy goes to the transceiver circuit power (PTC), which takes into account the consumption of device electronics, such as mixers, filters and DACs, and is bitrate independent.

With a non-zero PTC the energy consumption is:

$PTot=∑i=0kPTx,i+PTC (8)$

The bitrate used in the calculations represents an upper bound. In physical systems the choice of MCS determines the actual bitrate. This bitrate is below the optimal for the given SNR, but is equal to the optimal for a channel with an SNR lower by a factor Γ. This factor is called the “SNR gap” and depends on the MCS used, as well as the desired bit error rate (BER). The energy per bit now becomes:

$ETxb=∑i=0kPtx,i+PTC∑i=0kWlog2(pTx,igiN0WΓ) (9)$

where, gc = coding gain

$Γ=log(Pe0.2)​​gcpe = 4log2MQ{ aγlog2M(M−1) }$

and Pe is Probability of error.

### 4.3 Problem Description and Formulation

At each time-slot n, the scheduler chooses an action depending on the current system states. A decision rule denoted with μ specifies the action at time-slot. Decision rules for all time-slots over which communications takes place, constitute a policy of the problem. We consider a countably infinite horizon (i.e., horizon H → ∞) problem, where our objective is to optimize long term average expected cost for different goals to be achieved. In this paper, we are to minimize the long term average transmission power under specified long-term average buffer delay and packet overflow. Let Π denote the set of all admissible policies π, i.e., the set of all sequences of functions μ={μ1, μ2, …} with μn:SnS where Sn denotes the set of actions possible in state S. The cost function for a stationary policy is denoted by Gp. The objective of our cross-layer adaptation problem is to find the optimal stationary policy μ such that, the following objective is achieved.

where, Gdth and Geth are the maximum allowable average delay and maximum allowable probability of error, respectively. GP(Sn) is the immediate transmission power cost at time slot n for action Sn. The long-term average expected queueing delay cost, Gd and packet overflow cost, GO can be expressed in terms of the buffer backlog and the number of packets arriving per slot etc.

### 4.4 Cost and Constraints

#### 4.4.1 Transmission power cost

Transmission power cost in a particular time-slot is the actual transmitter power used for transmitting packets. Suppose, our target is to keep average BER of the transmission the same irrespective of modulation scheme and channel state. The BER requirement can be specified from the application being handled. For a certain channel state and action Si, and with a fixed specified average BER Pe, for all channel states, the power cost Gp is estimated with appropriate BER expression or using with instantaneous received SNR γ.

#### 4.4.2 Queueing delay cost

Delay is an important parameter to consider for communication systems involving transmission buffers. The maximum tolerable packet delay for a particular system depends on the QoS requirements of the application being handled. For example, real-time traffic must have very low delay. For this traffic, the received packets are useful only when the strict delay requirements are maintained by the scheduler. On the other hand, best-effort traffic is not real-time and is quite tolerable to delay. The delay experienced by a packet is composed of buffer-queuing, encoding, propagation and decoding delay. In this paper, we consider only buffer delay, since encoding, propagation and decoding delay are usually fixed and are negligible compared to buffer delay. The average packet delay in the buffer is related to the average buffer occupancy via Little’s theorem, as follows:

$Go(n)=Q(n)a(n) (11)$

where, a(n) is the instantaneous packet arrival in slot n and Q(n) is number of packets (backlog) present in queue at time slot n.

#### 4.4.3 Packet overflow cost

When the buffer is nearly full and the empty space is smaller than the number of packets arrival, packet overflow happens. Suppose, current buffer state is Q(n) and scheduler takes b(n) packets from the buffer. Therefore, buffer can accommodate r(n) = B − Q(n) + b(n) arriving packets in the current time-slot. Now, if arriving packets a(n) in particular traffic state is larger than r(n), (a(n)-r(n)) packets will be dropped with probability 1.

Therefore, packet overflow rate, for buffer state Q(n), traffic state f(n) and action Sn can be expressed by,

$Go(n)=∑a(n)ϕ(a(n),(B−Q(n)+b(n)))*P(a(n)) (12)$

where (x, y) is a positive difference function, which returns the difference of x and y when x > y, and it returns 0 when xy. P(a(n)) is the probability of arrival rate a(n) at time slot n.

#### 4.4.4 Delay constraint

Delay is an important parameter to consider for communications systems involving transmission buffers. The maximum tolerable packet delay for a particular system depends on the QoS requirements of the application being handled. We should maintain the delay at each slot to be less than the maximum permissible value (~Buffer delay threshold).

$GD(n)≤GDthLet gd=GD(n)−GDththen gd≤0$

and hence, we should maintain gd as a negative value.

#### 4.4.5 Error constraint

Our target is to keep average BER of the transmission the same irrespective of modulation scheme and channel state. The BER requirement can be specified from the application being handled. We should maintain probability of error less than some typical value based on QoS

$Ge(n)≤GethLet ge=Ge(n)−Geththen ge≤0$

we should maintain ge as negative value.

#### 4.4.6 Overflow constraint

We assume that the size of the transmission buffer is finite and it can hold a maximum of B packets. Note that since the traffic is random in nature, the buffer may be empty sometimes and it may be full other times. If the buffer does not have enough space for all incoming packets, some packets will be dropped. It may require retransmission which causes increase in energy. So our goal is to maintain zero overflow.

$go=Go(n)i.e., go=0$

## 5 Stochastic Optimization

### 5.1 Drift-Plus-Penalty Algorithm

The Drift-Plus-Penality algorithm is used to minimize the objective function on energy consumption subject to the constraints defined in our problem, that is, the Penalty functions whose time average should be minimized. Hence our problem as defined before is,

Min GD = Etot

Subject to:

• gd(n)≤ 0
• g(n)e≤ 0
• go(n)=0

#### 5.1.1 Virtual queue

For each constraint i in {1, …, K}, virtual queue with dynamics over slots n in {0, 1, 2, …, N} is given as follows, [15]:

Delay:

$ZD[n+1]=max(ZD(n)+gd(n),0) (13)$

BER:

$Ze[n+1]=max(Ze(n)+ge(n),0) (14)$

Overflow:

$Ho[n+1]=Ho(n)+gD(n) (15)$

where ZD, Ze, Ho are Lyapunov parameters used for creating virtual queue.

By stabilizing these virtual queues ensures the time averages of the constraint functions are less than or equal to zero, and hence the desired constraints are satisfied.

#### 5.1.2 Lyapunov function

To stabilize the queues, the Lyapunov function L(n) is defined as a measure of the total queue backlog on slot n:

$L(θ(n))=12∑k=1kQk(n)2 (16)$

Squaring the queueing equation results in the following bound for each queue

$L(θ(n))=12{(Q(n)2)+ZD(n)2+Ze(n)2+H(n)2} (17)$

#### 5.1.3 Lyapunov drift

The Lyapunov drift is given below and is used with the penalty functions in order to identify the control action to be taken.

$Δ(n)=L(n+1)−L(n) (18)$

The drift-plus-penalty algorithm takes control actions in every slot n to minimize Cost function. Intuitively, taking an action that minimizes the drift alone would be beneficial in terms of queue stability but would not minimize penalty. Taking an action that minimizes the penalty alone would not necessarily stabilize the queues. Thus, taking an action to minimize the weighted sum incorporates both objectives of queue stability and penalty minimization as indicated below.

Lemma [15]:

$Δ[θ(n)]+VE{ yo(n)θ(n) }≤B+VE{ yo(n)θ(n) } +∑k=1KQkE{ ak(n)−bk(n)θ(n) }+∑l=1Lzl(n)E{ yl(n)θ(n) } +∑j=1JHj(n)E{ ej(n)θ(n) } (19)$

where

$B≥ +12∑k=1KE{ ak(n)2−bk(n)2θ(n) } +12∑l=1LE{ y1(n)2θ(n) }+12∑j=1JE{ ej(n)2θ(n) } −∑k=1KE{ bk(n)ak(n)θ(n) } (20)$

#### 5.1.4 Cost function

The expression for the cost function can be obtained by using the above lemma, as

$Cost=V*gp(n) + (1−V)* {Q(n)*[a(n)−b(n)] + gD(n)*ZD(n) + ge(n)*Ze(n) + H(n)*go(n) } (21)$

where V = 0.5 states that we are giving equal importance to objective (drift function) as well as penalty function. In this work, we estimate the cost function for all six possible states and select the best out of them for each slot thereby approaching the optimized solution.

#### 5.1.5 Simulation results

In this work, the above described optimization approach is used considering the traffic state, buffer state and the channel state that is measured for an indoor scenario using the WARP SDR module as explained in Sections 2 and 3. The performance of the adaptation policies with respect to departure rate in relay based wireless transmission downlink system with a transmitter and a receiver is shown. This indicates how the energy of transmission (Energy per bit) varies for each time slot based on overflow and delay (QSI) and SNR (CSI).

The performance was observed for 1000 time slots to gain an understanding of the dynamics and the inter-relationships. The SNR variation and Queue backlog as function of the time slot index are shown in Figure 3 and the variation in the probability of error and transmission energy at different time slots are shown in Figure 4. From these plots we can clearly observe that whenever SNR goes low, energy consumption goes high but vice versa is not true for the same entities. This is because energy consumption not only depends on the SNR, it also depends on other constraints as defined in our problem.

Figure 3 Variation in SNR and queue backlogs vs time slot index.

Figure 4 Variation in probability of error and transmitted energy vs time slot index.

It is further observed that around slot number 770, the transmitted energy is very high. This can be attributed to the increased queue backlog around that time and hence an increase in probability of error, which necessitates a corrective action.

The corresponding Lyapunov function and the Lyapunov drift at different time slot index are shown in Figure 5. We can notice that lyapunov drift is very high at initial slots. This is because of the sudden transition of Queue backlog from lower values (zero for initial slot) to higher values.

Figure 5 Lyapunov functions & lyapunov drift vs time slot index.

In Figure 6, we can observe that overflow is maintained zero throughout transmission due to the corrective actions being taken at each time slot based on our optimization. It is further observed from all these performance plots that the Cost function, though dependant on many constraints, is seen to be predominantly affected by Queue backlogs, which lead buffer delays.

Figure 6 Buffer overflow and cost function vs time slot index.

The performance in terms of cost function and energy consumption are compared for the conventional CSI based adaptation approach and the crosslayer based approach proposed in this work and are shown in Figures 7 and 8, respectively. It can be observed that the proposed model improves the energy efficiency and also stabilize the cost function. Stability of cost function is achieved because the proposed model guerentees the stability of physical and virtual queues. The following estimates are made based on the above performances.

Figure 7 Cost function and energy consumption without cross layer.

Figure 8 Cost function and energy consumption with cross layer.

Total Energy Consumption (without cross layer approach) for 1000 slots = 1.4832 × 103 mW

Energy Consumption (with cross layer approach) for 1000 slots = 547.67 mW

Total Cost (without cross layer approach) for 1000 slots = 4.01 × 1012

Total Cost(with cross layer approach) for 1000 slots = 2.23 × 1012

Thus the proposed approach is seen to significantly reduce the energy consumption by nearly 64% during the observation period, in comparison to the conventional adaptation strategy, in addition to stabilizing the cost function at a much reduced value.

## 6 Conclusion

In this paper, we have shown a possible strategy to design an intelligent packet transmission scheduler, which takes optimal transmission decisions using cross-layer information, based on Markov decision process formulations. We have discussed the method to compute the optimal policies when the channel states are perfectly observable and when they are partially observable. We have shown the benefits of a cross-layer policy over a single layer adaptation policy in terms of energy efficiency. By delaying packet transmissions in an optimal way, a huge amount of power can be saved for delay-tolerant data traffic applications. The amount of saving depends on factors such as the memory of a fading channel and the packet arrival rate. Such a cross-layer optimized packet transmission scheduling method will be a key component in future-generation green wireless networks.

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## Biographies

L. Senthil Kumar received B.E degree in Electronics and Communication Engineering from Coimbatore Institute of Engineering and Technology, Coimbatore, India, in 2009. He successfully completed M.E in Communication systems at College of Engineering, Anna University, Chennai, India in 2012. He is currently working toward the Ph.D degree at College of Engineering Guindy, Anna university, Chennai, India. His current research interests include Cross-Layer design, Green optimization in telecommunication and cooperative communication.

J. Vasantha Kumar is a M.E. Post Graduate student at the Department of Electronics and Communication Engineering, College of Engineering Guindy, Anna University, Chennai, India. He pursued his B.E in Electronics and Communication Engineering from Veltech multi tech Dr. RR Dr. SR Engineering College, Avadi, Chennai, Tamil Nadu, India. His field of interest is wireless communication and networks and Green Communication Networks.

M. Meenakshi Professor, Department of Electronics and Communication Engineering, Anna University Chennai, Guindy campus, Chennai - 600025; (e-mail: meena68@annauniv.edu), India, completed B.E (Honours), M.E and Ph.D in the years 1989, 1992 and 1998 respectively. She has been a faculty at Anna University Chennai, Since 1998. She is a member of IEEE, ISTE and Anna University Research gate. She has published nearly 35 national and international journal papers also more than 60 national and international conference papers in the field of Optical Communication & Networks, and Wireless Communications. Currently her research works are focussed on Green mobile communication, EMP effects, Wireless Body Area Networks, Radio over Fiber network Optimization, etc.