Energy Cooperation and Traffic Management in Cellular Networks with Renewable Energy

Transcription

1 Energy Cooperation and Traffic Management in Cellular Networks with Renewable Energy Hyun-Suk Lee Dept. of Electrical and Electronic Eng., Yonsei University, Seoul, Korea Jang-Won Lee Dept. of Electrical and Electronic Eng., Yonsei University, Seoul, Korea Abstract In this paper, we study joint energy cooperation and traffic management in renewable energy powered cellular system where a centralized unit manages the traffic and the energy cooperation among BSs. We first formulate a stochastic optimization problem which aims at minimizing the total on-grid energy consumption while satisfying the quality-of-service (QoS) requirement of classes of services, i.e., the minimum average data rates. By using the Lyapunov optimization framework, we develop a joint adaptive energy cooperation and traffic management algorithm which does not need the statistical information of the system. Then, we provide the performance analysis which shows our proposed algorithm is asymptotically optimal. Through the simulation results, we verify the theoretical analysis and show that the performance of our algorithm. I. INTRODUCTION By 00, it is predicted that the amount of the carbon footprint from cellular networks grows up to 51% of the total carbon footprint from the information and communication technology (ICT) industry [1]. Especially, the energy consumption by base stations (BSs) occupies more than 50% of the total energy consumption in cellular networks []. Thus, there are many researches focus on reducing the energy consumption by BSs, such as topology management and sleep mode control of BSs. Recently, as another promising solution to reduce the carbon footprint in cellular networks, green cellular networks which is powered by renewable energy, such as solar energy and wind energy, is considered [3]. In such green cellular networks, the utilization of renewable energy should be optimized while considering the mobile traffic in order to minimize the on-grid energy consumption since the amount of harvested renewable energy strongly depends on the time and the location of the power generator [4]. To this end, there are three main approaches in green cellular networks: traffic management considering renewable energy, energy cooperation among BSs, and joint traffic management and energy cooperation. In the traffic management considering renewable energy approach, the network adjusts its topology [5], [6], the amount of its transmitted traffic [7], [8], or both of them [9] to minimize the on-grid energy consumption. In the energy cooperation approach, the BSs which have renewable energy sources can share their surplus renewable energy to each other in order to This work was supported in part by Mid-career Researcher Program through NRF grant funded by the MSIP, Korea (013R1AAA ). reduce the on-grid energy consumption by utilizing the surplus renewable energy [10]. Traffic management and energy cooperation approaches are different approaches to save the on-grid energy consumption. Thus, intuitively, we infer that each of them is effective to save the on-grid energy consumption in different environments such as different traffic and weather conditions. Thus, in our prior work [11], by comparing the on-grid energy consumption of traffic management, energy cooperation, and joint traffic management and energy cooperation approaches, we show that a joint traffic management and energy cooperation approach is most effective to deal with the various environments. Besides, in practice, the environments such as traffic demand and weather conditions change dynamically and randomly over time. Thus, in order to deal with such a stochastic environment, the joint traffic management and energy cooperation approach should be adaptively utilized according to a stochastic system condition. In this paper, we study a joint energy cooperation and traffic management problem minimizing the average on-grid energy consumption while guaranteeing quality-of-service (QoS) requirements of classes of services, i.e., minimum average data rates, in an OFDMA cellular system. In the system, BSs have both on-grid and renewable power sources and can share their surplus energy with other BSs via power lines connected between them. In addition, there is a centralized unit which has the capability to conduct traffic management and energy cooperation among BSs. In our problem, we consider a stochastic time-slotted system model where user arrival, packet arrival, channel conditions, and amount of harvested energy are randomly generated in each timeslot. Compared to the previous works, our problem not only jointly decides the amount of shared energy among BSs, the user association, the bandwidth allocation and the transmission power of each BS, but also adaptively decides them according to the stochastic system condition. By using the Lypunov optimization framework [1], we develop a joint adaptive energy cooperation and traffic management algorithm minimizing the average on-grid energy consumption while guaranteeing the minimum average data rate of classes of services. Our algorithm is an online algorithm which does not need the statistical information of the system a priori. We then provide the performance analysis of our algorithm which shows our algorithm is asymptotically optimal. Through simulation results, the performance analysis /16/$ IEEE

2 Sub-area N Energy and Traffic Management Unit Downlink traffic state Sub-area... Sub-area 1... Class 1 Class Class... M... Class 1 Class Class M Class 1 Class Class M Sub-areas BS1 Sub-area capacity BS1 Power allocation Bandwidth allocation BS Power allocation Bandwidth allocation BS... N Fig. 1. System model for the traffic network. is verified and the performance of our algorithm is shown. The rest of this paper is organized as follows. Section II provides the system model. In Section III, we formulate a joint energy cooperation and traffic management problem, develop a joint adaptive energy cooperation and traffic management algorithm, and provide its performance analysis. We provide numerical results in Section IV. Finally, we conclude in Section V. II. SYSTEM MODEL We consider a downlink of an OFDMA cellular system powered by both on-grid energy source and renewable energy sources such as wind and solar. We assume that it is timeslotted and all packets have the same fixed size. It consists of base stations (BSs) which can share their energy with each other through the power line between them. The set of BSs is denoted by K = {1, }. 1 In our system, we consider both traffic network and energy network which handle packets and energy, respectively, in the cellular system. We also consider that a centralized unit called an energy and traffic management unit (ETMU) which has a capability to manage the traffic network and the energy network in the cellular system. A. Traffic Network Model In the traffic network, packets arrive at the centralized unit, i.e., the ETMU, and then, the ETMU delivers the packet to its destination user through the BS to which the user is associated. To model this, all users in the network, their packets, and their channel conditions should be considered in the traffic network model. However, the traffic dynamics of the traffic network is too complex to address when the number of the users is large. Moreover, it is hard to capture the mobility of the users and the variation of the channel conditions of the users due to the mobility. Hence, to mitigate this problem, we introduce a novel traffic network model in which the coverage area of the BSs is divided into N sub-areas and the traffic is managed according to the sub-areas where the traffic is heading as in 1 In this paper, we consider the system model with two BSs for the sake of the simple presentation. However, it can be generalized into a system model with multiple BSs. Fig. 1. The set of sub-areas is denoted by N = {1,,..., N}. Moreover, to exploit the fact that the users in the same subarea have similar channel conditions with a high probability, in the traffic network model, we assume that the users in same sub-area have same channel conditions. In our traffic network model, we can adjust the trade-off between the complexity of the traffic dynamics and the realistic modeling of the traffic network by controlling the size of each sub-area. We consider M classes of packets and the set of classes is denoted by M = {1,,..., M}. Each class m has a different QoS requirement, Γ m, which represents its required minimum average throughput. In each time slot, the number of arriving packets of each class in each sub-area depends on the number of users in the sub-area. Let u n (t) be the number of users in sub-area n at timeslot t, which is an independent and identically distributed (i.i.d.) random variable. We assume that there is the maximum number of users per sub-area, u max, due to the spatial constraint of each sub-area. Thus, the number of users in sub-area n at timeslot t is bounded as 0 u n (t) u max, n N. Then, the number of arriving packets of each class m in subarea n, A nm (t), which depends on u n (t) can be also defined as an i.i.d. random variable. We consider the OFDMA cellular system which has the system bandwidth W. Thus, each BS allocates its power and bandwidth in order to serve the packets for each sub-area. The transmission power allocation of BS k to sub-area n at timeslot t is denoted by p n k (t). Each BS k has its maximum transmission power, Pk max, and thus, the total transmission power of BS k at timeslot t is bounded as n N p n k(t) P max k, k K. (1) The bandwidth allocation of BS k to sub-area n at timeslot t is denoted by b n k (t). The bandwidth is orthogonally allocated to each sub-area. Thus, the total bandwidth allocation of BS k at timeslot t is bounded as b n k(t) W, k K. () n N With given bandwidth allocation to each sub-area, the BS has the maximum number of serving packets for each sub-area, i.e., the capacity of BS k for sub-area n at timeslot t, C n k (t). It can be obtained by several ways, and in this paper, we approximate it with the Shannon capacity. We assume that the interference cancellation schemes are precisely conducted between the BSs, and thus, we ignore the inter-cell interference If the coverage area is divided into sub-areas which are small enough to assume that at most one user can be located in each sub-area, then this traffic network is identical to the real network.

3 [13]. 3 Then, the capacity of BS k for sub-area n at timeslot t, Ck n (t), is obtained by Ck n (t) = 1 ( b n N k(t)log 1+ hn k (t)pn k (t) ) pkt b n k (t)n, 0 n N, k K, (3) where N pkt is the packet size, h n k (t) is the channel gain of sub-area n to BS k at timeslot t, and n 0 is the noise. For each sub-area, each BS should decide the number of serving packets for each class. Let μ nm k (t) be the number of serving packets of class m for sub-area n by BS k at timeslot t. The total serving packets for sub-area n by BS k at timeslot t cannot exceed the capacity of BS k for sub-area n at timeslot t as μ nm k (t) Ck n (t), n N, k K. (4) m M The aggregate number of serving packets of class m for subarea n at timeslot t, μ m n (t), is obtained as μ nm (t) = k K μ nm k (t), n N, m M. Then, the average throughput of class m in sub-area n, ρ nm, is obtained as ρ nm 1 t 1 = lim E[μ nm (τ)], n N, m M τ=0 and it should satisfy its QoS requirement as ρ nm Γ m, n N, m M. (5) In each timeslot, the packets of each class in each sub-area are served in a first-come-first-serve order, and the unserved packets of each class in each sub-area is buffered to its traffic queue in the ETMU. Let D nm (t) be the traffic queue length of class m in sub-area n at timeslot t, i.e., the number of buffered packets. Then, the traffic queue length of class m in sub-area n is obtained as D nm (t +1)=[D nm (t) μ nm (t)] + + A nm (u n (t)), n N, m M, (6) where [ ] + =max[0, ] The vector of the traffic queue lengths of all class in all sub-area at timeslot t is denoted as D(t) = {D nm (t)} m M, n N. B. Energy Network Model In our system, BSs are powered by both on-grid and renewable energy sources. Moreover, BSs have an energy transfer capability, and thus, they can share their surplus energy in their batteries by using the power lines between them as in Fig.. The ETMU manages the amounts of on-grid energy consumption and transferred energy between BSs according to the amount of harvested renewable energy and traffic condition at each BS. The amount of harvested renewable energy of BS 3 It is worth noting that the stochastic optimization framework in the next section can be also applied to the system model with more realistic capacity equation where the inter-cell interference is not ignored. Renewable energy sources for BS 1 BS1 Power grid Power lines BS Fig.. System model for energy network. Renewable energy sources for BS k at timeslot t is denoted by H k (t) which is considered as an i.i.d. random variable 4 whose support is bounded as 0 H k (t) Hk max, k K. The amount of transferred energy of BS k to k at timeslot t is denoted by T k (t), where k is the index of the other BS that is not BS k. Due to the capacity limitation of the power line, the amount of transferred energy is bounded as 0 T k (t) Tk max, k K. (7) Each BS can utilize on-grid energy from the conventional power plant. The amount of on-grid energy consumed by BS k at timeslot t is denoted by G k (t) and bounded as 0 G k (t) G max k, k K, (8) where G max k is the maximum amount of on-grid energy consumption during a timeslot due to the capacity limitation of the power line. Since the total energy consumption of each BS cannot exceed the total available energy of the BS, the following condition should be satisfied: ξt k(t)+h k (t)+g k (t) p n k(t)+t k (t), k K, (9) n N where ξ<1 is the power transferring efficiency. III. STOCHASTIC OPTIMIZATION In this section, a joint energy and traffic management problem is formulated to minimize the on-grid energy consumption while guaranteeing the QoS requirement of each class in each sub-area. Then, we use the Lyapunov optimization to develop an adaptive energy and traffic management policy for the problem. A. Problem Formulation We formulate the joint energy and traffic management problem as minimize 1 t 1 lim E {G 1 (τ)+g (τ)} τ=0 subject to (1), (), (4), (5), (7), (8), (9), (10) traffic queue stability. Given the problem, we develop a control policy, A(t), which minimizes the on-grid energy consumption while guaranteeing 4 In spite of the system model with i.i.d. random variables, it is known that the optimization framework used to develop the proposed algorithm in Section III is robust to non-i.i.d. and non-ergodic statistic behaviors [14].

4 the QoS requirement of each class in each sub-area by the Lyapunov optimization framework. The control policy is denoted by A(t) ={(p n k(t),b n k(t),μ m nk(t),t k (t),g k (t)) n,m,k }. Through the control policy, the ETMU jointly controls resource allocation, energy consumption of the BSs, and energy sharing between the BSs in order to minimize the on-grid energy consumption while satisfying the QoS requirements. For the constraint of the traffic queue stability in (10), we introduce a mean rate stability in [1]. Definition 1: A queue is mean rate stable if its queue length, Q(t), satisfies E[ Q(t) ] lim =0. (11) For the constraint of the QoS requirement in (5), we introduce a QoS virtual queue. 5 The QoS queue is not an actual queue in the system but is implemented only in the algorithm. Let Z nm (t) be the QoS queue length of class m in sub-area n at timeslot t. Then, the QoS queue length is updated by using the QoS requirement Γ m and the aggregated number of serving packets μ nm (t) as Z nm (t +1)=[Z nm (t)+γ m μ nm (t)] +. (1) The vector of the QoS queue lengths of all classes in all sub-areas at timeslot t is denoted as Z(t) = {Z nm (t)} m M, n N. The QoS queue length of each class in each sub-area increases when the aggregated number of served packets is larger than its QoS requirement, and vice versa. Thus, the QoS queue length of each class in each sub-area represents the degree of the satisfaction of its QoS requirement. The mean rate stability of the QoS queue for class m implies the QoS requirement of class m is satisfied by the following theorem. Due to space limitations, all proofs of theorems and lemmas are given in our technical report [15]. Theorem 1: For each class m in each sub-area n, iftheqos queue Z nm (t) is mean rate stable, then its QoS requirement is satisfied, i.e., ρ nm Γ m. According to Theorem 1, we can omit the constraint for the QoS requirement from the problem by adding the constraint for the stability of the QoS queues. Then, the problem is reformulated as minimize 1 t 1 lim E {G 1 (τ)+g (τ)} τ=0 subject to (1), (), (4), (7), (8), (9) (13) traffic and QoS queue stability. 5 In the rest of this paper, we omit virtual from the QoS virtual queue for the convenience. B. Lyapunov Optimization Let Θ(t) = [D(t), Z(t)] T be the system state of the combined queue vector. We now define the Lyapunov function as the following quadratic form: L(Θ(t)) = 1 D nm (t) + 1 Z nm (t). (14) We also define the one-step conditional Lyapunov drift Δ(Θ(t)) as Δ(Θ(t)) = E [L(Θ(t +1)) L(Θ(t)) Θ(t)]. Then, the Lyapunov drift satisfies Δ(Θ(t)) B + E [D nm (t)(a nm (u(t)) μ nm (t)) Θ(t)] + E [Z nm (t)(γ m μ nm (t)) Θ(t)], (15) where B is a finite constant satisfying B 1 [ ] E μ nm (t) + A nm (u(t)) Θ(t) + 1 [ ] E (Γ m μ nm (t)) Θ(t) E [ μ nm (t)a nm (u(t)) Θ(t)], where μ nm (t) =min{d nm (t),μ nm (t)}. The derivation of (15) is provided in [15]. By using (15), the drift-plus-penalty can be defined and bounded as Δ(Θ(t)) + V E[G 1 (t)+g (t) Θ(t)] RHS of (15) + V E[G 1 (t)+g (t) Θ(t)], (16) where V is a design parameter. Then, we adopt the min driftplus-penalty algorithm in [1] to solve the problem in (13). In the min drift-plus-penalty algorithm, in each timeslot t, an action A(t) is decided by solving the following Lyapunov optimization problem: minimize V [G 1 (t)+g (t)] μ nm (t)(d nm (t)+z nm (t)) (17) subject to (1), (), (4), (7), (8), (9), where for each sub-area n and each class m, the traffic queue lengths D nm (t) s and the QoS queue lengths Z nm (t) s are updated by (6) and (1), respectively. Note that the problem in (17) depends only on the current state Θ(t). Thus, this algorithm is an online algorithm which does not need the statistical information of the system a priori. We address the following property which is helpful to simplify the algorithm. Lemma 1: In the problem in (17), for any given p n k (t) s, b n k (t) s, G k(t) s, and T k (t) s which satisfy the constraints, the

5 number of served packets of class m in sub-area n by BS k at timeslot t, μ m nk (t), is decided as { } C μ m n nk(t) = k (t), if m =argmax m {Dn m (t)+zn m (t), 0, otherwise n N, m M, k K. 00 m 00 m Fig. 3. Simulation settings. # # Sub-area BS Lemma 1 provides helpful insights for simplifying the algorithm. According to Lemma 1, in each timeslot, BSs serve only the class which has the largest sum of the traffic and QoS queue lengths for each sub-area n. Then, the problem in (17) can be further simplified as minimize V [G 1 (t)+g (t)] Q n (t) Ck n (t) n N k K subject to (1), (), (3), (7), (8), (9) (18) Q n (t) = max m M {Dnm (t)+z nm (t)}, n N. Thus, the complexity of the algorithm significantly decreases, since for each sub-area, only the class which has the largest sum of queues needs to be considered. Then, the joint adaptive energy and traffic management algorithm is outlined in Algorithm 1. Algorithm 1 Joint Adaptive Energy Cooperation and Traffic Management Algorithm 1: Initialize D m n (0), Z nm (0), n, m, and t =1 : while TRUE do 3: Each BS k obtains H k (t) 4: ETMU obtains A(t) by solving the problem in (18) 5: ETMU updates D nm (t) s as (6) 6: ETMU updates Z nm (t) s as (1) 7: t t +1 8: end while As in Algorithm 1, the ETMU should solve the problem in (18) in each timeslot t to decide its action A(t), which is a convex programming which is easy to solve in general. Thus, we can solve the problem by using the software such as CVX [16]. C. Performance Analysis The proposed joint energy and traffic management algorithm adaptively controls resource allocation, energy consumption of the BSs, and energy sharing between the BSs in order to minimize the on-grid energy consumption while satisfying the QoS requirements. It is an online algorithm in which the statistic information of the system such as user arrival, packet arrival, and channel conditions is not needed. Moreover, it is known that the min drift-plus-penalty algorithm which is adopted to develop our proposed algorithm is robust to non-i.i.d. and non-ergodic statistic behaviors [14]. Thus, the proposed algorithm can work in practice for the real system which have non-i.i.d. and non-ergodic statistic behaviors. The following theorem provides the performance bound of the proposed algorithm. Theorem : Under the proposed algorithm with any control parameter V > 0, all queues are mean rate stable, and thus, the QoS requirements are satisfied. Moreover, the average on-grid power consumption, ˆg, satisfies: ˆg g + B/V, (19) where g is the optimal average on-grid power consumption and B is the constant in (15). Note that Theorem implies that the performance of the proposed algorithm asymptotically achieves the optimal performance as V. However, as V increases, the number of served packets in each timeslot decreases, and thus, the average traffic queue length increases, which implies increasing delay. Hence, in the proposed algorithm, V can be used to address the trade-off between the average on-grid energy consumption and delay. IV. NUMERICAL RESULTS In this section, we provide simulation results to provide the performance of our joint adaptive energy cooperation and traffic management algorithm. In Fig. 3, the simulation settings are provided. We consider 8 sub-areas, where each sub-area is a 00m 00m square, and BSs. We set the bandwidth of the system to be 10 Mhz, the pathloss exponent to be -3.76, the noise spectral density to be -150 dbm/hz. The duration of each timeslot is set to be a millisecond. For each timeslot, the number of users in each sub-area is uniformly generated within [0, 0]. We consider high class and low class traffics which have the minimum average sumrate requirements of 0 Mbps and 10 Mbps, respectively. The number of each class of packets in each sub-area is generated from a Poisson random variable of which the rate is the number of users in the sub-area. The sizes of high class packet and low class packet are set to be kbits and 1 kbits, respectively. The channel gain of each sub-area to each BS is determined as the pathloss from a uniformly random point in the sub-area to the BS. The amount of harvested energy of each BS in each timeslot is uniformly generated within [0, 0.5] mj. We set the maximum transmission energy of BSs, the maximum on-grid energy of BSs, and the maximum transfer energy between BSs during a timeslot to be mj. To show the performance of our proposed algorithm, we consider a myopic algorithm which is not adaptive and does not conduct energy cooperation and traffic management between BSs. In each timeslot, the myopic algorithm decides bandwidth and transmission power allocation by following rules: (1) Energy cooperation between BSs is not allowed. () Sub-area 1,, 5, and 6 are served by BS 1, and sub-area

6 Average on grid energy consumption (mj) Average traffic queue length (Mbits) Proposed Myopic V V (a) Average on-grid en-(bergy Average traffic queue consumption. length. Fig. 4. Average on-grid energy consumption and average traffic queue length varying V of the proposed algorithm and the myopic algorithm. Average data rate (Mbps) Timeslot (ms) Low class High class QoS requirement Fig. 5. Average data rate of sub-area 1 with V =10settings. 3, 4, 7, and 8 are served by BS. (3) Each BS finds the bandwidth and transmission power allocation minimizing the total transmission power while achieving the QoS requirements. In Fig. 4, the average on-grid energy consumption and average traffic queue lengths varying V of our proposed algorithm and the myopic algorithm is shown. 6 From it, we first show the effectiveness of our proposed algorithm, and then, we verify the performance analysis of our proposed algorithm in Theorem. We first show the effectiveness of our algorithm by comparing its average on-grid energy consumption and average traffic queue length with those of the myopic algorithm. As in Fig. 4a, our proposed algorithm consumes on-grid energy much less than the myopic algorithm regardless of the value of V. From Fig. 4b, we see that the average traffic queue length of our proposed algorithm is less than that of the myopic algorithm when V < 7. When the average traffic queue length of our proposed algorithm is similar to that of the myopic algorithm, i.e., V =7, our proposed algorithm consumes only about 6.3% of the average on-grid energy consumption of the myopic algorithm. We now show the effects from the different V to our proposed algorithm and verify its performance analysis. The average on-grid energy consumption decreases inversely proportional to V as in Fig. 4a, and this verifies Theorem which implies the asymptotic optimality of our proposed algorithm. However, from Fig. 4b, we see that the average 6 For Fig. 4a and 4b, we set the maximum transmission energy and the maximum on-grid energy of BSs to be a value which is large enough to show the performance. traffic queue length keeps increasing as V increasing, which implies increasing delay. Thus, V should be chosen to address the trade-off between on-grid energy consumption and delay. In Fig. 5, the satisfaction of the QoS requirement of each class is shown, which implies the mean rate stability of the QoS queue. V. CONCLUSION In this paper, based on the Lyapunov optimization framework, we developed a joint adaptive energy cooperation and traffic management algorithm minimizing the on-grid energy consumption while guaranteeing the minimum average data rate of classes of services. The proposed algorithm is an online algorithm dealing with a stochastic environment without the a priori information of the system statistics. 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