Coordinated Caching Model for Minimizing Energy ...

Coordinated Caching Model for Minimizing Energy Consumption in Radio Access Network Yuemei Xu† , Yang Li† , Zihou Wang£ , Tao Lin† , Guoqiang Zhang‡ and Song Ci§,† Performance Network Lab, Institute of Acoustics, Chinese Academy of Sciences § Department of Computer and Electronics Engineering, University of Nebraska-Lincoln £ National Computer Network Emergency Response Technical Team, Coordination Center of China ‡ School of Computer Science and Technology, Nanjing Normal University, Nanjing, China Email: †,£ {xuym, liy, lint, wangzh}@hpnl.ac.cn, ‡ [email protected], § [email protected] † High

Abstract—To reduce network access latency, network traffic volume, and server load, caching capacity was proposed as a component of eNodeBs in the ratio access network (RAN). These eNodeB caches require less transport energy but bring additional caching energy through providing each eNodeB with caching capacity. It is thus challenging for eNodeBs to make content placement and request routing decisions so as to minimize the total energy consumption, especially when considering different caching hardware technologies, arrival rate of requests and content popularity. To address this problem, we first build an energy model to formulate the problem of minimizing energy consumption at eNodeB caches. Then a Lagrangian relaxation technique is adopted to find a near-optimal solution to the proposed model. Based on the proposed model and the obtained solution, we design a practical scheme for coordinating the content placement and request routing, and thus ensure the minimum-energy eNodeB caches. Compared with the existing works, our proposal significantly reduces the energy consumption by approximately 28% while keeps a good network performance. Our results also indicate that caching hardware technologies and content popularity greatly affect the content placement, therefore are crucial to the energy efficiency of eNodeB caches.

I. I NTRODUCTION To date, both the traditional Web contents and the increasing video contents have been delivered through the Internet, and are expected to grow even more tremendously in the next few years [1], [2] (e.g., video-on-demand traffic alone is predicted to grow to 3 × 1019 Bytes by 2015 [3]). To support large-scale content dissemination, data centers with hundreds of thousands machines are deployed across different geographic regions. Due to sheer size of data centers, significant energy is consumed. For example, the U.S. Environmental Protection Agency (EPA) estimates that servers and data centers consumed 100 billion kilowatt hours at a cost of $7.4 billion in 2011 [4]. To minimize the network energy consumption, a number of different approaches have been proposed . One possible method is to deploy content delivery networks (CDN) for reducing the the delivered traffic in the network backbone, such as Akamai [5] and Limelight [6]. As a result, the data ∗ This work is supported by the National High Technology Research and Development Program (863 Program) under Grant No. 2013AA013503-2, the Strategic Pilot Project of Chinese Academy of Sciences under Grant No.XDA06010302 and the National Natural Science Foundation of China under Grant (No. 61202419, No. 61100178 and No. 61303243).

transport energy is saved. However, when a content located at a CDN server is required by a mobile device, the content has to travel through a wireless carrier core network (CN) and a radio access network (RAN) before reaching the mobile device. Moreover, massive repeating requests from mobile devices will put strain on the carrier’s CN and RAN backhaul and also consume considerable energy. To improve energy efficiency of content transmission and to realize the so called energy-proportional networking [7], an emerging way is to equip eNodeBs in RAN with storage capacity to cache popular contents. As such, most requests can be satisfied at eNodeB caches, which reduces the content delivery between eNodeBs and CDN content servers and in turn, consumes less transport energy. But to the best of our knowledge, there is no existing model in analyzing the energy consumption of eNodeB caches. Moreover, most existing works presume that enabling eNodeBs with caches leads to less energy consumption, but this conclusion is not well quantified in theoretical details. In terms of energy consumption, eNodeB caches potentially result in less transport energy consumption by effectively reducing the content access distance and eliminating duplicated content transmission. However, eNodeBs incur additional caching energy consumption in providing storage capacities. Generally, there exists an inverse relationship between the transport energy consumption and the caching energy consumption. We need to distribute caches carefully and make caching decisions in considering the tradeoff between these two energy consumption. To be specific, various caching hardware technologies have different power efficiency (watt/bit) and will affect the content placement and request forwarding, then finally leading to different energy consumptions. For example, when the caching power efficiency is too large, some unpopular contents may need to be removed at eNodeBs for saving energy and instead users fetch these contents from CDN servers. Thus it is crucial to construct a theoretical model, which aims to minimize the total energy consumption and also considers the relation between the transport and the caching energy. In this paper, we explicitly consider the tradeoff between the transport and caching energy and develop a theoretical

model to formulate the energy consumption at eNodeB caches, aiming at minimizing the total network energy consumption. Our main contributions are: • A system model is developed to capture the energy characteristics of eNodeBs caches as discussed above. Then the energy consumption in such a system is formulated and analyzed in a linear programming. • We further prove the problem of minimizing energy consumption in a RAN is an NP-hard problem, and thus adopt Lagrangian dual decomposition techniques to solve the problem and achieve a near-optimal solution. • Inspired by the near-optimal solution, a coordinated caching scheme is proposed to make content placement and request routing decisions so as to ensure the minimum cost of energy. The scheme avoids additional energy by coordinating all the eNodeBs in a RAN. • Extensive simulation results show that the proposed model and scheme lower the energy consumption by approximately 28% as compared with the existing works. The rest of the paper is organized as follows. Section II presents a survey of the related work. The system model is described in section III. Then section IV presents the energy consumption formulations in such a system and solves it with lagrangian relax techniques. Section V proposes a coordinated scheme inspired by the near-optimal solution. Section VI is the experiment evaluation and the conclusions are in section VII. II. R ELATED W ORK Techniques have been proposed to reduce the Internet energy consumption. Nedevschi et al. propose to periodically switch network devices into sleep mode for saving energy [8]. This approach is not feasible to real-time network applications, since it can result in unacceptable delays. Raghavan et al. provide an approximate analysis of the Internet energy consumption [9]. They calculate both the operating energy consumption and the emergy required to conduct the Internet. Seetharam et al. show that building data centers can reduce the energy consumption of streaming applications by 30% [10]. However, these related works [8], [9], [10] that evaluate energy consumption do not involve eNodeB caches in RANs. Ahlehagh et al. introduce a content scheduling approach for eNodeB caches, aiming at avoiding data transmission in core networks [11]. But the works mainly focus on the caching policies without energy efficiency discussion on eNodeB caches. To the best of our knowledge, no system model has been proposed to formulate the energy consumption at eNodeB caches, or to analyze the relation between the transport and caching energy. Compared with these existing works, this paper develops a refined energy model for eNodeBs caches in a RAN, aiming at minimizing the total network energy consumption. The optimal solution of the proposed model is also given and guides us to design a practical energy-minimum scheme by coordinating content placement and request routing. Based on the extensive simulations, we also discuss the relation between the transport and caching energy in depth.

III. S YSTEM M ODEL A. Network Model

Fig. 1.

An overview of eNodeB caches at the edge of the RAN.

The network model follows the eNodeB caches deployment as described in [11]. As shown in Fig. 1, a RAN consists of several eNodeBs under a centralized control of a service gateway (SGW). Let N0 denote the SGW and Ni denote the eNodeB, i = 1, ..., M . Ni is endowed with caches of size Bi , while N0 is responsible for request aggregation, request forwarding and caching policy distributing without storage capacity. Content category is a static collection of K content items of size sk , k = 1, ..., K. Requests issued by mobile devices are first directed to a nearby eNodeB Ni and could be served immediately, if the contents are available at the cache of Ni . If the requests are not satisfied at Ni , they will be routed either to other eNodeBs Nj , j ̸= i or to CDN servers, which is decided by the SGW. For convenience, a request for content k is said to be a type-k request. Let λik be the rate of type-k requests at Ni . B. Energy Model The energy consumption is mainly caused by the content caching at eNodeBs and the data transmission between peer eNodeBs or between eNodeBs and original servers. Thus the total consumed energy Etot consists of two major parts: the caching energy consumption Eca and the transport energy consumption Etr . Based on the energy-proportional model, Eca is proportional to the power efficiency of caching, denoted by wca , which depends on the caching hardware devices. The common hardware devices for caches are high-speed state disk (SSD), dynamic random access memory (DRAM) and static random access memory (SRAM). The wca value of SSD, DRAM and SRAM are 6.25 × 10−12 watt/bit, 2.50 × 10−19 watt/bit and 1.50 × 10−8 watt/bit, respectively [4]. Given the storage decision at Ni as Xik , the caching energy consumed at Ni during time interval t is expressed as: ∑ Xik sk wca t Eca,i = k∈K

Similar to the models used in [12], Etr mainly consists of the energy consumption at network routers and the energy

consumption along the links. eNodeBs first send their local unsatisfied requests to the SGW, then the SGW decides to forward the requests to other eNodeBs with the desired contents in a same RAN or to the original server. The transport energy consumed by transmitting a content k from Ni to Nj (i.e., j = −1 representing the original server) is expressed as: Etr,ijk = sk [pr (dij + 1) + pl dij ] where pr and pl are the energy density of routers and links, respectively, and dij is the hop distance between Ni to Nj . Generally, pr and pl are set as 1.7 × 10−8 and 5 × 10−9 J/bit. IV. E NERGY C ONSUMPTION F ORMULATION AND L AGRANGIAN R ELAX S OLUTION In this section, we propose an energy model to formulate the problem of minimizing the energy consumption in a RAN, and then we adopt the technique of Lagrangian relaxation to find the near-optimal solution.

objective function as follows: K M ∑ ∑

(wca sk Xik + λik sk pi,−1 (1 − Xik ))

(4)

i=1 k=1

By dropping the constant term λik sk pi,−1 , the objective function (4) further reduces to ∑M ∑K i=1 k=1 (wca − λik pi,−1 )sk Xik . We can rewrite the formulation L as follows: (Lr ) min s.t.

M ∑ K ∑

cik Xik

i=1 k=1 K ∑

Xik sk ≤ Bi , ∀i = 1, ..., M

(5)

k=1

Xik ∈ {0, 1}, ∀i = 1, ..., M, k = 1, ..., K where cik = (wca − λik pi,−1 )sk . Note that Lr is the classical knapsack problem, which is known to be NP-hard [13]. B. Lagrangian Relax Solution

Due to the NP-hardness of formulation L , it unable to find a polynomial algorithm to obtain the optimal solution of L . Instead, a Lagrangian relaxation is adopted to find a Let a 0-1 decision variable Xik indicate whether the content near-optimal solution of L . We ∑ simplify the formulation by k is stored in Ni or not, and let a 0-1 decision variable Xijk incorporating Xi,−1k = 1−Xik − j̸=i Xijk into the objective indicate whether requests for the content k at Ni are served function. Then because of removing the ∑ variable Xi,−1k , the by Nj or not. Then problem (L ) of minimizing the energy formulation has a new constraint Xik + j̸=i Xijk ≤ 1 and consumption in a given time interval t is formulated as follows: can be incorporated into the objective function by associating M ∑ K ∑ ∑ with a Lagrangian multiplier ηik . The during time interval min [wca sk tXik + λik sk t(pi,−1 Xi,−1k + pij Xijk )] t is a constant and can be be omit without affecting the i=1 k=1 j̸=i formulation. As such, the objective function L (ηik ) of the Lagrangian dual problem is: K ∑ M ∑ K ∑ s.t. Xik sk ≤ Bi , ∀i ∈ [1, M ] (1) L (η ) =min (wca sk − λik sk pi,−1 + ηik )Xik − ηik ik k=1 ∑ i=1 k=1 Xijk = 1, ∀i ∈ [1, M ], k ∈ [1, K] (2) Xik + Xi,−1k + M ∑ K ∑ ∑ j̸=i + [λik sk (pij − pi,−1 ) + ηik ]Xijk Xijk ≤ Xjk , ∀i ∈ [1, M ], k ∈ [1, K] (3) i=1 k=1 j̸=i A. Energy Consumption Formulation

where pi,−1 equals to pr (di,−1 + 1) + pl di,−1 and pij equals to pr (dij + 1) + pl dij as discussed in above section III-B. Constraint (1) states that the total number of stored contents is constrained by the available caching capacity. Constraint (2) states that requests are satisfied either by the first encountered eNodeB, or by another eNodeB in a same RAN, or by the original server. Constraint (3) guarantees an eNodeB does not forward requests to another eNodeBs which do not cache the desired contents. We can observe that the problem (L ) of minimizing the energy consumption in a RAN is an NP-hard problem, which has been proved in proposition 1. Proposition 1. Problem (L ) is NP-hard. Proof. We prove the ∑proposition by restriction. Consider the special case with j̸=i Xijk = 0 and Xik + Xi,−1k = 1, which means the requests are satisfied either by the first encountered eNodeB or by the original server. We assume the caching duration time t equals to 1 unit time and simplify the

To be specific, L (ηik ) can be decomposed into a |M | dimension content placement problem and a |M | dimension request forwarding problem. Both of the subproblems can be solved by means of subgradient optimization [14]. However, the subgradient optimization algorithm needs to update the multipliers ηik at each iteration, which is time-consuming and not adaptive to the high volatile of content flows. Instead, we try to find a near-optimal solution with a heuristic algorithm. First the Lagrangian dual problem L (ηik ) is decomposed into two subproblems L P 1 and L P 2 , where (L P1 ) min s.t.

M ∑ K ∑

(wca sk − λik sk pi,−1 + ηik )Xik

i=1 k=1 K ∑

Xik sk ≤ Bi , ∀i = 1, ..., M

k=1

Xik ∈ {0, 1}, ∀i = 1, ..., M, k = 1, ..., K

(L P2 ) min

M ∑ K ∑ ∑

[λik sk (pij − pi,−1 ) + ηik ]Xijk

i=1 k=1 j̸=i

s.t. Xijk ≤ Xjk , ∀i ̸= j = 1, ..., M, k = 1, ..., K Xijk ∈ {0, 1}, ∀i = 1, ..., M, k = 1, ..., K L P1 is a content placement problem, while L P2 is a request forwarding problem, which can be solved after L P1 . L P1 is a knapsack problem and is solved in a greedy manner. ENodeBs decide their local content placements through solving L P1 as: { 1, k ∈ [1, ki0 ) and aik ≤ 0; Xik (t) = (6) 0, k ∈ [ki0 , K] or aik > 0. where aik =wca sk − λik sk pi,−1 + ηik represents the tradeoff between the caching energy consumption and the transport energy consumption. Thereinto, wca sk denotes the energy consumed by caching the content k in local caches, while λik sk pi,−1 denotes the transport energy when eNodeBs do not store the content and have to fetch it from the original server. ENodeBs consider to store a content k only when its caching energy consumption is less than its transport energy consumption, denoted as aik ≤ 0. In solving L P1 , contents are sorted in an ascending order ∑j according to aik . The critical value ki0 equals to min{j : k=1 sk Xik (t) > Bi }. ENodeBs forward their local unsatisfied requests to the SGW, then the SGW decide the requests routing by solving L P2 . Let bijk be λik sk (pij − pi,−1 ) + ηik in L P2 , which denotes the transport energy consumption tradeoff: fetching a content from Nj or from the original server. If pij > pi,−1 , it is better for Ni to fetch contents from the server, and vice versa. Alg.1 is an algorithm for solving L P2 . Algorithm 1 An Algorithm for Solving L P2 Input: Content placement decision Xik (t), i=[1, M ],k=[1, K]; Output: Request forwarding decision Xijk (t); Begin 1: for each content k with Xik = 0, k = [1, K] do 2: if ∃ bijk < 0 and Xjk = 1 then 3: Let j0 = min{j : bijk < 0, Xjk = 1}; 4: else 5: Let j0 = −1; 6: end if 7: Set Xij0 k (t) = 1 and Xijk (t) = 0, j ̸= j0 = [1, M ]; 8: end for The SGW is then responsible for gathering temporal results from eNodeBs, and then updates ηik and distributes it to eNodeBs for the next iteration. ηik reflects the interest of storing a particular content and the capacity of sharing contents between eNodeBs and is updated as: ∑ ηik (t + 1) = ηik (t) + ϕ(t)(Xik + Xijk − 1). (7) j̸=i

The insufficient storage provision in eNodeBs for a content k will decrease the value of ηik , which inspires Ni to store the

content k. ϕ(t) = 1/t is the step-length. A near-optimal solution of L (ηik ) is obtained by repeating the operations of Eq.(6) and Alg.1 until the multiplier ηik tends to be stable. In general, ηik is initialized as ηik (0) = 0. V. C OORDINATED C ONTENT P LACEMENT AND R EQUEST ROUTING S CHEME It can be observed that eNodeBs make their storage decisions (see Eq.(6)) and request forwarding decisions (see Alg.1) with priori knowledge of parameters ηik and λik . Given fixed values of λik and initial values of ηik (i.e., ηik (0)=0), eNodeBs and the SGW need to repeat the operations of Eq.(6) and Alg.1 until the convergence of ηik for an optimal solution. However, eNodeBs cannot obtain the rate of type-k requests (i.e., λik ) in advance, since the content flows are changing with time. To conquer this obstacle, we divide a continuous time T into a plurality of time slots (i.e., 0, t, 2t, 3t, ..., T ) and let Ni record λik (nt) during the time interval [(n − 1)t, nt], considering it as the predicted rate of type-k requests in the next time slot [nt, (n + 1)t]. At the beginning, ηik (0)=0, λik (0)=0 are initialized and eNodeBs make decisions based on the current ηik and λik . At the end of each time slot, the SGW and eNodeBs update ηik and λik and use them for the next time slot. In the followings, we first describe the content placement and request routing strategies with fixed ηik and λik and then discuss the process of updating these parameters. A. Content Placement and Request Forwarding The key idea of content placement strategy is that eNodeBs associate every content with a value aik to indicate its caching benefits and store contents according to Eq.(6). After receiving a content packet, eNodeBs make their content placement decisions as presented as: (1) For a content k, calculate its value aik . If aik > 0, discard the content k; otherwise go to (2). (2) If the storage space is not full, place the content k; otherwise go to (3). (3) Contents sorted in a descending order of aik are evicted until there is enough room for the new coming content k. (4) Stop content placement. The key idea of request forwarding strategy is that eNodeBs send their local unsatisfied requests to the SGW, which will associate the pending requests with a value bijk to indicate their transport energy consumptions. Based bijk , the SGW makes the request forwarding decision: sending requests either to the original content server or to an eNodeB with a temporary copy of content k inside the same RAN. In details, after the SGW receiving requests from bottom eNodeBs, it runs Alg.1 to calculate bijk and get the parameter j0 . If j0 = −1, the SGW sends requests to the content server; otherwise sends requests to the bottom eNodeB Nj0 . B. Parameters Update At the end of each time slot, eNodeBs need to update λik used for the next time slot and the SGW is responsible for updating ηik . The steps of parameter update is presented as:

VI. P ERFORMANCE E VALUATION In this section, we evaluate our coordinated content placement and request routing scheme, termed as Coordinated, in a Java-built simulation environment and compare it against: i) LCE (leave copy everywhere) placement strategy proposed in [15]; ii) Random placement strategy, where eNodeBs store the passed by contents with a random generated probability. Both the LCE and random placement schemes use the LRU algorithm [16] for content replacement, therefore are termed as LCE+LRU and Random+LRU in experiments.

Fig. 3 depicts the caching energy consumption curved as function of cache size for different schemes. It is observed that the caching energy consumptions in LCE and Random schemes increase with the increment storage capacity of eNodeBs (e.g., from 10% to 50%) in both wca = 6.25 × 10−12 and wca = 3.75 × 10−9 . While the caching energy consumption of the Coordinated scheme increases with the growing storage capacity of eNodeBs in wca = 6.25 × 10−12 , but maintains almost stable in wca = 3.75 × 10−9 . This is because when the caching power efficiency is low (e.g., wca = 6.25×10−12 ), the Coordinated scheme allows eNodeBs to place as many content copies as possible in their local storages for saving transport energy, while as the caching power efficiency increases (e.g., wca = 3.75 × 10−9 ), the Coordinated scheme suggests eNodeBs place fewer content copies and to fetch contents from the original server for saving caching energy. 100

100

100 =6.25

=3.75

Fig. 2.

60 40 20

80

Number of Cached Contents

80

0

A 3-level simulated topology.

ca



ca

60 40 20 0

1 2 3 4 5 6 7 8 9 10 eNodeB ID

Coordinated LCE+LRU Random+LRU

=6.25

ca

10%

20%

30%

40%

50%

Total Cache Size (of all contents)

Fig. 3.

600000 Coordinated

500000

LCE+LRU Random+LRU

400000 300000 200000

=3.75

100000 0

20%

30%

40%

50%


Caching Energy Consumption vs. Cache Size.

=15

ca

60 40 20

eNodeB ID

1 2 3 4 5 6 7 8 9 10 eNodeB ID

The number of cached copies at eNodeBs depending on wca .

Fig. 4 plots the average number of content copies that eNodeBs cache in the Coordinated scheme when the cache size of each eNodeB is 100 content items. As wca increases, the number of copies cached at eNodeBs reduces. In case of wca = 6.25 × 10−12 , most of eNodeBs cache the content copies up to their storage capacities. In case of wca = 3.75 × 10−9 , the number of cached content copies at eNodeBs is about a fifth of their storage capacities. In case of wca = 15 × 10−9 , eNodeBs try not to cache content copies as the caching energy consumption is much higher than the given transport energy consumption in experiments.

80000

Coordinated LCE+LRU

72000

Random+LRU

64000 56000 48000

=6.25

ca

10%

20%

30%

40%

50%


ca

10%

Fig. 4.

Transport Energy Consumption (J)

900 800 700 600 500 400 300 200 100

Caching Energy Consumption (J)

Caching Energy Consumption (J)

As illustrated in Fig. 2, the simulated network is a 3-level RAN topology, where the red node represents the original server, the yellow node represents the SGW, and the blue nodes indicate 10 edge eNodeBs equipped with storage capacity under the SGW control. The original server holds all the contents (2000 content items) and the total size of 10 eNodeBs are ranged from 10% to 50% of the whole contents. Contents are set with equal sizes for convenience and are fetched by 50000 requests. The content popularity distribution is assumed to be a Zipf mode with parameter α = 1. We also test the performance of Coordinated scheme under different values of caching power efficiency wca . Then we can observe the impact of different caching hardware technologies on the proposed scheme. wca is set as 6.25 × 10−12 watt/bit in SSD, as 3.75 × 10−9 watt/bit in reduced latency DRAM and as 15 × 10−9 watt/bit in SRAM.

80

0

1 2 3 4 5 6 7 8 9 10

Fig. 5.

Transport Energy Consumption (J)

i) Each bottom eNodeB updates λik ((n + 1)t) = λik (nt) and informs λik ((n + 1)t) to the SGW together with its storage decision Xik (nt). ii) The SGW updates ηik ((n + 1)t) according to Eq.(7) and distributes it to the all bottom eNodeBs. iii) Stop parameter update.

80000

Coordinated LCE+LRU Random+LRU

72000 64000 56000

=3.75

ca

10%

20%

30%

40%

50%


Transport Energy Consumption vs. Cache Size.

Fig. 5 shows the transport energy consumption for different caching schemes. Obviously, the transport energy consumption

80000

LCE+LRU Random+LRU

72000 64000 56000 48000

=6.25

ca

10%

20%

30%

40%

50%

Total Energy Consumption (J)

Total Energy Consumption (J)

600000 Coordinated

Coordinated

500000

Random+LRU

400000 300000 200000 100000


Fig. 6.

LCE+LRU

=3.75

ca

10%

20%

30%

40%

50%


Total Energy Consumption vs. Cache Size.

To sump up, the Coordinated can flexibly decide how to cache contents and route requests based on the relation between the caching and transport efficiency, therefore greatly reduces the total energy consumption about 28% than the LCE and Random schemes (see Fig. 6). We also note that in order to pursue a minimum total energy consumption, the Coordinated may incur larger path stretch but much less caching energy consumption (see Fig. 7). For the future work, the energy consumption and the metric of path stretch will be considered in the objective function at the same time. VII. C ONCLUSION

reduces as the cache sizes of eNodeBs increase. This is due to the fact that the larger cache sizes of eNodeBs are, the more content copies can be cached at the edge of RAN, which then requires less content transmission between the original server and eNodeBs. Note that the transport energy consumption of the Coordinated scheme in cache size of 40%, 50%, wca = 3.75×10−9 is larger than that of the LCE and Random schemes. This can be explained by the following: when the caching power efficiency is large, only the most popular contents can be cached by eNodeBs for saving the total energy but increasing the associated transport energy. Fig. 6 gives the performance of total energy consumption in different caching schemes. Obviously, the Coordinated greatly reduces the total energy consumption by approximately 27%, 28.2%, 27.3%, 23.5% and 18.9% against the LCE scheme in the cache size of 10% to 50% (wca =6.25 × 10−12 ), respectively. 0.80 Coordinated(

Path Stretch

0.72

Coordinated(

=6.25

)

ca

=3.75

)

ca

LCE+LRU

0.64

Random+LRU

0.56 0.48 0.40 10%

20%

30%

40%

50%


Fig. 7.

Path Stretch vs. Cache Size.

Finally, Fig. 7 examines the performance comparison of different schemes in path stretch d/|P | metric, where d is the number of hops that the content has actually traveled, and |P | is the path length from the requested user to the content originator. Note that d = 0 when the content is at the edge eNodeB and d = |P | when the content is not cached by any eNodeB, therefore d/|P | ∈ [0, 1]. Compared with the LCE and Random schemes, the Coordinated approach significantly reduces the path stretch about 28% in wca = 6.25 × 10−12 , while has a bit larger path stretch value in wca = 3.75×10−9 . The reason lies in that when the caching energy is large (e.g., wca = 3.75 × 10−9 ) and costs more than the transport energy, the Coordinated choose to acquire the content from the remote server rather than to cache the content locally, therefore consume a larger path stretch value.

We have developed an energy consumption model for eNodeB caches and have solved it with a Lagrangian relaxation technique, which achieves a near-optimal solution, with favorable energy savings. Besides interested in the right of the solution, we have also designed a practical scheme to ensure the minimum energy consumption by coordinating the content placement and request routing. The simulations demonstrate the effectiveness of the proposed model and scheme, as compared with the exiting works. R EFERENCES [1] L. Yanhua, X. Haiyong, W. Yonggang, and Z. Zhi-Li. Coordinating innetwork caching in content-centric networks: Model and analysis. IEEE ICDCS, pages 1–12, 2013. [2] Guoqiang Zhang, Yang Li, and Tao Lin. Caching in information centric networking: a survey. Computer Networks, 57(16):3128–3141, 2013. [3] Cisco. Cisco visual networking index: Forecast and methodology: 20112015. White Paper, 2012. [4] Uichin Lee, Ivica Rimac, and Volker Hilt. Greening the internet with content-centric networking. In the 1st International Conference on Energy-Efficient Computing and Networking, pages 179–182. ACM, 2010. [5] Ao-Jan Su, David R Choffnes, Aleksandar Kuzmanovic, and Fabi´an E Bustamante. Drafting behind akamai (travelocity-based detouring). ACM SIGCOMM Computer Communication Review, 36(4):435–446, 2006. [6] Warren J Leonard. Tslp: finally in the limelight. Nature immunology, 3(7):605–607, 2002. [7] Luiz Andr´e Barroso and Urs Holzle. The case for energy-proportional computing. Computer, 40(12):33–37, 2007. [8] Sergiu Nedevschi, Lucian Popa, Gianluca Iannaccone, Sylvia Ratnasamy, and David Wetherall. Reducing network energy consumption via sleeping and rate-adaptation. In NSDI, volume 8, pages 323–336, 2008. [9] Barath Raghavan and Justin Ma. The energy and emergy of the internet. In ACM Workshop on Hot Topics in Networks, page 9. ACM, 2011. [10] Anand Seetharam, Manikandan Somasundaram, Don Towsley, Jim Kurose, and Prashant Shenoy. Shipping to streaming: is this shift green? In ACM SIGCOMM workshop on Green networking, pages 61– 68. ACM, 2010. [11] Hasti Ahlehagh and Sujit Dey. Video caching in radio access network: Impact on delay and capacity. In IEEE WCNC, pages 2276–2281. IEEE, 2012. [12] Nakjung Choi, Kyle Guan, Daniel C Kilper, and Gary Atkinson. Innetwork caching effect on optimal energy consumption in content-centric networking. In IEEE ICC, pages 2889–2894. IEEE, 2012. [13] Silvano Martello and Paolo Toth. Knapsack problems: algorithms and computer implementations. John Wiley & Sons, Inc., 1990. [14] M. Held, P. Wolfe, and H. P. Crowder. Validation of subgradient optimization. Mathematical programming, 6(1):62–88, 1974. [15] Nikolaos Laoutaris, Sofia Syntila, and Ioannis Stavrakakis. Meta algorithms for hierarchical web caches. In IEEE IPCCC, pages 445–452. IEEE, 2004. [16] Elizabeth J O’neil, Patrick E O’neil, and Gerhard Weikum. The lruk page replacement algorithm for database disk buffering. In ACM SIGMOD Record, volume 22, pages 297–306. ACM, 1993.