Modeling Energy-Delay Tradeoffs in Single Base Station with Cache

Abstract

With the explosive increase of mobile data traffic, the energy efficiency issue in cellular networks is a growing concern. Recently, the advantages of in-network caching in Internet have been widely investigated, for example, speeding up content distribution and improving network resource utilization. In this paper, we analyze the energy-delay tradeoff problem in the context of single base station (BS), which has a cache capacity to buffer the contents through it. Although additional power is consumed by the cache, work load of BS and network delay will be improved, which makes a tradeoff between network power consumption and delay. Simulation results reveal that, by introducing the cache in a BS, the network power and delay can be obviously reduced in different network conditions compared to the scenario without a cache. In addition, we find that a large cache size does not always mean a less network cost because of the more cache power consumption.

1. Introduction

With the explosive growth of the mobile data traffic, mobile hosts will overtake fixed ones, not only in terms of numbers but also in terms of traffic load [1], which makes energy efficiency a growing concern in the current cellular networks due to the increasing network cost (e.g., BS power consumption and network delay) [2, 3]. However, given the centralized architecture of current cellular networks, the wireless link capacity as well as the bandwidth of the Radio Access Networks and the backhaul network cannot practically cope with the explosive growth in mobile traffic [4]. Recently, the advantages of in-network caching in cellular networks have been widely investigated to speed up content distribution and improve network resource utilization.

Several works have been studied on this new field. Sarkissian [5] analyzes embedding caches in wireless networks to achieve significant reduction in response time and thus provide exceptional wireless user experience. Woo et al. [6] argue that caching in the cellular networks is an attractive approach that can address the backhaul congestion in core networks and compare the benefits and tradeoffs of different promising caching solutions. Erman et al. [7] explore the potential of forward caching in 3G cellular networks and develop a caching cost model to realize the tradeoffs between deploying forward caching at different levels in the 3G network hierarchy. Wang et al. [4] first study techniques related to caching in current mobile networks, discuss potential techniques for caching in 5G mobile networks, and then propose a novel edge caching scheme based on the concept of content-centric networking or information-centric networking. Le et al. [8] propose a byte caching scheme to cache repetitive portions of an object, which functions at the network layer by looking for common sequences of data in the bytes of packet flows and does not need to split flows into segments but continuously penetrates into the byte strings to cache the often used bytes and eliminate any redundant ones. Golrezaei et al. [9] envision femtocell-like base stations with weak backhaul links but large storage capacity, which form a wireless distributed caching network that assists the macrobase station by handling requests of popular files that have been cached. Ahlehagh and Dey [10] demonstrate the feasibility and effectiveness of using microcaches at the base stations of the Radio Access Network (RAN), coupled with new caching policies based on video preference of users in the cell and a new scheduling technique that allocates RAN backhaul bandwidth in coordination with requesting video clients.

Although these excellent works have been done on caching in the cellular networks, far little effort has been dedicated to study the problem from the viewpoint of tradeoff between energy and delay. In this paper, we analyze the energy-delay tradeoff problem in the context of single base station with a cache capacity to buffer network contents. Although additional power is consumed by the cache, the work load of BS and network delay will be reduced, which makes a tradeoff between network power and delay.

2. System Model

We analyze the energy-delay tradeoff problem in single BS scenario, where the BS has a limited cache capacity C. Moreover, we assume that the packet error has been guaranteed by the physical layer technique, and the retransmission is not considered.

2.1. Content Popularity Model

We assume that the number of different contents provided by a content provider is F ranked from one (the most popular) to F (the least popular) based on its popularity. By letting the total number of requests in a given time duration t be R, the number of requests to the content of popularity k, $R_k$ , follows a Zipf-like distribution [11, 12] as

$$\begin{array}{cc}& R_k=R\frac{k^{-\alpha }}{{\sum }_{k=\mathrm{1}}^F{k}^{-\alpha }}=\frac{R}{a_{\mathrm{0}}}{k}^{-\alpha },k=\mathrm{1,2},\dots ,F,\end{array}$$

(1)

where $a_{\mathrm{0}}$ is a constant to normalize the request rate. A large value for α indicates that the number of popular contents increases.

2.2. Power Model

We consider single BS with a cache scenario where users arrive according to a Poisson process with arrival rate λ. Each user requires a random amount of downlink service with average length l bits, for example, non-realtime file download with average file size l, and then the user leaves after being served. Assuming the arrival rate can be well estimated [13], with time varying traffic intensity in practice, we just need to operate according to the current arrival rate.

In the following, we use an energy-proportional model [14] to model the power consumption in single BS with a cache.

2.2.1. Cache Power

We assume that there is a fixed cache power cost $P_s$ for each user request search. The total power consumed by the cache is given by [11, 12]

$$\begin{array}{cc}& P_{\text{cache}}=P_s+N_{c}l{w}_{\text{ca}},N_c\in \left[\mathrm{0},C\right],\end{array}$$

(2)

where $N_c$ represents the number of contents cached in the BS cache and $w_{\text{ca}}$ is the power efficiency of caching. The value of $w_{\text{ca}}$ strongly depends on the caching hardware technology. In this paper, we consider high-speed solid state disk (SSD), dynamic random access memory (DRAM), static random access memory (SRAM), and ternary content-addressable memory (TCAM). The power efficiency of these technologies is listed in Table 1.

Table 1

Power efficiency $$w_{\text{ca}}$$ of different caching hardware technologies.

Caching hardware technology	Power efficiency (Watt/bit)
High-speed solid state disk (SSD)	$$\mathrm{6.25}\times \mathrm{1}{\mathrm{0}}^{-\mathrm{12}}$$
Dynamic random access memory (DRAM)	$$\mathrm{2.5}\times \mathrm{1}{\mathrm{0}}^{-\mathrm{9}}$$
Static random access memory (SRAM)	$$\mathrm{1.5}\times \mathrm{1}{\mathrm{0}}^{-\mathrm{8}}$$
Ternary content-addressable memory (TCAM)	$$\mathrm{1.88}\times \mathrm{1}{\mathrm{0}}^{-\mathrm{6}}$$

2.2.2. Base Station Power

The $M/G/\mathrm{1}$ processor sharing (PS) model is used here [15, 16]. The traditional BS power can be modeled as

$$\begin{array}{cc}& P_{\text{BS}}=P_{\mathrm{0}}+{\Delta }_P{P}_t,\end{array}$$

(3)

where $P_{\mathrm{0}}$ is the static power consumption in the active mode, ${\Delta }_P$ is the slope of the load-dependent power consumption, and the transmit power $P_t$ adapts to the system traffic load.

Assume that the BS service capacity or service rate is x bits per second, which adapts to the system traffic load and is equally shared by all users being served. So the user departure rate is $\mu =x/l$ , and the traffic load (or busy probability) at the BS is $\rho =\lambda /\mu =\lambda l/x$ . The relationship between the service rate x and the transmit power $P_t$ is

$$\begin{array}{cc}& P_t=\frac{\rho }{\gamma }\left({\mathrm{2}}^{x/B}-\mathrm{1}\right),P_t\in \left[\mathrm{0},P_t^{\max }\right],\end{array}$$

(4)

where $\gamma =\eta g/N_{\mathrm{0}}B$ , g represents the channel gain, B is the bandwidth, $N_{\mathrm{0}}$ denotes the noise density, and η is a constant related to bit error rate (BER) requirement when adaptive modulation and coding are used [17].

Therefore, with service rate x, the traditional BS power expression (3) can be rewritten as

$$\begin{array}{cc}& P_{\text{BS}}=P_{\mathrm{0}}+\frac{{\Delta }_P\rho }{\gamma }\left({\mathrm{2}}^{x/B}-\mathrm{1}\right)=P_{\mathrm{0}}+\frac{\lambda l}{x}\frac{{\Delta }_P}{\gamma }\left({\mathrm{2}}^{x/B}-\mathrm{1}\right).\end{array}$$

(5)

However, with a cache, all the user requests to the BS will be partly satisfied by it. We assume that the contents with content popularity of the top $N_c$ are buffered in the cache. Then, the number of requests unsatisfied by the cache is

$$\begin{array}{cc}& {\rho }^{\prime }=\frac{\rho }{a_{\mathrm{0}}}{\displaystyle \sum }_{k=N_c+\mathrm{1}}^F{k}^{-\alpha }=\frac{\lambda l}{a_{\mathrm{0}}x}{\displaystyle \sum }_{k=N_c+\mathrm{1}}^F{k}^{-\alpha }.\end{array}$$

(6)

Therefore, based on (6), the total BS power expression with a cache can be written as

$$\begin{array}{l}{P}_{\text{BS}}^{\prime }=P_{\mathrm{0}}+\frac{{\Delta }_P{\rho }^{\prime }}{\gamma }\left({\mathrm{2}}^{x/B}-\mathrm{1}\right)\\ =P_{\mathrm{0}}+\frac{\lambda l}{a_{\mathrm{0}}x}\frac{{\Delta }_P}{\gamma }\left({\mathrm{2}}^{x/B}-\mathrm{1}\right){\displaystyle \sum }_{k=N_c+\mathrm{1}}^F{k}^{-\alpha }.\end{array}$$

(7)

2.3. Delay Model

According to the property of $M/G/1$ PS queue [18] and Little's Law [19], the average delay of a BS without a cache is

$$\begin{array}{cc}& D_{\text{BS}}=\frac{l}{x-\lambda l}=\frac{\rho }{\lambda \left(\mathrm{1}-\rho \right)}.\end{array}$$

(8)

Similarly, the average delay of a BS with a cache is

$$\begin{array}{cc}& D_{\text{BS}}^{\prime }=\frac{{\rho }^{\prime }}{\lambda \left(\mathrm{1}-{\rho }^{\prime }\right)}=\frac{l{\sum }_{k=N_c+\mathrm{1}}^F{k}^{-\alpha }}{a_{\mathrm{0}}x-\lambda l{\sum }_{k=N_c+\mathrm{1}}^F{k}^{-\alpha }}.\end{array}$$

(9)

2.4. System Cost

The objective is to minimize the system cost, which is a weighted combination of average total power $P_{{\mathcal{T}}_{\text{sleep}},x}^{\text{tot}}$ and average delay $D_{{\mathcal{T}}_{\text{sleep}},x}$ . Here, ${\mathcal{T}}_{\text{sleep}}$ represents the parameter in the BS sleeping control: for the N-based sleeping control, ${\mathcal{T}}_{\text{sleep}}=N$ ; ${\mathcal{T}}_{\text{sleep}}=\mathrm{0}$ denotes that there is no sleeping control. In this paper, we assume that the system runs without considering the BS sleeping control. Therefore, we seek to find the service rate x and sleeping control parameter ${\mathcal{T}}_{\text{sleep}}$ that minimize

$$\begin{array}{cc}& z\left(\mathrm{0},x\right)=P_{\mathrm{0},x}^{\text{tot}}+\beta D_{\mathrm{0},x}.\end{array}$$

(10)

The positive weighting factor β indicates the relative importance of the average delay over the average power which can be thought of as a Lagrange multiplier on an average delay constraint [20, 21]. The “delay” we consider in this paper is the average response time from the user's service request arriving at the BS until this request is finished. From Little's Law, we know that the mean delay is directly related to the average queue length.

3. Simulation Results and Discussions

In this section, we use computer simulations to evaluate the performance of the proposed energy-delay tradeoff model. We first describe the simulation settings and then compare it with the traditional network cost model [22], which does not have a cache.

3.1. Simulation Settings

The simulation is assumed to be carried out in a single urban microcell scenario. According to the ITU test environments [23], the system bandwidth $B=\mathrm{10}$  MHz, the maximum transmit power $P_t^{\max }=\mathrm{15}$  W, and the channel gain $\gamma =\mathrm{10}$  (dB) in the simulation. We take the micro-BS energy consumption parameters $P_0=\mathrm{100}$  W and $\Delta P=\mathrm{7}$ [24].

Users arrive according to a Poisson process with arrival rate $\lambda =\mathrm{4}$ , and each user requests exactly one file whose size is exponentially distributed with mean $l=\mathrm{2}$  MB from the BS and leaves the system after being served. The system operates in a time-slotted fashion and the BS schedules users in a round robin way, serving one user in each time slot. Moreover, we assume that the average user arrival rate x is $\mathrm{70}$  Mbps.

In the simulation, we assume that there are $\mathrm{10000}$ different contents in the network, where values of skewness factor α range between $\mathrm{0.6}$ [25] and $\mathrm{1.5}$ [11]. We abstract the cache size for a BS as a proportion that the cache size is defined as the relative size to the total amount of different contents in the network, which varies from $\mathrm{0.1}\%$ to $\mathrm{5}\%$ [26]. Besides, we assume that the DRAM caching hardware technology is used, and the average search power of a cache uses fraction $\mathrm{50}\%$ of its power once fully utilized [14].

3.2. Performance Evaluation Results

Figure 1 shows the energy-delay tradeoffs of the two models versus content popularity with different cache sizes when weight factor β is $\mathrm{10}$ . From Figure 1, we can observe that the content popularity and cache size have some effect on the energy-delay tradeoffs of the proposed model. When the Zipf skewness parameter α increases, the content diversity decreases and the number of popular contents increases, which makes the network power consumption, delay, and cost decrease gradually, while these parameters of the traditional model remain the same because it does not consider the content popularity or have a cache capacity. As for cache capacity, a larger buffer means that more popular contents can be cached, which reduces the network delay, as shown in Figure 1(b). However, a larger cache size does not always mean a better energy-delay tradeoff, as shown in Figures 1(a) and 1(c). The reason is that the larger cache size is, the more cache power is consumed, which can influence the energy-delay tradeoff.

Figure 1

Comparisons between energy-delay tradeoffs of a BS with and without a cache versus content popularity and cache size (β is $\mathrm{10}$ ).

Figure 2 shows the energy-delay tradeoffs of the two models versus weight factor β with different cache sizes. From Figure 2, we can observe that the weight factor and cache size have some effect on the energy-delay tradeoffs of the two models. The increase of weight factor indicates that the average delay is more important than the network power. That is to say, network cost is more sensitive to average delay. Therefore, the network cost increases with the constant power consumption of a BS and cache. However, a larger cache size does not always mean a better energy-delay tradeoff, which has been analyzed above.

Figure 2

Comparisons between total cost of a BS with and without a cache and weight factor.

4. Conclusions and Future Work

In this paper, we have studied the issues of the energy-delay tradeoff problem in the context of single base station with a cache capacity to buffer network contents. Although additional power is consumed by the cache, the work load of BS and network delay will be improved, which makes a tradeoff between network power and delay. Simulation results reveal that, by introducing the cache, the network power and delay can be obviously reduced in different network conditions compared to the situation without a cache.

With recent advances of wireless mobile communication technologies and devices, more and more end users access the Internet via mobile devices, such as smart phones and tablets. Therefore, we will study user mobility in the proposed model in the future. Moreover, it would be interesting to discuss how to find a proper cache size to minimize network cost in the future work. Finally, future work is in progress to adopt the sleeping schemes to reduce network cost in the proposed model.