云计算竞价实例价格预测：马尔科夫状态切换模型与动态ARIMA

92 浏览量更新于2024-07-14 收藏 1.74MB PDF 举报

"云计算中竞价型实例的价格预测" 这篇研究论文探讨了云计算中竞价型实例的价格预测问题，特别是在未来计算机系统（Future Generation Computer Systems）期刊上发表的一项研究。竞价型实例是云服务提供商如Amazon Web Services (AWS) 提供的一种经济型计算资源，用户可以以低于常规按需实例的价格购买，但可能在任何时候因市场供需关系被中断。这种实例的定价模式具有高度波动性，对用户成本管理和资源调度策略具有重要影响。研究论文提出了两种预测方法：基于马尔科夫状态切换的自回归模型（Markov regime-switching autoregressive based forecasting methods）和动态ARIMA模型（Dynamic-ARIMA）。马尔科夫状态切换模型考虑了竞价价格的转变规律，通过识别和建模不同价格模式之间的转换来预测未来的波动。而动态ARIMA模型是一种适应价格时间序列变化的自回归积分滑动平均模型，能够处理非平稳时间序列数据，从而更准确地预测价格动态。文章还提供了选择合适预测方法的指导，帮助用户根据实际情况和需求选择最佳预测策略。这对于优化云计算资源的使用，特别是对于需要大量计算资源但预算有限的企业或个人来说，具有很高的实用价值。此外，准确的价格预测有助于用户制定更有效的资源调度策略，避免因价格突然上涨导致的成本增加，同时也能在价格低位时获取更多计算资源。关键词包括：云计算、竞价价格、预测、马尔科夫状态切换、调度。这些关键词突出了研究的核心内容，即在云环境中的价格管理与资源优化。这篇研究论文深入研究了云计算竞价实例价格的预测技术，通过引入统计学和概率论的方法，为云服务消费者提供了一种理解和应对价格波动的工具，以实现成本效益最大化。这对于云服务市场参与者，无论是服务提供商还是消费者，都是一个重要的研究贡献。

Z. Cai et al. / Future Generation Computer Systems 79 (2018) 38–53 41

is an extension of TAR with a much more flexible regime transition

strategy. In MRS-AR, the regime transition is defined by a Markov

process rather than transition variables. MRS-AR has been used

to model many different time series with changing regimes such

as exchange rates [21,40] and financial time series [20]. For each

prediction step, the absolute probability distribution (APD) over

regimes, obtained from the last conditional probability distribu-

tion multiplying multi-step transition probabilities, can be used to

forecast prices [21]. However, APDs of non-seasonal Markov chains

usually converges to equilibrium distributions quickly. Therefore,

APDs are only suitable for predicting short-term regimes rather

than long-term ones. For example, Chen et al. [19] used the regime

with the largest absolute probability to produce a one-step fore-

cast. Expectation based prediction is another way to produce fore-

cast values. Yuan et al. [21] used the expected mean to forecast,

without specifying regimes, which is determined by the probability

distribution of regimes and the mean of each regime. However,

specifying appropriate regimes is benefit in improving the ac-

curacy of predictions. Therefore, in this paper, two methods are

proposed to predict regimes which use ARMA to model historical

durations of regimes combined with the probability transition

matrix among regimes.

To summarize, statistical probability models have been widely

used to recognize changes in spot prices without considering

trends in sequential prices. Existing time series based models such

as autoregression, ARIMA, SES, DES and TES with a single model

cannot describe nonlinear Spot prices with multiple regimes well.

Therefore, in this paper, two Markov regime-switching autoregres-

sive model based prediction methods are proposed which build

separate models for different regimes. For comparison, a dynamic-

ARIMA is proposed too which differentiates prices to deal with

large fluctuations.

3. Problem description

As stated, there are mainly two kinds of pricing models in

Cloud computing platforms [2]: (1) Fixed pricing models: prices of

resources are fixed, e.g., Amazon’s EC2 On-demand VM instances

and Reserved VM instances; (2) Variable pricing models: prices

of resources change stochastically according to real-time market

demands, e.g., Amazon’s EC2 prices of spot VM instances (spot

prices). Amazon’s EC2 spot VM instances are sold to users via

auctions. When a user rents a spot instance, the user places a bid

price. Only when the bid price is higher than the spot price, does

the user have the possibility of getting the VM instance. After the

user gets the VM, the user needs to pay according to the spot

price. If the spot price is higher than the bid price, the Cloud

computing provider will withdraw the VM (out-of-bid event) and

the last interval will not be charged. When out-of-bid events occur,

recovery from previous checkpoints will consume additional time

and cost. Spot instances are usually cheaper than On-demand VM

instances with the same configurations. However, spot instances

are unreliable because of out-of-bid events resulting from the

stochastic prices. Choosing appropriate VM types, selecting the

correct rental periods and elaborating bids based on forecasted

spot prices (predicted trends) is helpful in minimizing resource

rental costs.

In this paper, we aim to develop several prediction algorithms

to forecast spot prices accurately. For a spot price time series,

using all the past data to forecast future prices is time consuming.

Therefore, only data of a fixed length of time (a window) is usually

used, e.g., the prices of past 480 h. As time progresses, the time

window moves forward. For each time window, the time series of

spot prices is represented by {Y

}

t=1

, where t indicates the index

of time units (e.g., the index of hours, minutes or seconds) and

T is the length of the time series in the current time window.

The objective of the proposed forecasting methods is to minimize

forecasting errors. To evaluate the performance of predictions the

popular Mean Absolute Percentage Error (MAPE) [41] is used as

defined in the following.

MAPE

100

∑

l=1

(l) − A

(l)

| (1)

where A

(l) is the actual value,

(l) is the forecasted value of

prediction step l and n is the length of the forecast period. Note

that MAPE has been criticized in the past, most notably in [42].

However, it is still the easiest to understand and most widely used

error measure in the literature.

4. Preliminaries

4.1. Autoregressive integrated moving average model

Autoregressive-Moving Average (ARMA) is a popular model for

describing a (weakly) stationary stochastic process. ARMA consists

of two parts, an autoregressive (AR) part and a moving average

(MA) part. The AR part involves regressing past values and the

MA part is a linear combination of past error terms. The model of

ARMA(p, q) is as follows.

∑

i=1

t−i

∑

j=1

t−j

+ ε

(2)

where ε

∼ i.i.d.N(0, σ

) is the error item of time t, p is the order

of the autoregression part, φ

is the autoregression parameter of

t−i

, q is the order of the moving average part and θ

is the moving

average parameter of ε

t−j

. ARMA is usually suitable for stable time

series and large fluctuations in spot prices will decrease the pre-

diction accuracy of ARMA. ARIMA is an extension of ARMA which

applies an initial differencing step to reduce the non-stationarity

which improves the prediction accuracy of spot prices with large

fluctuations. The model of ARIMA(p, 1, q) is as follows.

− Y

t−1

= θ

∑

i=1

t−i

− Y

t−i−1

) +

∑

j=1

t−j

+ ε

(3)

where ε

∼ i.i.d.N(0, σ

4.2. Markov regime-switching AR model

The linear based ARIMA uses a single model to describe time

series. However, spot prices in some VM types have switching

regimes, i.e., different periods have different regimes (different sta-

tistical characteristics). Therefore, different time series models are

needed to describe different regimes. For example, two different

autoregressive (AR) models are required to model two different

regimes. For the first regime, the AR model might be

= c

∑

i=1

i,1

t−i

+ ε

t,1

(4)

where ε

t,1

∼ i.i.d.N(0, σ

), c

is the intercept value and φ

i,1

is the

autoregressive parameter of Y

t−i

. For the second regime, the AR

model might be

= c

∑

i=1

i,2

t−i

+ ε

t,2

(5)

where ε

t,2

∼ i.i.d.N(0, σ

), c

is the intercept value and φ

i,2

is the

autoregressive parameter of Y

t−i

. Different regimes have different

intercept values and autoregressive parameters. Each regime can

be defined as a state of a Markov process. The spot price switches

剩余15页未读，继续阅读

weixin_38658982

粉丝: 7
资源: 941

云计算竞价实例价格预测：马尔科夫状态切换模型与动态ARIMA

虚拟机竞价型实例价格统计建模1

降低云计算成本的方法.doc

根据《非招标方式采购代理服务规范》(2018 年版),竞价采购中天于元1"r~-确的是() 。 A质量交货期等可量化的技术或商务因 素，可以作为竟价因素 B交货期不得作为竞价因素 C质量不得作为竞价因素 D价格是唯一竞争因素

计算广告中竞价广告是什么意思

基于大数据方式开展电力设备及材料竞价平台核心技术

集合竞价价格逐步上升代码怎么写

竞价抢筹.tn6指标

在竞价模块中 会出现oom的场景 有哪些

古诺竞价模型matlab

请提供一份Python代码，用途为：根据开盘前逐笔委托行情数据计算集合竞价价格的价格

最新资源

根据《非招标方式采购代理服务规范》(2018 年版),竞价采购中天于元1"r~-确的是() 。 A质量交货期等可量化的技术或商务因素，可以作为竟价因素 B交货期不得作为竞价因素 C质量不得作为竞价因素 D价格是唯一竞争因素

在竞价模块中会出现oom的场景有哪些