QoS4IVSaaS: a QoS management framework for intelligent video surveillance as a service

Abstract

Quality of service (QoS) is critical for real-time intelligent video surveillance as a service (IVSaaS) platform, which is both computation intensive and data intensive by nature. However, there is scarce work on a QoS framework for IVSaaS platform. In this paper, we propose QoS for intelligent video surveillance as a service, a QoS framework to make computing resources highly available. In the framework, multiple metrics such as throughput, loads of CPU/GPU, memory and IO are taken into account with different time series models to enhance the adaptivity of different video services. A model selection algorithm is proposed to choose the model that achieves the best performance under various error indicators. At the same time, a resource abnormality detection algorithm is designed to detect anomalies when a service is underperformed. Evaluation results show that the proposed QoS framework can successfully ensure QoS by dynamically scheduling computing resources.

Appendices

Appendices

1.1 Metric models

• Moving average (MA) For a metric time series $M_t$, MA models the time series with a fixed window size W to give an estimation of the metric $\hat{M}_{t+1}$ which is generated from

  $$\begin{aligned} {\hat{M}}_{t+1}=\frac{\sum _{i=t-(W-1)}^{i=t}M_{i}}{W}. \end{aligned}$$

  A MA model can be extended to a weighted MA (WMA) model in which a factor $w_i$ is weighted on each $M_i$ in the window, and in this paper we set $w_i=1/W$ for all $i= 1,2,...,W$.

• Simple exponential smoothing (SES) SES assigns exponentially decreasing weights as the observations get older. In other words, recent observations are given relatively more weight in forecasting than the older observations. It begins by setting $\hat{M}_2$ to $M_1$ and shifts the exponential window by

  $$\begin{aligned} {\hat{M}}_t=\alpha M_{t-1}+(1-\alpha )\hat{M}_{t-1} \end{aligned}$$

  where $0<\alpha \le 1,\,\,t\ge 3$.

• Double exponential smoothing (DES) DES is a refinement of SES model, but adds another component which takes into account any trend in the data. SES works best with data where there is no trend or seasonality components to the data. Double exponential smoothing takes into account the increasing or decreasing trend in the data. It begins by setting $\hat{M}_1$ to $M_1$ and by setting $b_1$ to $M_2-M_1$, and then iterates by

  $$\begin{aligned} \hat{M}_t= \,& {} \alpha M_t+(1-\alpha )(\hat{M}_{t-1}+b_{t-1})\\ b_t= \,& {} \gamma (\hat{M}_t-\hat{M}_{t-1})+(1-\gamma )b_{t-1} \end{aligned}$$

• Linear regression (LR) Assuming that an observed metric $m_o$ is the sum of a random error $\varepsilon$ and a real metric $m_r$, LR model essentially attempts to put a straight line through N metric points, that is, $m_o^i=m_r^i+\varepsilon ^i$ where $m_r^i=a+bt^i,~i=1,2,...,N$. The goal is to get the estimation $\hat{a},~\hat{b}$ of a,  b by minimizing

  $$\begin{aligned} Q=\sum _{i=1}^{i=N}(\varepsilon ^i)^2=\sum _{i=1}^{i=N}(m_o^i-a-bt^i)^2. \end{aligned}$$

  Setting the partial derivative of a and b on Q to 0, we can get $\hat{a}=\overline{m}_o-\hat{b}\overline{t}~,~~~ \hat{b}=l_{tm_o}/l_{tt}$ where $\overline{m}_o,~\overline{t}$ are the means on the N metric points, respectively, and

  $$\begin{aligned} l_{tm_o}=\sum _{i=1}^{i=N}t^im_o^i-N\overline{t}\overline{m}_o\qquad l_{tt}=\sum _{i=1}^{N}(t^i)^2-N\overline{t}^2 \end{aligned}$$

• Polynomial regression (PR) In the PR model, the relationship between the independent variable t and the dependent variable m is modeled as an nth degree polynomial, which is denoted by

  $$\begin{aligned} m_i=\sum _{p=0}^{p=P}a_pt_i^p+\varepsilon _i \end{aligned}$$

  where P is the order of the model. It can be expressed in matrix form in terms of a design matrix T, a response vector $\overrightarrow{m}$, a parameter vector $\overrightarrow{a}$ and a vector $\overrightarrow{\varepsilon }$ of random errors. Then, the model can be written as a system of linear equations:

  $$\begin{aligned} \left[ \begin{matrix} m_1 &{}\\ m_2 &{}\\ m_3 &{}\\ \vdots \\ m_N \end{matrix}\right] = \left[ \begin{matrix} 1 &{} t_1 &{} t_1^2 &{} ... &{} t_1^P\\ 1 &{} t_2 &{} t_2^2 &{} ... &{} t_2^P\\ 1 &{} t_3 &{} t_3^2 &{} ... &{} t_3^P\\ \vdots &{}\vdots &{}\vdots &{} &{}\vdots \\ 1 &{} t_N &{} t_N^2 &{} ... &{} t_N^P \end{matrix}\right] \left[ \begin{matrix} a_0\\ a_1\\ a_2\\ \vdots \\ a_P\\ \end{matrix}\right] + \left[ \begin{matrix} \varepsilon _0\\ \varepsilon _1\\ \varepsilon _2\\ \vdots \\ \varepsilon _N\\ \end{matrix}\right] \end{aligned}$$

  (1)

  which when using pure matrix notation is written as $\overrightarrow{m}=\varvec{T}\overrightarrow{a}+\overrightarrow{\varepsilon }$. The vector of estimated polynomial regression coefficients (using ordinary least squares estimation) is

  $$\begin{aligned} \hat{\overrightarrow{a}}=(\varvec{T}^T\varvec{T})^{-1}\varvec{T}^T\overrightarrow{m} \end{aligned}$$

1.2 Error indicators

In the following, N is the number of metric samples, $m_e^t,~m_o^t$ are the estimation by a model and observation from the IVSaaS, respectively.

• Akaike information criteria:

  $$\begin{aligned} \mathrm{AIC}=N\ln {2\pi }+\ln {\frac{\sum _{t=1}^{N}(m_e^t-m_o^t)^2}{N}}+2(\pi +2) \end{aligned}$$

• Mean square error:

  $$\begin{aligned} \mathrm{MSE}=\frac{\sum _{t=1}^{N}(m_e^t-m_o^t)^2}{N} \end{aligned}$$

• BIAS:

  $$\begin{aligned} \mathrm{BIAS}=\frac{\sum _{t=1}^{N}(m_e^t-m_o^t)}{N} \end{aligned}$$

• Mean absolute percent error:

  $$\begin{aligned} \mathrm{MAPE}=\frac{\sum _{t=1}^{N}|(m_e^t-m_o^t)/m_o^t|}{N} \end{aligned}$$

• Mean absolute difference:

  $$\begin{aligned} \mathrm{MAD}=\frac{\sum _{t=1}^{N}|(m_e^t-m_o^t)|}{N} \end{aligned}$$

• Sum of absolute error:

  $$\begin{aligned} \mathrm{SAE}=\sum _{t=1}^{N}|(m_e^t-m_o^t)| \end{aligned}$$