1. Dynamic Placement of Virtual Machines for managing sla violations
Norman Bobroff
Andrzej Kochut
Kurk Beaty
IBM T.J. Watson Research Center
IFIP/IEEE International Symposium on Integrated Network Management, 2007
Presented by: Yun Liaw

2. Outline
Introduction
Server Workload Signatures that Benefit from Dynamic Placement
Forecasting
Placement Algorithm
Simulation Studies
Related Works
Conclusion and Comments
2019/10/30

3. Introduction
Low average utilization of servers is a well-known cost concern in datacenter
To guarantee good performance at periods of peak demand, processing capacity is over-provisioned for many business applications
The demand’s strong daily variability leading to low average utilization
Traditional deployment pattern: One application per OS, and one OS per one physical machine
Consolidation at application and OS levels can mitigate inefficiencies in using physical resources
Application level consolidation requires considerable skill to ensure isolation between co-hosted applications within an OS image
OS-based consolidation: A hypervisor executes on a physical machine (PM) and presents an abstraction of the underlying hardware to multiple virtual machines (VM)
2019/10/30

4. Introduction Server consolidation can be static or dynamic
Static consolidation: Use historical average resource utilization as input to an algorithm that maps VMs to PMs
Recomputed for a long period of time
Mapping algorithm is done off-line
Dynamic consolidation: Implemented at shorter timescale
Need the ability to do live migration of VMs
Live Migration: To migrate a VM from one PM to another without service interruption
2019/10/30

5. Introduction
In this paper, a management algorithm for dynamic resource allocation in virtualized server environments is proposed
Three parts of the algorithm (MFR)
Measuring historical data
Forecasting the future demand
Remapping VMs to PMs

6. Introduction This paper’s contribution
Method for classification of workload signatures to servers which benefit most from dynamic migration
Forecasting technique suited for handling time series of resource demands
Algorithm that remaps VMs to PMs
Goal: minimizing the number of PMs
Constraints: To support the workload at a specific rate of SLA violations p
2019/10/30

7. The algorithm – Key insight
Consider a single PM that hosts a single VM
The PM’s CPU capacity can be dynamically adjusted at time intervals of length τ
Goal: To adjust CPU demand to ensure the probability of VM’s CPU demand exceeding capacity of PM is no greater than p

8. The algorithm – Key insight
Ui: The CPU demand
Prob. Density function of VM’s historical CPU demand
Time series of VM’s CPU demand

9. Server workload signatures
The properties that make a VM workload suitable for dynamic management:
The timescale over which the resource demand varies must exceed the rebalancing interval τ
Large resource variability
Resource demand must be predictable
The resource demand has deterministic periodic component
Strong autocorrelation – possible to obtain low-error predictor
2019/10/30

10. 2 1 3 [A] 1: raw CPU demand time series 2: autocorrelation function
3: cumulative dist. of demand
4: periodogram 1 3 2 4
[A]: strong autocorrelation, large variability and now distinct periodic component
[B]: low autocorrelation, low variability and no distinct periodic component
[C]: strong autocorrelation, large variability, and distinct periodic component
[C]
[B] 1 3
2019/10/30

11. Analytical formula for gain from dynamic management
Notations:
Reallocation interval: τ
Demand probability density function: u(x)
p-percentile of distribution u: Lp
Distribution of predicted time series: ūτ(x)
p-percentile of distribution of predictor error: Ep(τ)
Gain G(τ):
2019/10/30

12. Forecasting
Goal: building a predictor that forecasts the probability distribution of a demand in a future observation interval based on the historical usage data
Approach (based on the work [20])
Decomposing the demand time series Ui into a sum of periodic components Dj
S.t.
where n is an integer and pj is a period
Residual component of the demand
2019/10/30
[20] G.Jenkins, et al., Time Series Analysis: Forecasting and Control, Prentice Hall, 1994

13. Forecasting Approach (cont’d) Decouple Dj from the time series Ui
Use a low-pass filter to smooth the time series
Subdivide the smoothed time series into contiguous intervals of length pj
Average the intervals together to form Dj
Subtract the Dj from the Ui
Model ri using a class of autoregression process -- AR(2)
εi : the error term represented by Gaussian variable
α: parameters estimated from data

14. [A]
“The key to achieving a gain from dynamic management is the width of the predictor ‘s error distribution being less than the width of the total demand distribution”
[B]
[C]
2019/10/30

15. Management algorithm Management Objective: The remapping algorithm
To minimize: the time-averaged number of active PMs hosting VMs
Constraint: the rate of demand overloading the resource capacity is bounded by a specified threshold p
The remapping algorithm
A version of bin-packing problem (NP-hard)
based on the first-fit heuristic approximation
2019/10/30

16. Management algorithm Notations:
For each VM, use the forecast approach described earlier to forecast the max usage
Sort VMs in descending order
2019/10/30

17. Management algorithm Notations:
cp(μ, σ2): the capacity needed to guarantee an error rate less than p
Taken off the VMs from the ordered list and attempt to place it on the PMs
For each target PM, compute the distribution of the sum of the resource demands of all VMs allocated to this PM
2019/10/30

18. Management algorithm Notations:
Taken off the VMs from the ordered list and attempt to place it on the PMs
If p-percentile of this distribution is no greater than the capacity of the PM, the VM is allocated to this PM
If the list of PMs is exhausted without satisfying this condition, the VM is assigned to the PM that has the smallest difference between allocated demands and its capacity
2019/10/30

19. Simulation studies
The methodology is validated using simulations driven by traces gathered from hundreds of production servers running multiple OSes, and broad variety of applications
The simulation studies include:
Verify that MFR meets SLA targets
Quantify the reduction in number of SLA violations
Quantify the number of PMs used to support a workload
Explore the relationship between the remapping interval and the gain from dynamic management
Perform measurements on the VMWare ESX testbed
To determine properties of a practical VM migration
2019/10/30

20. Simulation studies Meeting SLA objects
For a given p, a set of 10 simulations is executed
2019/10/30

21. Simulation studies Quantifying the reduction in rate of SLA violations
Map a single set of 25 VMs onto a set of PMs
2019/10/30

22. Simulation studies Quantifying the reduction in number of used PMs
Compare the time-averaged number of active PMs required by MFR and static allocation at a specific target rate p
2019/10/30

23. Simulation studies Quantifying the reduction in number of used PMs
Compare the required PMs under different target rate p
2019/10/30

24. Simulation studies
Relationship between the remapping interval and the gain
The quality of predictor decreases with the length of the prediction horizon
2019/10/30

25. Related Works Virtualization Time series forecasting
Storage-based virtualization
OS-level virtualization
Application-level virtualization
Time series forecasting
Resource Management
bin-packing heuristics
resource economy in the datacenter
The alg. trying to minimize the number of migrations
2019/10/30

26. Conclusions
A management algorithm for dynamic allocation of VMs to PMs is presented
providing probabilistic SLA guarantees
Time series analysis and bin-packing heuristic combined to minimize the number of PMs required to support a workload
A method for characterizing the gain that a given VM can achieve from migration is presented
2019/10/30

27. Comments Only one measured attribute – CPU
Some functions are mysterious… for me
The perspective of recent paper in VM consolidation are similar
2019/10/30

28. Analytical formula for gain from dynamic management
The G(τ) above can be simplified to
We apply the approximation that
Thus
Note: The mean of the predictor is the same as the mean of underlying distribution since the predictor is unbiased
2019/10/30