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1 CMG, 2006 Reno
Yiping Ding and Ethan Bolker
How Many Guests Can You Serve?How Many Guests Can You Serve?- On the Number of Partitions- On the Number of Partitions
4CMG 06 Reno
Common SenseCommon Sense
“Figure out how many will fit around your dining room table even before you begin to think about how much they will eat.”
Three questions follow:1. What is the size of the dining room?
2. What is the size of the table?
3. How many tables can fit in the dining room?
5CMG 06 Reno
A huge table in a large dining room: no partitionA huge table in a large dining room: no partition
High Utilization
6CMG 06 Reno
Small tables in a large dining room: partitionSmall tables in a large dining room: partition
Low OverheadLow Overhead
7CMG 06 Reno
Large tables in a huge dining room: partitionLarge tables in a huge dining room: partition
High OverheadHigh Overhead
9CMG 06 Reno
A Basic Computer System without VirtualizationA Basic Computer System without Virtualization
Applications Operating System
Processors
NetworkInterface
I/O Subsystem
Memory
Hardware
13CMG 06 Reno
Two virtual machines on one physical systemTwo virtual machines on one physical system
Memory
Processors
Hardware
Operating System
Applications
I/O Subsystem Network Interface
Memory Processors, V1(P)
Hardware
I/O Subsystem Network Interface
Virtualized Layer
Hardware
Operating System
Applications
Memory Processors, V2(P)
I/O Subsystem Network Interface
Virtualized Layer
Virtualization Manager
14CMG 06 Reno
Memory
Processors
Hardware
Operating System
Applications
I/O Subsystem Network Interface
Memory Processors, V1(P)
Hardware
I/O Subsystem Network Interface
Virtualized Layer
Hardware
Operating System
Applications
Memory Processors, V2(P)
I/O Subsystem Network Interface
Virtualized Layer
Virtualization Manager
A Queueing Model for Two GuestsA Queueing Model for Two Guests
2/x0s
2/x0s
x s
sx S
15CMG 06 Reno
Partition or not?Partition or not?
You pay overhead for partitionbut it is easy to manage andresults are more predictable.
Without partition, you may serve more
16CMG 06 Reno
Two ways to serve guestsTwo ways to serve guests
Each guest owns a (virtual) server Separate queuesSupermarket model
Guests share the physical processor(s)Single queueBank model
21CMG 06 Reno
How Many Guests Can You Serve?How Many Guests Can You Serve?
Memory
Processors
Operating System
Applications
I/O Subsystem Network Interface
Memory Processors
Hardware
I/O SubsystemNetwork Interface
Virtualized Layer
Virtualization Manager
Operating System
Applications
Memory Processors
I/O SubsystemNetwork Interface
Virtualized Layer … Operating System
Applications
Memory Processors
I/O SubsystemNetwork Interface
Virtualized Layer
22CMG 06 Reno
The Difference: Virtualized vs. PhysicalThe Difference: Virtualized vs. Physical
Memory
Processors
Operating System
Applications
I/O Subsystem Network Interface
Memory Processors
Hardware
I/O SubsystemNetwork Interface
Virtualized Layer
Virtualization Manager
Operating System
Applications
Memory Processors
I/O SubsystemNetwork Interface
Virtualized Layer … Operating System
Applications
Memory Processors
I/O SubsystemNetwork Interface
Virtualized Layer
s
sx
23CMG 06 Reno
Model as M/M/m or M/M/1, with OverheadModel as M/M/m or M/M/1, with Overhead
Memory
Processors
Operating System
Applications
I/O Subsystem Network Interface
Memory Processors
Hardware
I/O SubsystemNetwork Interface
Virtualized Layer
Virtualization Manager
Operating System
Applications
Memory Processors
I/O SubsystemNetwork Interface
Virtualized Layer
…Operating System
Applications
Memory Processors
I/O SubsystemNetwork Interface
Virtualized Layer
s
sx
24CMG 06 Reno
Three types of overheadThree types of overhead
Consolidate m (identical) separate physical servers each with utilization u as guests on a single machine n times as powerful as the individual servers
Constant Overhead for virtualization management: c
1. Overhead proportional to number m of guests: f0 per partition, m×f0 total
2. Overhead proportional to guest utilization u: f per second per guest, f×m×u total
Total Utilization:
U = (1+f)×m×u/n + m×f0 + c
25CMG 06 Reno
Example: consolidate 50 serversExample: consolidate 50 servers
29
5 4 3 2 2 3 2
Server Distribution by Utilization
Assuming Processing Power = 1for each server
26CMG 06 Reno
Processing power needed for supporting Processing power needed for supporting the number of partitions (SLA = 2 seconds)the number of partitions (SLA = 2 seconds)
Throughput per partition
Relative Processing Power
Max Number of Partitions
0.1 3.4 29
0.2 1.5 5
0.3 1.7 4
0.4 1.7 3
0.5 1.5 2
0.6 1.7 2
0.7 2.6 3
0.9999 2.5 2
29
54 3 2 2 3 2
Server Distribution by Utilization
Assuming Processing Power = 1for each server
27CMG 06 Reno
Throughput per partition
Relative Processing Power
Max Number of Partitions
0.1 3.4 29
0.2 1.5 5
0.3 1.7 4
0.4 1.7 3
0.5 1.5 2
0.6 1.7 2
0.7 2.6 3
0.9999 2.5 2
28CMG 06 Reno
Overhead Reduces Number of Supportable Partitions for Same SLAOverhead Reduces Number of Supportable Partitions for Same SLA
Max Number of Partitions with and without Overhead(SLA = 2 Seconds)
0
10
20
30
40
0 0.2 0.4 0.6 0.8 1 1.2
Server Utilization before Virtualization
Relative Processing Power Max Number of Partition without Overhead
Max Number of Partitions (10% Fixed Overhead)
s
Throughput per Partition
Relative Proc. Power
Max Number of Partition without Overhead
Max Number of Partitions (10% Fixed Overhead)
0.1 3.4 29 25
0.2 1.5 5 4
0.3 1.7 4 3
0.4 1.7 3 2
0.5 1.5 2 1
0.6 1.7 2 1
0.7 2.6 3 2
0.9999 2.5 2 1
29CMG 06 Reno
Throughput per Partition
Relative Proc. Power
Max Number of Partition without Overhead
Max Number of Partitions (10% Fixed Overhead)
0.1 3.4 29 25
0.2 1.5 5 4
0.3 1.7 4 3
0.4 1.7 3 2
0.5 1.5 2 1
0.6 1.7 2 1
0.7 2.6 3 2
0.9999 2.5 2 1
30CMG 06 Reno
Increase Processing Power to Compensate for Overhead to Increase Processing Power to Compensate for Overhead to Support the Number of PartitionsSupport the Number of Partitions
Throughput per Partition
Relative Processing Power (10% more for Fixed Overhead)
Relative Processing Power (without Overhead)
Max Number of Partitions (10% Fixed Overhead)
0.1 3.8 3.4 29 (25)
0.2 1.7 1.5 5 (4)
0.3 1.9 1.7 4 (3)
0.4 1.9 1.7 3 (2)
0.5 1.7 1.5 2 (1)
0.6 1.9 1.7 2 (1)
0.7 2.9 2.6 3 (2)
0.9999 2.8 2.5 2 (1)
33CMG 06 Reno
If we choose one type of sever to support all If we choose one type of sever to support all
Relative Processing Power
Min Number of Servers Needed
1.5 13
1.7 11
2.5 8
2.6 8
3.4 6
How many do we need for each server type ?
29
5 4 3 22 3 2
Server Distribution by Utilization
Assuming Processing Power = 1for each server
34CMG 06 Reno
SLA Matters TooSLA Matters Too
Min Number of Servers Needed (10% Fixed Overhead, Different SLA)
0
5
10
15
20
0 0.5 1 1.5 2 2.5 3 3.5 4
Relative Processing Power (10% more for Fixed Overhead)
Min Number of Servers Needed (SLA = 1 Seconds)
Min Number of Servers Needed (SLA = 2 Seconds)
Relative Power
Min Number of Servers Needed (SLA = 1 Seconds)
Min Number of Servers Needed (SLA = 2 Seconds)
1.5 16 13
1.7 14 11
2.5 10 8
2.6 9 8
3.4 7 6
How many servers do we need?
35CMG 06 Reno
The impact of fixed overhead and overhead per partition for the Same The impact of fixed overhead and overhead per partition for the Same
SLASLA
Throughput per Partition
Relative Proc. Power
Max Number of Partition without Overhead
Max Number of Partitions (10% Fixed Overhead)
0.1 3.4 29 25
0.2 1.5 5 4
0.3 1.7 4 3
0.4 1.7 3 2
0.5 1.5 2 1
0.6 1.7 2 1
0.7 2.6 3 2
0.9999 2.5 2 1
Max Number of Partitions (10% Fixed Overhead and 2% Overhead per Partition)
15
3
3
2
1
1
2
1
Max Number of Partitions (10% Fixed Overhead and 5% Overhead per Partition)
9
3
2
2
1
1
2
1
36CMG 06 Reno
The relationship between Memory Size and Paging RateThe relationship between Memory Size and Paging Rate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 200 400 600 800 1000 1200 1400
Memory Size (MB)
Pag
ing
Rate
(P
ag
es /
Seco
nd
)
When you ask for what’s not in memory, paging occurs; the larger the memory, the higherthe chance what you ask is in memory
37CMG 06 Reno
Example: VMware ESX Memory ManagementExample: VMware ESX Memory Management
“… With ESX Server it is possible to have 10 virtual machines, each with 3.6GB of RAM available to their operating systems and applications, on a 2 CPU system with 16 GB of physical RAM.” - VMware White Paper: “Virtualization: Architectural Considerations And Other
Evaluation Criteria”
It that true?
38CMG 06 Reno
When average demand is low, virtualization is betterWhen average demand is low, virtualization is better
-0.02
0
0.02
0.04
0.06
0.08
0.1
0 0.2 0.4 0.6 0.8 1 1.2
Mean memory demand per server (GB)
Prob
abili
ty
Prob. of requiring more than 16 GB for 10 virtual servers
Prob of requiring more than 3.6 GB for 1 physical server
A crossing point: average memory demand of 900MB
39CMG 06 Reno
WMware ESX Virtual Ethernet SwitchWMware ESX Virtual Ethernet Switch
Virtual Machines / Guests
Outbound Adapter
Virtual NetworkVirtual Network
40CMG 06 Reno
Virtual Machines / Guests
Outbound Adapter
Communication pattern determines how many guests Communication pattern determines how many guests it can support (communicate among guests)it can support (communicate among guests)
41CMG 06 Reno
Virtual Machines / Guests
Outbound Adapter
Communication pattern determines how many guests Communication pattern determines how many guests it can support (communicate to outside world)it can support (communicate to outside world)