Efficient Distributed Workload (Re-)Embedding Monika Stefan Stefan Henzinger Neumann Schmid
Many Years Ago • Single server • Systems were fixed and workload-agnostic • Simple communication patterns (if at all), endpoints fixed https://www.flickr.com/photos/jurvetson/157722937 2
Nowadays • Large distributed systems (even geographically distributed): communication over network • Virtualization technologies enable workload-aware operations that improve system e ffi ciency • Communicating processes can be far away and re-locating them is costly https://wikileaks.org/amazon-atlas/map/ 3 https://commons.wikimedia.org/wiki/File:Bacloud.com_data_center.JPG
Nowadays • Large distributed systems (even geographically distributed): communication over network • Virtualization technologies enable workload-aware operations that improve system e ffi ciency • Communicating processes can be far away and re-locating them is costly • Communication requests contain patterns https://wikileaks.org/amazon-atlas/map/ 3 https://commons.wikimedia.org/wiki/File:Bacloud.com_data_center.JPG
Nowadays • Large distributed systems (even geographically distributed): communication over network • Virtualization technologies enable workload-aware operations that improve system New challenge e ffi ciency • Communicating processes can When to be far away and re-locate workloads? re-locating them is costly • Communication requests How to exploit the patterns? contain patterns https://wikileaks.org/amazon-atlas/map/ 3 https://commons.wikimedia.org/wiki/File:Bacloud.com_data_center.JPG
The Model 4
The Model ℓ servers 4
The Model data centers RACK scale ℓ servers computing 4
The Model server ℓ data centers RACK scale ℓ servers computing 4
The Model server ℓ occupied n VM slot The VMs are the workloads. n virtual machines (VMs) 5
The Model server ℓ occupied n VM slot free ε n VM slot ε n additional slots for VMs 6
The Model server ℓ occupied n VM slot free ε n VM slot Communication requests arrive online 7
The Model server ℓ occupied n VM slot free ε n VM slot Communication requests arrive online 7
The Model server ℓ occupied n VM slot free ε n VM slot 0 Communication requests arrive online 7
The Model server ℓ occupied n VM slot free ε n VM slot 0 0 Communication requests arrive online 7
The Model server ℓ occupied n VM slot free ε n VM slot 0 0 0 Communication requests arrive online 7
The Model server ℓ occupied n VM slot free ε n VM slot Old communication links stay forever 8
The Model server ℓ occupied n VM slot free ε n VM slot Communication requests arrive online 9
The Model server ℓ occupied n VM slot free ε n VM slot 1 Communication requests arrive online 9
The Model server ℓ occupied n VM slot free ε n VM slot 1 1 Communication requests arrive online 9
The Model server ℓ occupied n VM slot free ε n VM slot 1 1 1 Communication requests arrive online 9
The Model server ℓ occupied n VM slot free ε n VM slot re-location Re-locate VMs to avoid cost cross-server communication α > 1 10
The Model server ℓ occupied n VM slot free ε n VM slot α re-location Re-locate VMs to avoid cost cross-server communication α > 1 11
The Model server ℓ occupied n VM slot free ε n VM slot α re-location Re-locate VMs to avoid cost cross-server communication α > 1 12
The Model server ℓ occupied n VM slot free ε n VM slot re-location Re-locate VMs to avoid cost cross-server communication α > 1 13
The Model server ℓ occupied n VM slot free ε n VM slot α re-location Re-locate VMs to avoid cost cross-server communication α > 1 14
The Model server ℓ occupied n VM slot free ε n VM slot α re-location Re-locate VMs to avoid cost cross-server communication α > 1 15
The Model server ℓ occupied n VM slot free ε n VM slot re-location Re-locate VMs to avoid cost cross-server communication α > 1 16
The Model server ℓ occupied n VM slot free ε n VM slot α re-location Re-locate VMs to avoid cost cross-server communication α > 1 17
The Model server ℓ occupied n VM slot free ε n VM slot α re-location Re-locate VMs to avoid cost cross-server communication α > 1 18
The Model server ℓ occupied n VM slot free ε n VM slot re-location Re-locate VMs to avoid cost cross-server communication α > 1 19
The Model server ℓ occupied n VM slot • Internal server communication cost: free 0 ε n VM slot • Server-server communication cost: 1 • VM re-location cost: α ➡ Given an online sequence of communication requests, minimize total cost paid for communication α 1 0 20
The Model server ℓ occupied n VM slot • Internal server communication cost: free 0 ε n VM slot • Server-server communication cost: 1 After all • VM re-location cost: α communications finished: ➡ Given an online sequence of communication requests, 1 server = minimize total cost paid for communication 1 component 20
Analysis server ℓ occupied n VM slot free • Competitive analysis comparing to OPT: ε n VM slot • OPT knows all communications in advance • OPT computes solution with optimal cost ALG • (Strict) competitive ratio = OPT 21
Results server 2 occupied n VM slot • For servers: free ℓ = 2 ε n VM slot O ( ) log n • Algorithm which is -competitive ε • Lower bound: Any algorithm must be -competitive Ω (1/ ε + log n ) ➡ Our results are almost tight for two servers 22
Results server ℓ occupied n VM slot free • For servers: ℓ ε n VM slot O ( ( ℓ log n log ℓ )/ ε ) • Algorithm which is -competitive ➡ E ffi cient when is small, ℓ e.g., for communication across data centers ➡ Implementable for distributed computation ℓ = O ( ε n ) communication cost ≤ communication for re-locating VMs (if ) 23
Applications • Distributed Union Find Data Structure (with small cost for re-locating the sets across servers) • Online Balanced k-way Partition (with small cost for re-assigning numbers to balanced partitions) 24
Algorithm for Two Servers Color each VM based on its initial server 25
Algorithm for Two Servers 26
Algorithm for Two Servers 26
Algorithm for Two Servers Move small component to larger one 26
Algorithm for Two Servers Move small component to larger one 26
Algorithm for Two Servers Move small component to larger one 27
Algorithm for Two Servers Move small component to larger one 28
Algorithm for Two Servers Move small component to larger one 28
Algorithm for Two Servers Move small component to larger one 28
Algorithm for Two Servers Move small component to larger one 29
Algorithm for Two Servers Move small component to larger one 30
Algorithm for Two Servers 30
Algorithm for Two Servers 31
Algorithm for Two Servers Contains more yellow than green VMs 31
Algorithm for Two Servers Contains more yellow than green VMs Majority-voting step 31
Algorithm for Two Servers Contains more yellow than green VMs assign to yellow server Majority-voting step 31
Algorithm for Two Servers Contains more yellow than green VMs assign to yellow server Majority-voting step 32
Algorithm for Two Servers Contains more yellow than green VMs assign to yellow server Ensures that we stay Majority-voting step close to initial assignment 32
For each new communication request: • Move smaller component to the server of the larger one • If size of new component exceeds a power of 2: Perform majority-voting step • If server capacity exceeded: Find cheapest balanced Can only happen assignment using O ( ) log n times brute-force enumeration ε 33
Generalization to Servers ℓ S 0 S 1 S 2 S 3 S 4 S 5 S 6 S 7 34
Generalization to Servers ℓ S 0 S 1 S 2 S 3 S 4 S 5 S 6 S 7 34
Generalization to Servers ℓ S 0 S 1 S 2 S 3 S 4 S 5 S 6 S 7 34
Generalization to Servers ℓ S 0 S 1 S 2 S 3 S 4 S 5 S 6 S 7 Traverse tree from root downwards and perform majority voting step at each internal node 34
Generalization to Servers ℓ S 0 S 1 S 2 S 3 S 4 S 5 S 6 S 7 Traverse tree from root downwards and perform majority voting step at each internal node 34
Generalization to Servers ℓ S 0 S 1 S 2 S 3 S 4 S 5 S 6 S 7 Traverse tree from root downwards and perform majority voting step at each internal node 34
Recommend
More recommend
