Hierarchical Scheduling fo r Diverse Datacenter Workl oads

Hierarchical Scheduling fo r Diverse Datacenter Workl oads

Arka A. Bhattacharya, David Culler, Ali Ghodsi, Scott Shenker, and Ion Stoica

University of California, Berkeley

Eric Friedman

International Computer Science Institute, Berkeley

ACM SoCC’13

Hierarchical Scheduling

 A feature of cloud schedulers.

 Enables scheduling resources to re flect organizational priorities.

Hierarchical Share Guarant ee

 Assign to each node in the weighted tr ee some guaranteed share of the resour ces.

◦A node n_L is guaranteed to get at least x s hare of resources from it parent, where x e quals to

 W_i: weight of node n_i

 P(): parent of a node

 C(): the set of children of a node

 A(): the subset of demanding nodes

Example

 Given 480 servers

240

48

96

96 48

80

96 160

9 6 0

Multi-resource Scheduling

 Workloads in data centers tend to be diverse.

◦CPU-intensive, memory-intensive, or I /O intensive.

◦Ignoring the actual resource needs of jobs leads to poor performance isolat ion and low throughput for jobs.

Dominant Resource Fairness (DRF)

 A generalization of max-min fairne ss to multiple resource types.

 Maximize the minimum dominant shar es of users in the system.

◦Dominant share s_i is the maximum shar e of resource among all shares of a u ser.

◦Dominant resource is the resource cor responding to the dominant share.

} {

max ₁ ^,

j j m i

j

i r

s  _ u

Example

 Dominant resource

◦Job 1: memory

◦Job 2: CPU

 Dominant share

◦60%

How DRF Works

 Given a set of users, each with a resource demand vector.

◦The resources required to execute one job.

 Starts with every user being allocated with zero resources.

 Repeatedly picks the user with the lowest dominant share.

 Launches one of the user’s job if there are enough resources availab le in the system.

Example

 System with 9 CPUs and 18 GB RAM.

◦User A: <1 CPU, 4 GB>

◦User B: <3 CPUs, 1 GB>

Hierarchical DRF (H-DRF)

 Static H-DRF

 Collapsed hierarchies

 Naive H-DRF

 Dynamic H-DRF

Static H-DRF

 A static version of DRF to handle hierarchies.

 Algorithm

◦Given the hierarchy structure and the amount of resources in the system.

◦Starts with every leaf nodes being al located with zero resources.

◦Repeatedly allocates resource to a le af node until no more resources can b e assigned to any node.

Resource Allocation in Static H-D RF

 Start at the root of the tree and travers e down to a leaf.

 At each step picking the demanding child that has the smallest dominant share.

◦Internal nodes are assigned the sum of all th e resources assigned to their immediate child ren.

 Allocate the leaf node an ε amount of it s resource demands.

◦Increases the node’s dominant share by ε.

Example

 Given 10 CPUs and 10 GPUs.

Weakness of Static H-DRF

 Re-calculating the static H-DRF al locations for each of the leaves a nd arrivals from scratch is comput ationally infeasible.

Collapsed Hierarchies

 Converts a hierarchical scheduler into a flat one and apply weighted DRF algorithm.

◦Works when only one resource is invol ved.

◦Violates the hierarchical share guara ntee for internal nodes in the hierar chy.

Example

 Given

 Flatten

n_r

n_1,1 <1,1>

50%

n_2,1 <1,0>

25%

n_2,2 <0,1>

25%

Weighted DRF

 Each user i is associated a weight vector W_i = {w_i,1, … w_i,m}.

◦w_i,j represents the weight of user i fo r resource j.

 Dominant share max ₁{ ^, }

j j m i

j

i r

s  _ u

w_i,j

Weighted DRF in Collapsed Hierarc hies

 Each node n_i has a weight w_i.

◦Let w_i,j = w_i for 1≦j≦m

◦The ratio between dominated resources allocated to user a and user b equals to w_a/w_b.

} {

max ₁ ^,

i j m i

j

i w

s  _ u

Example

 Given

 Collapsed Hierarchies

n_r

n_1,1 <1,1>

50%

n_2,1 <1,0>

25%

n_2,2 <0,1>

25%

Naive H-DRF

 A natural adaptation of the origin al DRF to the hierarchical setting .

 The hierarchical share guarantee i s violated for leaf nodes.

◦Starvation

Example

 Static H-DRF

 Naive H-DRF

Dominate share = 1.0

Dynamic H-DRF

 Does not suffer from starvation.

 Satisfy the hierarchical share gua rantee.

 Two key features:

◦Rescaling to minimum nodes

◦Ignoring blocked nodes

Rescaling to Minimum Nodes

 Compute the resource consumption o f an internal node as follows:

◦Find the demanding child with minimum dominant share M.

◦Rescale every child’s resource consu mption vector so that its dominant sh are becomes M.

◦Add all the children’s rescaled vect ors to get the internal node’s resou rce consumption vector.

Example

 Given 10 CPUs and 10 GPUs.

 After n_2,1 finishes a job and relea se 1 CPU:

<0.4, 0>

<0, 1>

<0, 1>

<0, 0.4>

<0.4, 0.4>

Dominate share =

<0.5, 0.4 0>

Dominate share = 0.5

Ignoring Blocked Nodes

 Dynamic H-DRF only consider non-bl ocked nodes for rescaling.

 A leaf node is blocked if either

◦Any of the resources it requires are saturated.

◦The node is non-demanding.

 An internal node is blocked if all of its children are blocked.

Example

 Static H-DRF

 Without blocked

Dominate share = 1/3

Allocation Properties

 Hierarchical Share Guarantees

 Group Strategy-proofness

◦No group of users can misrepresent their resource requirements in such a way that all of them are weakly better off, and at least one of them is strictly better off.

 Recursive Scheduling

 Not Population Monotonicity

◦ PM: Any node exiting the system should not decrease the resource allocation to any other node in the hie rarchy tree.

Example

Evaluation - Hierarchical Sharing

 49 Amazon EC2 severs

◦Dominant resource:

 n_1,1, n_2,1, n_2,2: CPU

 n_1,2: GPU

Result

 pareto-efficiency: no node in the hierarchy can be allocat ed an extra task on the cluster without reducing the share of some other node.

Conclusion

 Proposed H-DRF, which is a hierarc hical multi-resource scheduler.

◦Avoid job starvation and maintain hie rarchical share guarantee.

 Future works

◦DRF under placement constraints.

◦Efficient allocation vector update.