Xiaoqiao Meng, Vasileios Pappas, Li Zhang IBM T.J. Watson
Research Center Improving the Scalability of Data Center Networks
with Traffic-aware Virtual Machine Placement IEEE INFOCOM 2010
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INTRODUCTION The scalability of modern data centers has become
a practical concern and has attracted significant attention in
recent years. existing solutions that require changes in the
network architecture and the routing protocols to balance traffic
load With an increasing trend towards more communication intensive
applications in data centers, the bandwidth usage between virtual
machines (VMs) is rapidly growing.
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INTRODUCTION This paper proposes using traffic-aware virtual
machine (VM) placement to improve the network scalability Many VM
placement solutions seek to consolidate VMs for CPU, physical
memory and power consumption savings, yet without considering
consumption of network resources This paper tackling the
scalability issue by optimizing the placement of VMs on host
machines.
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INTRODUCTION e.g. VMs with large mutual bandwidth usage are
assigned to host machines in close proximity design a two-tier
approximate algorithm that efficiently solves the VM placement
problem for very large problem sizes
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INTRODUCTION Contributions 1.We address the scalability issue
of data center networks with network-aware VM placement. We
formulate it as an optimization problem, prove its hardness and
propose a novel two-tier algorithm.
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INTRODUCTION Contributions 2.We analyze the impact of data
center network architectures and traffic patterns on the
scalability gains attained by network-aware VM placement.
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INTRODUCTION Contributions 3.We measure traffic patterns in
production data center environments, and use the data to evaluate
the proposed algorithm as well as the impact analysis.
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INTRODUCTION Problem definition: the Traffic-aware VM Placement
Problem (TVMPP) as an optimization problem. Input: traffic matrix,
cost matrix Output: where VMs should be placed Goal: minimize the
total cost
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Data Center Traffic Patterns Examine traces from two
data-center-like systems: 1. a data warehouse hosted by IBM Global
Services the incoming and outgoing traffic rates for 17 thousand
VMs 2. the incoming and outgoing TCP connections for 68 VMs 10 days
measurement
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Data Center Traffic Patterns Uneven distribution of traffic
volumes from VMs
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Data Center Traffic Patterns Stable per-VM traffic at large
timescale:
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Data Center Traffic Patterns Weak correlation between traffic
rate and latency:
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Data Center Traffic Patterns The potential benefit : increased
network scalability and reduced average traffic latency. The
observed traffic stability over large timescale suggests that it is
feasible to find good placements based on past traffic
statistics
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Data Center Network Architectures
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Problem Formulation Cij: the communication cost from slot i to
j Dij: traffic rate from VM i to j ei: external traffic rate for
VMi gi:communication cost between VMi and the gateway
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Problem Formulation The above objective function is equivalent
to X: permutation matrix
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Problem Formulation we define Cij as the number of switches on
the routing path from VM i to j. Accordingly, optimizing TVMPP is
equivalent to minimizing average traffic latency caused by network
infrastructure. Offline scenario & Online scenario
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Complexity Analysis TVMPP falls into the category of Quadratic
Assignment Problem (QAP) QAP: n things are put into n location,
with distance & flows NP-hard, finding the optimality of QAP
problems with size > 15 is practically impossible
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Complexity Analysis Theorem 1: For a TVMPP problem defined on a
data center that takes one of the topology in Figure 4, finding the
TVMPP optimality is NP-hard
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Theorem 1 This can be proved by a reduction from the Balanced
Minimum K-cut Problem (BMKP) BMKP: G = (V,E) undirected, weighted
graph with n vertices A k-cut on G is defined as a subset of E that
partition G into k components BMKP is NP-hard
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Theorem 1 Now considering a data center network, regardless of
which topology being used, we can always create a network topology
that satisfy: n slots that are partitioned into k slot-clusters of
equal size n/k Every two slots have a connection with certain cost
within the same cluster : ci across clusters cost: co co >
ci
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Theorem 1 Suppose there are n VMs with traffic matrix D. By
assigning these n VMs to the n slots, we obtain a TVMPP problem if
we define a graph with the n VMs as nodes and D as edge weights, we
obtain a BMKP problem It can be shown that when the TVMPP is
optimal, the associated BMKP is also optimal. And vise versa
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Theorem 1 when the TVMPP is optimal, if we swap any two VMs i,
j that have been assigned to two slot-cluster r1, r2 respectively,
the k-cut weight will increase. Let s1 denote the set of VMs
assigned to r1 Let s2 denote the set of VMs assigned to r2
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the TVMPP objective value increases: The amount of change for
the k-cut weight is:
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ALGORITHMS Proposition 1: Suppose 0 a1 a2... an and 0 b1 b2...
bn, the following inequalities hold for any permutation on [1,...,
n]
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ALGORITHMS First, according to Proposition 1, solving TVMPP is
intuitively equivalent to finding a mapping of VMs to slots such
that VM pairs with heavy mutual traffic be assigned to slot pairs
with low-cost connections.
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ALGORITHMS The second design principle is divide-and-conquer:
we partition VMs into VM-clusters and partition slots into slot
clusters. VM-clusters are obtained via classical min-cut graph
algorithm which ensures that VM pairs with high mutual traffic rate
are within the same VM cluster Slot-clusters are obtained via
standard clustering techniques which ensures slot pairs with
low-cost connections belong to the same slot-cluster
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ALGORITHMS SlotClustering: Minimum k-clustering,NP-hard. ( an
approximation ratio 2 ) O(nk) VMMinKcut: minimum k-cut algorithm
O(n4) Assign VMs to slots Recursive call
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ALGORITHMS
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IMPACT OF NETWORK ARCHITECTURES AND TRAFFIC PATTERNS Global
Traffic Model: each VM sends traffic to every other VM at equal and
constant rate For any permutation, matrix X, holds This simplifies
the TVMPP problem to the following:
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IMPACT OF NETWORK ARCHITECTURES AND TRAFFIC PATTERNS which is
the classical Linear Sum Assignment Problem (LSAP). The complexity
for LSAP is O(n3) Random placement:
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IMPACT OF NETWORK ARCHITECTURES AND TRAFFIC PATTERNS
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Partitioned Traffic Model: Under the partitioned traffic model,
each VM belongs to a group of VMs and it sends traffic only to
other VMs in the same group The GLB is a lower bound for the
optimal objective value of a QAP problem
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IMPACT OF NETWORK ARCHITECTURES AND TRAFFIC PATTERNS
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observation
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EVALUATION
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DISCUSSION Combining VM migration with dynamic routing
protocols VM placement by joint network and server resource
optimization:
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Amos Brocco, Apostolos Malatras, Ye Huang, Beat Hirsbrunner
Department of Informatics University of Fribourg, Switzerland ARiA:
A Protocol for Dynamic Fully Distributed Grid Meta-Scheduling ICDCS
2010
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INTRODUCTION An advantage of grid systems is their ability to
guarantee efficient meta-scheduling (optimal allocation of jobs
across a pool of sites with diverse local scheduling policies ) The
centralized nature of current meta-scheduling solutions is not well
suited for the envisioned increasing scale and dynamicity
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INTRODUCTION This paper focuses on grid task meta-scheduling,
by presenting a fully distributed protocol named ARiA to achieve
efficient global dynamic scheduling across multiple sites The
meta-scheduling process is performed online, and takes into account
the availability of new resources as well as changes in actual
allocation policies
Job Submission Phase Jobs are assigned a universal unique
identifier (UUID) Nodes receiving job submissions are referred to
as initiators for these jobs Initiators issue resource discovery
queries across the grid peer-to-peer overlay by broadcasting
REQUEST messages
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Job Acceptance Phase If the request cannot be satisfied, the
message is further forwarded on the peer-to-peer overlay otherwise
a cost value for the job based on actual resources and current
scheduling is computed and sent back to the jobs initiator by means
of an ACCEPT message The initiator evaluates incoming ACCEPT
responses, and selects the best qualified node, and sends an ASSIGN
message
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Dynamic Rescheduling Phase the assignee attempts to find
candidates for rescheduling of jobs in its queue while their
execution has not yet started by the INFORM messagges The structure
of INFORM messages relates to that of REQUEST messages
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EVALATION For the evaluation of ARiA, an overlay of 500 nodes
with a target average path length of 9 hops was deployed in a
custom simulator The average nodes degree attained during
simulations was 4, resulting in about 2000 overlay links
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EVALATION In all scenarios a total of 1000 jobs is submitted to
random nodes on the grid. Unless otherwise specified, jobs are
submitted at 10 seconds intervals when dynamic rescheduling is
enabled, INFORM messages are sent for at most 2 scheduled jobs
every 5 minutes
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EVALATION REQUEST messages are forwarded on the overlay for at
most 9 hops; at each step, at most 4 random neighbors of the
current node are contacted INFORM messages a more lightweight
approach is followed, with at most 8 hops and up to 2
neighbors
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EVALATION
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Amir Epstein Dean H. Lorenz Ezra Silvera Inbar Shapira
Virtualization Technologies, System Technologies & Services IBM
Haifa Research Lab, Haifa, Israel Virtual Appliance Content
Distribution for a Global Infrastructure Cloud Service IEEE INFOCOM
2010
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INTRODUCTION An emerging cloud service is a virtual server
shop, that allows cloud customers to order virtual appliances to be
delivered virtually on the cloud Global cloud providers need to
create customized virtual-server disk images and deliver them on
time to meet the customer reservations and service level In order
to reduce provisioning time and meet reservation deadlines, one
approach is to stage images on storage near the customer
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INTRODUCTION This introduces an optimization problem of finding
an optimal staging schedule, according to network bandwidth,
pending reservations schedule, and customer value Continuous model
vs integral model
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Problem Definition a staging storage space with capacity C n
appliance deployment requests Each request i is for an appliance
that consume Ci staging capacity and has a desired due date di
propagation time pi (assume pi = kCi)
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Continuous model
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Lemma 4.1: Any feasible schedule S can be turned into
right-tight feasible schedule by right-shifting job execution
intervals. Lemma 4.2: There exists an optimal schedule in which the
jobs are processed in EDD (Earliest Due Date) order
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Continuous model Algorithm 1 is a dynamic program that finds an
optimal schedule that is right-tight and in EDD order O(nW ) time
and space
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THE INTEGRAL MODEL p1=3, d1=5 p2=3, d2=8 P3=2, d3=9 Capacity =
5 s1=2, s2=5, s3=0 But can not be an EDD order
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SOLUTION Our algorithms for the integral model have two steps
In the first step, we solve the problem for the continuous model In
the second step, we discard jobs from this schedule, without losing
too much weight, to obtain a feasible schedule for the integral
model
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THE INTEGRAL MODEL Lemma 5.1: For unweighted jobs, any feasible
schedule S for the continuous model can be transformed to a
feasible schedule S for the integral model with w(S)>=1/2w(S).
Lemma 5.2: For weighted jobs, any feasible schedule S for the
continuous model can be transformed to a feasible schedule S* for
the integral model with w(S*)>=1/2w(S)
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