There is no asymptotic PTAS for two-dimensional vector packing
Information Processing Letters
On multi-dimensional packing problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Server load balancing
Parallel Query Scheduling and Optimization with Time- and Space-Shared Resources
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Combinatorial Auction-Based Protocols for Resource Allocation in Grids
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
The Architecture of Virtual Machines
Computer
Journal of Parallel and Distributed Computing - Special issue: Design and performance of networks for super-, cluster-, and grid-computing: Part II
Improved approximation algorithms for multidimensional bin packing problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Performance Guarantees of Local Search for Multiprocessor Scheduling
INFORMS Journal on Computing
Selfish Grids: Game-Theoretic Modeling and NAS/PSA Benchmark Evaluation
IEEE Transactions on Parallel and Distributed Systems
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Entropy: a consolidation manager for clusters
Proceedings of the 2009 ACM SIGPLAN/SIGOPS international conference on Virtual execution environments
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
An auction method for resource allocation in computational grids
Future Generation Computer Systems
Automatic virtual machine configuration for database workloads
ACM Transactions on Database Systems (TODS)
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Improving the scalability of data center networks with traffic-aware virtual machine placement
INFOCOM'10 Proceedings of the 29th conference on Information communications
Resource allocation algorithms for virtualized service hosting platforms
Journal of Parallel and Distributed Computing
HotCloud'09 Proceedings of the 2009 conference on Hot topics in cloud computing
On the packing of selfish items
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Power-efficient video encoding on resource-limited systems: A game-theoretic approach
Future Generation Computer Systems
Mechanism Design for Stochastic Virtual Resource Allocation in Non-cooperative Cloud Systems
CLOUD '11 Proceedings of the 2011 IEEE 4th International Conference on Cloud Computing
Energy-aware service allocation
Future Generation Computer Systems
VM: placement in non-Homogeneous Iaas-clouds
ICSOC'11 Proceedings of the 9th international conference on Service-Oriented Computing
Policy based resource allocation in IaaS cloud
Future Generation Computer Systems
Future Generation Computer Systems
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Virtualization technology is widely used in clusters, data centers and cloud computing environments and enables easy resource allocation to realize the server load balance and high consolidation by allocating virtual machines (VMs) to physical machines (PMs). In this work, motivated by the operation mechanism of the market setting, we study non-cooperative games amongst VMs on multidimensional resource allocation problems which arise in cloud computing environments. In our model, there are a set of VMs controlled by selfish agents, and each VM requires a d-dimensional vector of resource for running a job. The agent can decide to lessen its payoff by relocating the VM to another PM according to a payoff function. We consider two variants of resource allocation games: 1) server load balancing game, in which there are a number of machines, and the payoff function of an agent is the maximum load on any dimension on a machine and each agent would like to minimize its own payoff function by switching machines; 2) virtual machine placement game, in which each bin has a d-dimensional capacity, the payoff function of an agent is proportional to the portion of the bin it occupies in a given packing and the agent attempts to minimize its own payoff by choosing different bins if there is enough space available. We investigate the existence of a pure Nash equilibrium and measure the inefficiency of equilibria by the price of anarchy and the price of stability. The social cost for the server load balancing game is defined to be the maximum load on any dimension on a machine and the social cost for the virtual machine placement game is defined to be the number of bins that are not empty. We show that the price of stability is 1 for both games. The price of anarchy for the server load balancing game is at least d and at most d+1-d/m, where m is the number of machines. The price of anarchy for the virtual machine placement game is at least d and at most d+16/5. Finally, we set up experiments to illustrate the price of anarchy, the price of stability and the average ratio of an equilibria to the optimal solution. The experiment shows that the ratios under the Google trace workload, and the uniform distribution are much smaller than the worst case ratios.