### Abstract

We consider a system of N parallel servers, where each server consists of B units of a resource. Jobs arrive at this system according to a Poisson process, and each job stays in the system for an exponentially distributed amount of time. Each job may request different units of the resource from the system. The goal is to understand how to route arriving jobs to the servers to minimize the probability that an arriving job does not find the required amount of resource at the server, i.e., the goal is to minimize blocking probability. The motivation for this problem arises from the design of cloud computing systems in which the jobs are virtual machines (VMs) that request resources such as memory from a large pool of servers. In this paper, we consider power-ofdchoices routing, where a job is routed to the server with the largest amount of available resource among d ≥ 2 randomly chosen servers. We consider a fluid model that corresponds to the limit as N goes to infinity and provide an explicit upper bound for the equilibrium blocking probability. We show that the upper bound exhibits different behavior as B goes to infinity depending on the relationship between the total traffic intensity λ and B. In particular, if (B - λ)/√λ → α, the upper bound is doubly exponential in √λ and if (B - λ)/logd λ → β, β > 1, the upper bound is exponential in λ. Simulation results show that the blocking probability, even for small B, exhibits qualitatively different behavior in the two traffic regimes. This is in contrast with the result for random routing, where the blocking probability scales as O(1/√λ) even if (B - λ)/√λ → α.

Original language | English (US) |
---|---|

Pages (from-to) | 321-334 |

Number of pages | 14 |

Journal | Performance Evaluation Review |

Volume | 43 |

Issue number | 1 |

DOIs | |

State | Published - Jun 24 2015 |

Event | ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2015 - Portland, United States Duration: Jun 15 2015 → Jun 19 2015 |

### Fingerprint

### Keywords

- Fluid limit analysis
- Loss model
- Randomized algorithms
- Resource allocation
- Virtual machine assignment

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications

### Cite this

*Performance Evaluation Review*,

*43*(1), 321-334. https://doi.org/10.1145/2796314.2745849

**Power of d choices for large-scale bin packing : A loss model.** / Xie, Qiaomin; Dong, Xiaobo; Lu, Yi; Srikant, Rayadurgam.

Research output: Contribution to journal › Conference article

*Performance Evaluation Review*, vol. 43, no. 1, pp. 321-334. https://doi.org/10.1145/2796314.2745849

}

TY - JOUR

T1 - Power of d choices for large-scale bin packing

T2 - A loss model

AU - Xie, Qiaomin

AU - Dong, Xiaobo

AU - Lu, Yi

AU - Srikant, Rayadurgam

PY - 2015/6/24

Y1 - 2015/6/24

N2 - We consider a system of N parallel servers, where each server consists of B units of a resource. Jobs arrive at this system according to a Poisson process, and each job stays in the system for an exponentially distributed amount of time. Each job may request different units of the resource from the system. The goal is to understand how to route arriving jobs to the servers to minimize the probability that an arriving job does not find the required amount of resource at the server, i.e., the goal is to minimize blocking probability. The motivation for this problem arises from the design of cloud computing systems in which the jobs are virtual machines (VMs) that request resources such as memory from a large pool of servers. In this paper, we consider power-ofdchoices routing, where a job is routed to the server with the largest amount of available resource among d ≥ 2 randomly chosen servers. We consider a fluid model that corresponds to the limit as N goes to infinity and provide an explicit upper bound for the equilibrium blocking probability. We show that the upper bound exhibits different behavior as B goes to infinity depending on the relationship between the total traffic intensity λ and B. In particular, if (B - λ)/√λ → α, the upper bound is doubly exponential in √λ and if (B - λ)/logd λ → β, β > 1, the upper bound is exponential in λ. Simulation results show that the blocking probability, even for small B, exhibits qualitatively different behavior in the two traffic regimes. This is in contrast with the result for random routing, where the blocking probability scales as O(1/√λ) even if (B - λ)/√λ → α.

AB - We consider a system of N parallel servers, where each server consists of B units of a resource. Jobs arrive at this system according to a Poisson process, and each job stays in the system for an exponentially distributed amount of time. Each job may request different units of the resource from the system. The goal is to understand how to route arriving jobs to the servers to minimize the probability that an arriving job does not find the required amount of resource at the server, i.e., the goal is to minimize blocking probability. The motivation for this problem arises from the design of cloud computing systems in which the jobs are virtual machines (VMs) that request resources such as memory from a large pool of servers. In this paper, we consider power-ofdchoices routing, where a job is routed to the server with the largest amount of available resource among d ≥ 2 randomly chosen servers. We consider a fluid model that corresponds to the limit as N goes to infinity and provide an explicit upper bound for the equilibrium blocking probability. We show that the upper bound exhibits different behavior as B goes to infinity depending on the relationship between the total traffic intensity λ and B. In particular, if (B - λ)/√λ → α, the upper bound is doubly exponential in √λ and if (B - λ)/logd λ → β, β > 1, the upper bound is exponential in λ. Simulation results show that the blocking probability, even for small B, exhibits qualitatively different behavior in the two traffic regimes. This is in contrast with the result for random routing, where the blocking probability scales as O(1/√λ) even if (B - λ)/√λ → α.

KW - Fluid limit analysis

KW - Loss model

KW - Randomized algorithms

KW - Resource allocation

KW - Virtual machine assignment

UR - http://www.scopus.com/inward/record.url?scp=84955609288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955609288&partnerID=8YFLogxK

U2 - 10.1145/2796314.2745849

DO - 10.1145/2796314.2745849

M3 - Conference article

AN - SCOPUS:84955609288

VL - 43

SP - 321

EP - 334

JO - Performance Evaluation Review

JF - Performance Evaluation Review

SN - 0163-5999

IS - 1

ER -