## On the Analysis of Randomized Load Balancing Schemes (1998)

### Cached

### Download Links

- [ftp.digital.com]
- [gatekeeper.research.compaq.com]
- [apotheca.hpl.hp.com]
- [www.eecs.harvard.edu]
- [www.hpl.hp.com]
- DBLP

### Other Repositories/Bibliography

Venue: | IN PROCEEDINGS OF THE 9TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES |

Citations: | 56 - 7 self |

### BibTeX

@INPROCEEDINGS{Mitzenmacher98onthe,

author = {Michael Mitzenmacher},

title = {On the Analysis of Randomized Load Balancing Schemes},

booktitle = {IN PROCEEDINGS OF THE 9TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES},

year = {1998},

pages = {292--301},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends a previous analysis of the supermarket model, a model that abstracts a simple, efficient load balancing scheme in the setting where jobs arrive at a large system of parallel processors. In this model, customers arrive at a system of n servers as a Poisson stream of rate #n, # < 1, with service requirements exponentially distributed with mean 1. Each customer chooses d servers independently and uniformly at random from the n servers, and is served according to the First In First Out (FIFO) protocol at the choice with the fewest customers. For the supermarket model, it has been shown that using d = 2 choices yields an exponential improvement in the expected time a customer spends in the syst...

### Citations

593 | Reversibility and Stochastic Networks - Kelly - 1979 |

413 | Queueing Systems (Volume I: Theory - Kleinrock - 1975 |

395 |
Adaptive Load Sharing in Homogeneous Distributed Systems
- Eager, Lazowska, et al.
- 1986
(Show Context)
Citation Context ...tributing the workload through load balancing can lead to significant performance improvements, in terms of both the mean and standard deviation of the time jobs spend in the system (for example, see =-=[7, 35]-=-). Moreover, simple randomized schemes with low overhead have proven effective in simulations; however, analyzing such schemes is often difficult. In this paper, we provide new analyses for several dy... |

262 | Balanced allocations
- Azar, Broder, et al.
(Show Context)
Citation Context ... two hash functions instead of one could provide an exponential improvement in the maximum load of a hash bucket [13]; this idea was further developed and aanalyzed by Azar, Broder, Karlin, and Upfal =-=[5]-=-. Our work demonstrates that making two choices leads to a similar exponential improvement in the dynamic setting as well. The justification of the relationship between the finite and limiting systems... |

208 | The power of two choices in randomized load balancing
- Mitzenmacher
(Show Context)
Citation Context ...milar to those for the static load balancing problem studied in [5]. Simulations verify that this behavior is apparent even in small systems; for example, see Figure 2. More details are given [27] or =-=[28]-=-. 3 Constant service times The assumptions underlying the supermarket model, namely that the arrival process is Poisson and that the service times are exponentially distributed, do not accurately desc... |

143 |
An optimal algorithm for on-line bipartite matching
- Karp, Vazirani, et al.
- 1990
(Show Context)
Citation Context ...to the load balancing problem. More details regarding the application of Kurtz's work these models can be found in [28]. This approach has been used similarly in several other works (for example, see =-=[4, 11, 14, 15, 27, 31, 33, 34]-=-). The rest of the paper proceeds as follows: in Section 2, we briefly review the work of [27] by examining the limiting system for the supermarket model. This allows us to introduce the necessary ter... |

142 |
A trace driven simulation study of dynamic load balancing
- Zhou
- 1988
(Show Context)
Citation Context ...tributing the workload through load balancing can lead to significant performance improvements, in terms of both the mean and standard deviation of the time jobs spend in the system (for example, see =-=[7, 35]-=-). Moreover, simple randomized schemes with low overhead have proven effective in simulations; however, analyzing such schemes is often difficult. In this paper, we provide new analyses for several dy... |

140 | Large Deviations for Performance Analysis
- Shwartz, Weiss
- 1995
(Show Context)
Citation Context ...to the load balancing problem. More details regarding the application of Kurtz's work these models can be found in [28]. This approach has been used similarly in several other works (for example, see =-=[4, 11, 14, 15, 27, 31, 33, 34]-=-). The rest of the paper proceeds as follows: in Section 2, we briefly review the work of [27] by examining the limiting system for the supermarket model. This allows us to introduce the necessary ter... |

134 |
Solutions of ordinary differential equations as limits of pure jump Markov processes
- Kurtz
- 1970
(Show Context)
Citation Context ...exponential improvement in the dynamic setting as well. The justification of the relationship between the finite and limiting systems relies on Kurtz's work on density dependent jump Markov processes =-=[10, 19, 20, 21, 22]-=-. Because Kurtz's work is rather technical, we only briefly describe it here, focusing instead on examining a variety of models and attempting to gain insight into the load balancing problem. More det... |

132 | A Comparison of Receiver-Initiated and Sender Initiated Adaptive Load Sharing,” Performance Evaluation
- Eager, Lazowski, et al.
- 1986
(Show Context)
Citation Context ...vious work Distributed load balancing strategies where individual customer decisions are based on information about a limited number of other processors have been studied analytically by Eager et al. =-=[7, 8, 9]-=- and through tracedriven simulations by Zhou [35]. In fact, Eager et al. also use Markovian models for their analysis [7, 8, 9]; however, the authors derive their results assuming that the state of ea... |

120 |
Differential equations for random processes and random
- Wormald
- 1995
(Show Context)
Citation Context ...to the load balancing problem. More details regarding the application of Kurtz's work these models can be found in [28]. This approach has been used similarly in several other works (for example, see =-=[4, 11, 14, 15, 27, 31, 33, 34]-=-). The rest of the paper proceeds as follows: in Section 2, we briefly review the work of [27] by examining the limiting system for the supermarket model. This allows us to introduce the necessary ter... |

104 | The limited performance benefits of migrating active processes for load sharing
- Lazowska, Eager, et al.
(Show Context)
Citation Context ...vious work Distributed load balancing strategies where individual customer decisions are based on information about a limited number of other processors have been studied analytically by Eager et al. =-=[7, 8, 9]-=- and through tracedriven simulations by Zhou [35]. In fact, Eager et al. also use Markovian models for their analysis [7, 8, 9]; however, the authors derive their results assuming that the state of ea... |

99 |
The Influence of Different Workload Descriptions on a Heuristic Load Balancing Scheme
- Kunz
- 1991
(Show Context)
Citation Context ...ld set for each choice, up to any fixed number of choices; here we model only the case where a customer has at most two choices. Although threshold systems have been shown to perform well in practice =-=[7, 18, 35]-=-, our results distinguishing these two models are new. 5.1 Limiting systems We consider the limiting system for the weak threshold model. The rate at which a queue changes size depends on whether it h... |

90 | How useful is old information
- Mitzenmacher
(Show Context)
Citation Context ... move to a server is zero, and that the servers are homogeneous. Many of our techniques, however, generalize to more complex systems, such as systems where transferring a customer incurs a delay (see =-=[24]-=-). Moreover, 2 even the simple systems we study demonstrate remarkably interesting behavior. In particular, we emphasize throughout that there is often a qualitative difference between systems where c... |

88 |
auf der Heide. Efficient PRAM simulation on a distributed memory machine
- Karp, Luby, et al.
- 1992
(Show Context)
Citation Context ...a static hash table. For example, Karp, Luby, and Meyer auf der Heide showed that using two hash functions instead of one could provide an exponential improvement in the maximum load of a hash bucket =-=[13]-=-; this idea was further developed and aanalyzed by Azar, Broder, Karlin, and Upfal [5]. Our work demonstrates that making two choices leads to a similar exponential improvement in the dynamic setting ... |

86 |
Maximum matchings in sparse random graphs
- Karp, Sipser
- 1981
(Show Context)
Citation Context |

72 |
Queueing system with selection of the shortest of two queues: An asymptotic approach. Problems Inform. Transmission 32
- Vvedenskaya, Dobrushin, et al.
- 1996
(Show Context)
Citation Context |

69 |
Strong approximation theorems for density dependent markov chains, Stochastic Process
- Kurtz
- 1978
(Show Context)
Citation Context ...exponential improvement in the dynamic setting as well. The justification of the relationship between the finite and limiting systems relies on Kurtz's work on density dependent jump Markov processes =-=[10, 19, 20, 21, 22]-=-. Because Kurtz's work is rather technical, we only briefly describe it here, focusing instead on examining a variety of models and attempting to gain insight into the load balancing problem. More det... |

69 |
Approximation of population processes
- Kurtz
- 1981
(Show Context)
Citation Context ...exponential improvement in the dynamic setting as well. The justification of the relationship between the finite and limiting systems relies on Kurtz's work on density dependent jump Markov processes =-=[10, 19, 20, 21, 22]-=-. Because Kurtz's work is rather technical, we only briefly describe it here, focusing instead on examining a variety of models and attempting to gain insight into the load balancing problem. More det... |

55 |
Limit theorems for sequences of jump markov processes approximating ordinary diffusion processes
- Kurtz
- 1971
(Show Context)
Citation Context |

49 | Qualitative Analysis of Large Scale Dynamical Systems - Michel, Miller - 1977 |

38 |
Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies
- Stamoulis, N
- 1991
(Show Context)
Citation Context ...mes reduce the expected delay in comparison to exponential service times often arises when one tries to use standard queueing theory results to find performance bounds on networks. (See, for example, =-=[12, 25, 26, 29, 32]-=-.) Generally, results comparing various service times are achieved using stochastic comparison techniques. Here, we instead compare the fixed points of the corresponding limiting systems. We show that... |

31 | Bounds on the greedy routing algorithm for array networks
- Mitzenmacher
- 1996
(Show Context)
Citation Context ...mes reduce the expected delay in comparison to exponential service times often arises when one tries to use standard queueing theory results to find performance bounds on networks. (See, for example, =-=[12, 25, 26, 29, 32]-=-.) Generally, results comparing various service times are achieved using stochastic comparison techniques. Here, we instead compare the fixed points of the corresponding limiting systems. We show that... |

29 | Analysis of simple algorithms for dynamic load balancing
- Alanyali, Hajek
- 1998
(Show Context)
Citation Context |

28 | Bounding Delays in Packet Routing Networks
- Harchol-Balter, Wolfe
- 1995
(Show Context)
Citation Context ...mes reduce the expected delay in comparison to exponential service times often arises when one tries to use standard queueing theory results to find performance bounds on networks. (See, for example, =-=[12, 25, 26, 29, 32]-=-.) Generally, results comparing various service times are achieved using stochastic comparison techniques. Here, we instead compare the fixed points of the corresponding limiting systems. We show that... |

22 |
Analysis of the symmetric shortest queue problem, Stochastic Models 6
- Adan, Wessels, et al.
- 1990
(Show Context)
Citation Context ..., perform extremely well. In another well-studied model, incoming customers join the shortest queue; see, for example, the work by Adan, van Houtum, and van der Wal [1] and by Adan, Wessels, and Zijm =-=[2, 3]-=- for results and further references. The shortest queue model appears more applicable to centralized systems, whereas the limited coordination enforced by our model corresponds nicely to models of dis... |

20 |
Analysis of the asymmetric shortest queue problem, Queueing Systems Theory
- Adan, Wessels, et al.
- 1991
(Show Context)
Citation Context ..., perform extremely well. In another well-studied model, incoming customers join the shortest queue; see, for example, the work by Adan, van Houtum, and van der Wal [1] and by Adan, Wessels, and Zijm =-=[2, 3]-=- for results and further references. The shortest queue model appears more applicable to centralized systems, whereas the limited coordination enforced by our model corresponds nicely to models of dis... |

18 | Load profiling: A methodology for scheduling real-time tasks in a distributed system
- Bestavros
- 1997
(Show Context)
Citation Context ...many load balancing scenarios. Indeed, the effectiveness of this general approach has been noted recently in practical load balancing scenarios [30] as well as for load profiling in real-time systems =-=[6]-=-. Although our methodology has been successful for several models, there remain several open questions. We conjecture that the closed model and the weak threshold model converge exponentially, althoug... |

17 |
Extremal properties of the FIFO discipline in queueing networks
- Righter, Shanthikumar
- 1992
(Show Context)
Citation Context |

13 |
Upper and lower bounds for the waiting time in the symmetric shortest queue system
- ADAN, HOUTUM, et al.
- 1994
(Show Context)
Citation Context ...g from a small subset of processors, perform extremely well. In another well-studied model, incoming customers join the shortest queue; see, for example, the work by Adan, van Houtum, and van der Wal =-=[1]-=- and by Adan, Wessels, and Zijm [2, 3] for results and further references. The shortest queue model appears more applicable to centralized systems, whereas the limited coordination enforced by our mod... |

13 |
Asymptotic Analysis of an Assignment Problem Arising in a Distributed Communications
- Hajek
- 1988
(Show Context)
Citation Context |

13 |
Density dependent jump markov processes and applications to load balancing
- Mitzenmacher
- 1996
(Show Context)
Citation Context ...ike previous similar analyses, we do not assume that in equilibrium each server is stochastically independent from other servers. One example of the type of problem we consider, previously studied in =-=[27]-=-, is the following natural dynamic model: customers arrive as a Poisson stream of rate #n, where #s1, at a collection of n servers. The service times for the customers are independent and exponentiall... |

12 | Constant time per edge is optimal on rooted tree networks
- Mitzenmacher
- 1996
(Show Context)
Citation Context |

1 |
Design of the RIO (Randomized I/O) storage server. Computer science division
- Santos, Muntz
- 1997
(Show Context)
Citation Context ...sample of possible destinations will prove effective in many load balancing scenarios. Indeed, the effectiveness of this general approach has been noted recently in practical load balancing scenarios =-=[30]-=- as well as for load profiling in real-time systems [6]. Although our methodology has been successful for several models, there remain several open questions. We conjecture that the closed model and t... |