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32
The Power of Two Random Choices: A Survey of Techniques and Results
 in Handbook of Randomized Computing
, 2000
"... ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately ..."
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Cited by 137 (6 self)
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ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...
How Useful Is Old Information
 IEEE Transactions on Parallel and Distributed Systems
, 2000
"... AbstractÐWe consider the problem of load balancing in dynamic distributed systems in cases where new incoming tasks can make use of old information. For example, consider a multiprocessor system where incoming tasks with exponentially distributed service requirements arrive as a Poisson process, the ..."
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Cited by 108 (9 self)
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AbstractÐWe consider the problem of load balancing in dynamic distributed systems in cases where new incoming tasks can make use of old information. For example, consider a multiprocessor system where incoming tasks with exponentially distributed service requirements arrive as a Poisson process, the tasks must choose a processor for service, and a task knows when making this choice the processor queue lengths from T seconds ago. What is a good strategy for choosing a processor in order for tasks to minimize their expected time in the system? Such models can also be used to describe settings where there is a transfer delay between the time a task enters a system and the time it reaches a processor for service. Our models are based on considering the behavior of limiting systems where the number of processors goes to infinity. The limiting systems can be shown to accurately describe the behavior of sufficiently large systems and simulations demonstrate that they are reasonably accurate even for systems with a small number of processors. Our studies of specific models demonstrate the importance of using randomness to break symmetry in these systems and yield important rules of thumb for system design. The most significant result is that only small amounts of queue length information can be extremely useful in these settings; for example, having incoming tasks choose the least loaded of two randomly chosen processors is extremely effective over a large range of possible system parameters. In contrast, using global information can actually degrade performance unless used carefully; for example, unlike most settings where the load information is current, having tasks go to the apparently least loaded server can significantly hurt performance. Index TermsÐLoad balancing, stale information, old information, queuing theory, large deviations. æ 1
On the Analysis of Randomized Load Balancing Schemes
 IN PROCEEDINGS OF THE 9TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1998
"... 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 ..."
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Cited by 59 (7 self)
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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...
Studying Balanced Allocations with Differential Equations
 COMBINATORICS, PROBABILITY, AND COMPUTING
, 1997
"... Using differential equations, we examine the GREEDY algorithm studied by Azar, Broder, Karlin, and Upfal for distributed load balancing [1]. This approach yields accurate estimates of the actual load distribution, provides insight into the exponential improvement GREEDY offers over simple random sel ..."
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Cited by 27 (3 self)
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Using differential equations, we examine the GREEDY algorithm studied by Azar, Broder, Karlin, and Upfal for distributed load balancing [1]. This approach yields accurate estimates of the actual load distribution, provides insight into the exponential improvement GREEDY offers over simple random selection, and allows one to prove tight concentration theorems about the loads in a straightforward manner.
Analyses of Load Stealing Models Based on Differential Equations
 In Proceedings of the 10th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1998
"... In this paper we develop models for and analyze several randomized work stealing algorithms in a dynamic setting. Our models represent the limiting behavior of systems as the number of processors grows to infinity using differential equations. The advantages of this approach include the ability to m ..."
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Cited by 24 (0 self)
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In this paper we develop models for and analyze several randomized work stealing algorithms in a dynamic setting. Our models represent the limiting behavior of systems as the number of processors grows to infinity using differential equations. The advantages of this approach include the ability to model a large variety of systems and to provide accurate numerical approximations of system behavior even when the number of processors is relatively small. We show how this approach can yield significant intuition about the behavior of work stealing algorithms in realistic settings.
ON LARGE DEVIATIONS IN LOAD SHARING NETWORKS
, 1998
"... Three policies, namely optimal repacking, least load routing, and Bernoulli splitting, are considered for dynamic resource allocation in load sharing networks with standard Erlang type statistics. Large deviations principles are established for the three policies in a simple network of three consume ..."
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Cited by 7 (1 self)
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Three policies, namely optimal repacking, least load routing, and Bernoulli splitting, are considered for dynamic resource allocation in load sharing networks with standard Erlang type statistics. Large deviations principles are established for the three policies in a simple network of three consumer types and two resource locations and are used to identify the network overflow exponents. The overflow exponents for networks with arbitrary topologies are identified for optimal repacking and Bernoulli splitting policies and conjectured for the least load routing policy.
Predictive routing to enhance QoS for streambased flows sharing excess bandwidth
 COMPUTER NETWORKS
, 2003
"... We propose a new routing algorithm based on online estimation of the link load dynamics and prior information on flow holding times. The motivation for this proposal lies in supporting traffic flows such as VBR or associated with rate adaptive applications. Such traffic requires a minimalgumal4qN) ..."
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Cited by 4 (0 self)
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We propose a new routing algorithm based on online estimation of the link load dynamics and prior information on flow holding times. The motivation for this proposal lies in supporting traffic flows such as VBR or associated with rate adaptive applications. Such traffic requires a minimalgumal4qN) bandwidth,bu can see improved performance when sharing excess bandwidth not ut4 to meet gu4q#Nq4k The key ideaua4j#BNj4 ou approach is to rouB traffic flows so that they see minimal expected flowperceived loads duds4 theirsojouq in the network. To this end we establish a rou5() framework where links estimate and advertise the parameters associated with their load dynamics in addition to their current load. New flows are rouB( based on this information and prior knowledge of their holding times so as to minimize the expected flowperceived load.SimuqB#(B4 of thisrou4q scheme in a (weighted) maxmin bandwidth sharing framework show gains of 2050% in the average flow bandwidth share over baseline routing schemes.
On Load Balancing in Erlang Networks
"... This chapter summarizes our recent work on the dynamic resource allocation problem. The question of interest is the performance of simple allocation strategies which can be implemented online. The chapter focuses on the least load routing policy. The analysis is based on fluid limit equations and t ..."
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Cited by 4 (0 self)
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This chapter summarizes our recent work on the dynamic resource allocation problem. The question of interest is the performance of simple allocation strategies which can be implemented online. The chapter focuses on the least load routing policy. The analysis is based on fluid limit equations and the theory of large deviations for Markov processes with discontinuous statistics.
Connectivity, performance, and resiliency of ipbased cdma radio access
 in Proceedings of IEEE Infocom
, 2004
"... Abstract—IPbased Radio Access Networks (RAN) are expected to be the next generation access networks in UMTS and CDMA networks. The question of connectivity, i.e., how best to connect base stations to the Radio Network Controllers (RNC) in an IPbased RAN, has not been addressed by researchers. Furt ..."
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Cited by 3 (1 self)
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Abstract—IPbased Radio Access Networks (RAN) are expected to be the next generation access networks in UMTS and CDMA networks. The question of connectivity, i.e., how best to connect base stations to the Radio Network Controllers (RNC) in an IPbased RAN, has not been addressed by researchers. Furthermore, given a connection configuration, an RNC selection algorithm that assigns an incoming call to an RNC is also necessary. This paper examines RAN connectivity and its impact on the performance and resiliency of the wireless network using different RNC selection algorithms. For homogeneous networks, we show that the proposed MinLoad1 algorithm, which allows at most one hard handoff in order to accommodate each incoming call request, delivers performance close to the optimal algorithm. We also show that allowing a few base stations to connect to two RNCs (a 10 percent increase in the number of links in our network) results in resiliency to RNC failures that is comparable to the resiliency of RANs with fullmesh connectivity. Finally, for heterogeneous networks, we show that the MinLoadk algorithm (with at most k hard handoffs per call) is effective in handling load imbalances. These results provide strong motivation for deploying IPbased RAN, as they suggest that enhancing current pointtopoint RAN with few additional links and allowing a few hard handoffs to accommodate incoming calls can result in significant gains in performance and resiliency. Index Terms—CDMA IPbased RAN, connectivity, resiliency, RNC selection algorithms. 1