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72
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 20 (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.
The Asymptotics of Selecting the Shortest of Two, Improved
 UNIVERSITY OF ILLINOIS
, 1999
"... We investigate variations of a novel, recently proposed load balancing scheme based on small amounts of choice. The static setting is modeled as a ballsandbins process. The balls are sequentially placed into bins, with each ball selecting d bins randomly and going to the bin with the fewest balls. ..."
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Cited by 18 (7 self)
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We investigate variations of a novel, recently proposed load balancing scheme based on small amounts of choice. The static setting is modeled as a ballsandbins process. The balls are sequentially placed into bins, with each ball selecting d bins randomly and going to the bin with the fewest balls. A similar dynamic setting is modeled as a scenario where tasks arrive as a Poisson process at a bank of FIFO servers and queue at one for service. Tasks probe a small random sample of servers in the bank and queue at the server with the fewest tasks. Recently
Fast Jackson Networks
 Annals of Applied Probability
, 1998
"... this paper, we consider networks of Jackson type whose nodes are stations of this kind, and show that flexibility of routing leads to improvement in network performance in a similar way. ..."
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Cited by 15 (2 self)
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this paper, we consider networks of Jackson type whose nodes are stations of this kind, and show that flexibility of routing leads to improvement in network performance in a similar way.
Practical load balancing for content requests in peertopeer networks
"... This paper studies the problem of balancing the demand for content in a peertopeer network across heterogeneous peer nodes that hold replicas of the content. Previous decentralized load balancing techniques in distributed systems base their decisions on periodic updates containing information ab ..."
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Cited by 15 (1 self)
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This paper studies the problem of balancing the demand for content in a peertopeer network across heterogeneous peer nodes that hold replicas of the content. Previous decentralized load balancing techniques in distributed systems base their decisions on periodic updates containing information about load or available capacity observed at the serving entities. We show that these techniques do not work well in the peertopeer context; either they do not address peer node heterogeneity, or they suffer from significant load oscillations which result in unutilized capacity. We propose a new decentralized algorithm, MaxCap, based on the maximum inherent capacities of the replica nodes. We show that unlike previous algorithms, it is not tied to the timeliness or frequency of updates, and consequently requires significantly less update overhead. Yet, MaxCap can handle the heterogeneity of a peertopeer environment without suffering from load oscillations.
Load Balancing with Memory
 In Proc. of the 43rd IEEE Symp. on Foundations of Computer Science (FOCS
, 2002
"... A standard load b lancing model considers placing n b lls into nb[K y choosing d possib: locations for eachb all independently and uniformly at random and sequentially placing each in the least loaded of its chosenb ins. It is well known that allowing just a small amount of choice (d = 2) greatly ..."
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Cited by 13 (2 self)
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A standard load b lancing model considers placing n b lls into nb[K y choosing d possib: locations for eachb all independently and uniformly at random and sequentially placing each in the least loaded of its chosenb ins. It is well known that allowing just a small amount of choice (d = 2) greatly improves performance over random placement (d = 1). In this paper, we show that similar performance gains occurb y introducing memory. We focus on the situation where each time ab all is placed, the least loaded of that b ll's choices after placement is rememb ered and used as one of the possibH choices for the nextb all. For example, we show that when eachb all gets just one random choice,be can also choose theb est of the lastb all's choices, the maximum numb er ofb alls in ab in is log log n/2log# +O(1) with high pro bbU:: y, where # =(1+ # 5)/2 is the golden ratio. The asymptotic performance is thereforeb etter with one random choice and one choice from memory than with two fresh random choices for eachb all; the performance with memory asymptotically matches the asymmetric policy using two choices introducedb y Vocking. More generally, we find that a small amount of memory, like a small amount of choice, can dramatically improve the loadb alancing performance. We also investigate continuous time variations corresponding to queueing systems, where we find similar results. 1
Asynchronous scheduling of redundant disk arrays
, 2000
"... Random redundant allocation of data to parallel disk arrays can be exploited to achieve low access delays. New algorithms are proposed which improve the previously known shortest queue algorithm by systematically exploiting that scheduling decisions can be deferred until a block access is actually s ..."
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Cited by 13 (5 self)
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Random redundant allocation of data to parallel disk arrays can be exploited to achieve low access delays. New algorithms are proposed which improve the previously known shortest queue algorithm by systematically exploiting that scheduling decisions can be deferred until a block access is actually started on a disk. These algorithms are also generalized for coding schemes with low redundancy. Using extensive experiments, practically important quantities are measured which have so far eluded an analytical treatment: The delay distribution when a stream of requests approaches the limit of the sytem capacity, the system efficiency for parallel disk applications with bounded prefetching buffers, and the combination of both for mixed traffic. A further step towards practice is taken by outlining the system design for α: automatically loadbalanced parallel harddisk array. 1
Reducing network congestion and blocking probability through balanced allocation
 in: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, FOCS
, 1999
"... We compare the performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks to a path selection algorithm that is based on the balanced allocations principle [4, 18] the Balanced Dynamic Alternative Routing (BDAR) algorithm. While ..."
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Cited by 12 (3 self)
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We compare the performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks to a path selection algorithm that is based on the balanced allocations principle [4, 18] the Balanced Dynamic Alternative Routing (BDAR) algorithm. While the standard technique checks alternative routes sequentially until available bandwidth is found, the BDAR algorithm compares and chooses the best among a small number of alternatives. We show that, at the expense of a minor increase in routing overhead, the BDAR gives a substantial improvement in network performance in terms of both network congestion and blocking probabilities. 1
On the power of two choices: balls and bins in continuous time
, 2005
"... Suppose that there are n bins, and balls arrive in a Poisson process at rate λn, whereλ>0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is placed into one with least load. Balls have independent exponential lifetimes with unit mean. We show that the system co ..."
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Cited by 11 (2 self)
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Suppose that there are n bins, and balls arrive in a Poisson process at rate λn, whereλ>0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is placed into one with least load. Balls have independent exponential lifetimes with unit mean. We show that the system converges rapidly to its equilibrium distribution; and when d ≥ 2, there is an integervalued function md(n) = ln ln n/ln d + O(1) such that, in the equilibrium distribution, the maximum load of a bin is concentrated on the two values md(n) and md(n) − 1, with probability tending to 1, as n →∞. We show also that the maximum load usually does not vary by more than a constant amount from ln ln n/ln d, even over quite long periods of time. 1. Introduction. Ballsandbins processes have been useful for modeling and analyzing a wide range of problems, in discrete mathematics, computer science and communication theory, and, in particular, for problems which involve load sharing, see, for example, [4, 5, 12, 15–17, 22]. Here is one central result, from [3]. Let d be a fixed integer at least 2. Suppose that there are n bins, and n balls arrive
On the maximum queue length in the supermarket model
, 2004
"... There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where0<λ<1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distrib ..."
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Cited by 8 (2 self)
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There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where0<λ<1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with probability tending to 1 as n →∞the maximum queue length takes at most two values, which are ln ln n / ln d + O(1). 1. Introduction. We
Stochastic Models for the design and management of customer contact centers: some research directions
 February 2005a. URL: http://www.columbia.edu/˜ww2040/submissionREV.pdf
, 2002
"... A (customer) contact center is a collection of resources providing an interface between a service provider and its customers. The classical contact center is a call center, containing a collection of service representatives (reps) who talk to customers over the telephone. In a call center, the servi ..."
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Cited by 7 (0 self)
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A (customer) contact center is a collection of resources providing an interface between a service provider and its customers. The classical contact center is a call center, containing a collection of service representatives (reps) who talk to customers over the telephone. In a call center, the service reps are supported by quite elaborate informationandcommunicationtechnology (ICT) equipment, such as a private branch exchange (PBX), an interactive voice response (IVR) unit, an automatic call distributor (ACD), a personal computer (PC) and assorted databases. With the rapid growth of ecommerce, contact between the service provider and its customers if often made via email or the Internet instead of by telephone. Thus the general interface between a service provider and its customers is now often called a contact center. The design and management of contact centers is important, and worthy of research, because contact centers comprise a large, growing part of the economy and because they are quite complicated. Classic call centers are complicated because