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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 139 (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.,...
On Choosing a Task Assignment Policy for a Distributed Server System
, 1999
"... We consider a distributed server system model and ask which policy should be used for assigning tasks to hosts. In our model each host processes tasks in FirstComeFirstServe order and the task's service demand is known in advance. We consider four task assignment policies commonly proposed f ..."
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Cited by 136 (21 self)
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We consider a distributed server system model and ask which policy should be used for assigning tasks to hosts. In our model each host processes tasks in FirstComeFirstServe order and the task's service demand is known in advance. We consider four task assignment policies commonly proposed for such distributed server systems: RoundRobin, Random, SizeBased, in which all tasks within a give size range are assigned to a particular host, and DynamicLeastWorkRemaining, in which a task is assigned to the host with the least outstanding work. Our goal is to understand the influence of task size variability on the decision of which task assignment policy is best. We evaluate the above policies using both analysis and simulation. We find that no one of the above task assignment policies is best and that the answer depends critically on the variability in the task size distribution. In particular we find that when the task sizes are not highly variable, the Dynamic policy is preferable. ...
To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems
 INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE, SPRINGER (HARDCOVER) 16 C.H. (2006), “HETEROGENEOUS AGENT MODELS IN ECONOMICS AND FINANCE,” HANDBOOK OF COMPUTATIONAL ECONOMICS, LEIGH TESFATSION
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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 107 (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
Task Assignment with Unknown Duration
 Journal of the ACM
, 2000
"... We consider a distributed server system and ask which policy should be used for assigning jobs (tasks) to hosts. In our server, jobs are ot preemptible. Also, the job's service demand is ot known a priori. We are particularly concerned with the case where the workload is heavytailed, as is ..."
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Cited by 84 (16 self)
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We consider a distributed server system and ask which policy should be used for assigning jobs (tasks) to hosts. In our server, jobs are ot preemptible. Also, the job's service demand is ot known a priori. We are particularly concerned with the case where the workload is heavytailed, as is characteristic of many empirically measured computer workloads. We analyze several natural task assignment policies and propose a new one T/IGS (Task Assignment based on Guessing Size). The T/IGS algorithm is counterintuitive in many respects, including load mbalancing, omworkconserving, and faithless. We find that under heavytailed workloads, T/IGS can outperform all task assignment policies known to us by several orders of magnitude with respect to both mean response time and mean slowdown, provided the system load is not too high.
Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling, Queueing Systems 13
, 1993
"... We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through th ..."
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Cited by 62 (4 self)
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We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian etwork models. Our main conclusion is that in many respects dynamic routing simplifies the behaviour of networks, and that under good control policies itmay well be possible to model the aggregate b haviour of a network quite straightforwardly.
Adaptive Scheduling of Master/Worker Applications on Distributed Computational Resources
, 2001
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A survey of Markov decision models for control of networks of queues
 QUEUEING SYSTEMS
, 1993
"... We review models for the optimal control of networks of queues, Our main emphasis on models based on Markov decision theory and the characterization f the structure of optimal control policies. ..."
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Cited by 27 (0 self)
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We review models for the optimal control of networks of queues, Our main emphasis on models based on Markov decision theory and the characterization f the structure of optimal control policies.
Optimality of the Round Robin Routing Policy
 Journal of Applied Probability
, 1994
"... In this paper we consider the problem of routing customers to identical servers, each with its own infinite capacity queue. Under the assumptions that i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and ii) st ..."
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Cited by 22 (3 self)
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In this paper we consider the problem of routing customers to identical servers, each with its own infinite capacity queue. Under the assumptions that i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and ii) state information is not available, we establish that the round robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues. Mathematics Subject Classification: primary: 60K25. secondary: 49K30, 49N30, 68M20, 90B22, 90B80. Keywords: Optimal Routing, Scheduling, Sample Path Analysis, Stochastic Ordering. This work was supported in part by the National Science Foundation under grant ASC 888802764 and NCR9116183. y The work of this author was also partially supported by CEC DGXIII under the ESPRITBRA grant QMIPS. 1 Introduction Consider a stream of customers arriving to a controller which immedi...
Minimizing Response Times and Queue Lengths in Systems of Parallel Queues
, 1999
"... We consider the problem of routing customers to one of two parallel queues. Arrivals are independent of the state of the system but otherwise arbitrary. Assuming that queues have infinite capacities and the service times form a sequence of i.i.d. random variables with Increasing Likelihood Ratio (IL ..."
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Cited by 22 (2 self)
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We consider the problem of routing customers to one of two parallel queues. Arrivals are independent of the state of the system but otherwise arbitrary. Assuming that queues have infinite capacities and the service times form a sequence of i.i.d. random variables with Increasing Likelihood Ratio (ILR) distribution, we prove that the Shortest Queue (SQ) policy minimizes various cost functionals related to queue lengths and response times. We give a counterexample which shows that this result is not generally true when the service times have Increasing Hazard Rate but are not increasing in the likelihood rate sense. Finally, we show that when capacities are finite the SQ policy stochastically maximizes the departure process and minimizes the loss counting process. Keywords: Routing; stochastic majorization; response times; increasing likelihood ratio distributions AMS subject classification: 60K25 1 Introduction A classical problem in the literature of control of queues is the determin...