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Network Adiabatic Theorem: An Efficient Randomized Protocol for Contention Resolution
"... The popularity of Aloha(like) algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multiaccess networks. Despit ..."
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Cited by 86 (9 self)
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The popularity of Aloha(like) algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multiaccess networks. Despite a long and exciting history of more than four decades, the question of designing an algorithm that is essentially as simple and distributed as Aloha while being efficient has remained unresolved. In this paper, we resolve this question successfully for a network of queues where contention is modeled through independentset constraints over the network graph. The work by Tassiulas and Ephremides (1992) suggests that an algorithm that schedules queues so that the summation of “weight ” of scheduled queues is maximized, subject to constraints, is efficient. However, implementing such an algorithm using Alohalike mechanism has remained a mystery. We design such an algorithm building upon a MetropolisHastings sampling mechanism along with selection of“weight” as an appropriate function of the queuesize. The key ingredient in establishing the efficiency of the algorithm is a novel adiabaticlike theorem for the underlying queueing network, which may be of general interest in the context of dynamical systems.
Maximum pressure policies in stochastic processing networks
, 2005
"... Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and largescale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of s ..."
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Cited by 70 (6 self)
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Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and largescale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of such systems. LPbased planning is critical in setting a medium range or longterm goal for many systems, but it does not translate into a daytoday operational policy that must deal with discreteness of jobs and the randomness of the processing environment. A stochastic processing network, advanced by J. Michael Harrison (2000, 2002, 2003), is a system that takes inputs of materials of various kinds and uses various processing resources to produce outputs of materials of various kinds. Such a network provides a powerful abstraction of a wide range of realworld systems. It provides highfidelity stochastic models in diverse economic sectors including manufacturing, service, and information technology. We propose a family of maximum pressure service policies for dynamically allocating service capacities in a stochastic processing network. Under a mild assumption on network structure, we prove that a network operating under a maximum pressure policy achieves maximum throughput predicted by LPs. These policies are semilocal in the sense that each
Dynamic routing in largescale service systems with heterogeneous servers
, 2005
"... Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is ..."
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Cited by 52 (12 self)
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Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is FSF which assigns customers to the Fastest Servers First. The asymptotic regime considered is the HalfinWhitt manyserver heavytraffic regime, which we refer to as the Quality and Efficiency Driven (QED) regime; it achieves high levels of both service quality and system efficiency by carefully balancing between the two. Additionally, expressions are provided for system limiting performance measures based on diffusion approximations. Our analysis shows that in the QED regime this heterogeneous server system outperforms its homogeneous server counterpart.
Queueing dynamics and maximal throughput scheduling in switched processing systems. Queueing systems
"... Abstract. We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the ..."
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Cited by 49 (14 self)
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Abstract. We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workloadintensive input traffic traces (arrival processes). Stability preserves the job inflow–outflow balance at each queue on the traffic traces. Two key families of service policies are shown to maximize throughput, under the mild condition that traffic traces have longterm average workload rates. In the first family of cone policies, the service mode is chosen based on the system backlog state belonging to a corresponding cone. Two distinct policy classes of that nature are investigated, MaxProduct and FastEmpty. In the second family of batch policies (BatchAdapt), jobs are collectively scheduled over adaptively chosen horizons, according to an asymptotically optimal, robust schedule. The issues of nonpreemptive job processing and nonnegligible switching times between service modes are addressed. The analysis is extended to cover feedforward networks of such processing systems/nodes. The approach taken unifies and generalizes prior studies, by developing a general tracebased modeling framework (samplepath approach) for addressing the queueing stability problem. It treats the queueing structure as a deterministic dynamical system and analyzes directly its evolution trajectories. It does not require any probabilistic superstructure, which is
Randomized Scheduling Algorithm for Queueing Networks
, 2009
"... There has recently been considerable interest in design of lowcomplexity, myopic, distributed and stable scheduling policies for constrained queueing network models that arise in the context of emerging communication networks. Here, we consider two representative models. One, a model for the collec ..."
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Cited by 28 (7 self)
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There has recently been considerable interest in design of lowcomplexity, myopic, distributed and stable scheduling policies for constrained queueing network models that arise in the context of emerging communication networks. Here, we consider two representative models. One, a model for the collection of wireless nodes communicating through a shared medium, that represents randomly varying number of packets in the queues at the nodes of networks. Two, a buffered circuit switched network model for an optical core of future Internet, to capture the randomness in calls or flows present in the network. The maximum weight scheduling policy proposed by Tassiulas and Ephremide [32] leads to a myopic and stable policy for the packetlevel wireless network model. But computationally it is very expensive (NPhard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of nonpremption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.
Local Scheduling Policies in Networks of Packet Switches with Input Queues
, 2002
"... A significant research effort has been devoted in recent years to the design of simple and efficient scheduling policies for Input Queued (IQ) and Combined Input Output Queued (CIOQ) packet switches. As a result, a number of switch control algorithms have been proposed. Among these, scheduling polic ..."
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Cited by 27 (5 self)
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A significant research effort has been devoted in recent years to the design of simple and efficient scheduling policies for Input Queued (IQ) and Combined Input Output Queued (CIOQ) packet switches. As a result, a number of switch control algorithms have been proposed. Among these, scheduling policies based on Maximum Weight Matching (MWM) were identified as optimal, in the sense that they were proved to achieve 100% throughput under any admissible arrival process satisfying the strong law of large number.
Switched networks with maximum weight policies: Fluid approximation and state space collapse. The Annals of Applied Probability
, 2011
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Optimal Control of Parallel Server Systems with Many Servers in Heavy Traffic
, 2008
"... We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the manyserver heavy traffic regi ..."
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Cited by 16 (7 self)
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We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the manyserver heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponentially distributed.
Stabilizing Queueing Networks with Setups
, 2002
"... For multiclass queueing networks, dispatch policies govern the assignment of servers to the jobs they process. Production policies perform the analogous task for queueing networks whose servers are subject to switchover delays or setups, a model we refer to as setup networks. ..."
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Cited by 8 (1 self)
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For multiclass queueing networks, dispatch policies govern the assignment of servers to the jobs they process. Production policies perform the analogous task for queueing networks whose servers are subject to switchover delays or setups, a model we refer to as setup networks.