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71
Maximizing Queueing Network Utility Subject to Stability: Greedy Primaldual algorithm
 Queueing Systems
, 2005
"... We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision \produces " a certain vector of \commodities"; it also has assoc ..."
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Cited by 204 (9 self)
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We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision \produces " a certain vector of \commodities"; it also has associated \traditional " queueing control eect, i.e., it determines traÆc (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to nd a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable. We introduce a dynamic control algorithm, which we call Greedy PrimalDual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traÆc sources and network processing nodes may be randomly timevarying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traÆc rate constraints.
Asymptotic optimality of maximum pressure policies in stochastic processing networks
 Annals of Applied Probability
, 2008
"... We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each q ..."
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Cited by 43 (4 self)
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We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89–148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5–25] from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks.
Delay analysis for multihop wireless networks
 IEEE INFOCOM
, 2009
"... Abstract—We analyze the delay performance of a multihop wireless network with a fixed route between each sourcedestination pair. There are arbitrary interference constraints on the set of links that can be served simultaneously at any given time. These interference constraints impose a fundamental l ..."
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Cited by 23 (2 self)
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Abstract—We analyze the delay performance of a multihop wireless network with a fixed route between each sourcedestination pair. There are arbitrary interference constraints on the set of links that can be served simultaneously at any given time. These interference constraints impose a fundamental lower bound on the delay performance of any scheduling policy for the system. We present a methodology to derive such lower bounds. For the tandem queue network, where the delay optimal policy is known, the expected delay of the optimal policy numerically coincides with the lower bound. We conduct extensive numerical studies to suggest that the average delay of the backpressure scheduling policy can be made close to the lower bound by using appropriate functions of queue length. I.
Switched networks with maximum weight policies: Fluid approximation and state space collapse. The Annals of Applied Probability
, 2011
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Dynamic SafetyStocks for Asymptotic Optimality in Stochastic Networks
 Queueing Syst. Theory Appl
, 2004
"... This paper concerns control of stochastic networks using statedependent safetystocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the DaiWang reentrant line. In each case, a single policy is proposed that is independent of network load # . ..."
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Cited by 16 (7 self)
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This paper concerns control of stochastic networks using statedependent safetystocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the DaiWang reentrant line. In each case, a single policy is proposed that is independent of network load # .
Stability and asymptotic optimality of generalized maxweight policies
 SIAM Journal on Control and Optimization
"... Abstract It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the "marginal disutility" at a buffer vanishes fo ..."
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Cited by 16 (2 self)
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Abstract It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the "marginal disutility" at a buffer vanishes for vanishingly small buffer population. This observation motivates the hMaxWeight policy, defined for a wide class of functions h. These policies share many of the attractive properties of the MaxWeight policy: (i) Arrival rate data is not required in the policy. (ii) Under a variety of general conditions, the policy is stabilizing when h is a perturbation of a monotone linear function, a monotone quadratic, or a monotone Lyapunov function for the fluid model. (iii) A perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately averagecost optimal in heavy traffic, with logarithmic regret. The first results are obtained for a general Markovian network model. Asymptotic optimality is established for a general Markovian scheduling model with a single bottleneck, and homogeneous servers.
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.
Positive Harris Recurrence and Diffusion Scale Analysis of a Push Pull Queueing Network
, 2009
"... We consider a push pull queueing network with two servers and two types of jobs which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is ..."
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Cited by 15 (11 self)
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We consider a push pull queueing network with two servers and two types of jobs which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is similar to the KumarSeidman RybkoStolyar (KSRS) multiclass queueing network, with the distinction that instead of random arrivals, there is an infinite supply of jobs of both types. Unlike the KSRS network, we can find policies under which our push pull network works at full utilization, with both servers busy at all times, and without being congested. We perform fluid and diffusion scale analysis of this network under such policies, to show fluid stability, positive Harris recurrence, and to obtain a diffusion limit for the network. On the diffusion scale the network is empty, and the departures of the two types of jobs are highly negatively correlated Brownian motions. Using similar methods we also derive a diffusion limit of a reentrant line with infinite supply of work.
G.: 2007, Compensating for failures with flexible servers
 Operations Research
"... Abstract We consider the problem of maximizing capacity in a queueing network with flexible servers, where the classes and servers are subject to failure. We assume that the interarrival and service times are independent and identically distributed, that routing is probabilistic, and that the failu ..."
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Cited by 15 (9 self)
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Abstract We consider the problem of maximizing capacity in a queueing network with flexible servers, where the classes and servers are subject to failure. We assume that the interarrival and service times are independent and identically distributed, that routing is probabilistic, and that the failure state of the system can be described by a Markov process that is independent of the other system dynamics. We find that the maximal capacity is tightly bounded by the solution of a linear programming problem and that the solution of this problem may be used to construct timed generalized round robin policies that approach the maximal capacity arbitrarily closely. We then give a series of structural results for our policies, including identifying when server flexibility can completely compensate for failures and when the implementation of our policies may be simplified. We conclude with a numerical example that illustrates some of the developed insights.
Stable and UtilityMaximizing Scheduling for Stochastic Processing Networks
"... ... manufacturing, communication, and service systems. In such a network, service activities require parts and resources to produce other parts. Because service activities compete for resources, a scheduling problem arises. This paper proposes a deficit maximum weight (DMW) algorithm to achieve thro ..."
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Cited by 15 (1 self)
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... manufacturing, communication, and service systems. In such a network, service activities require parts and resources to produce other parts. Because service activities compete for resources, a scheduling problem arises. This paper proposes a deficit maximum weight (DMW) algorithm to achieve throughput optimality and maximize the net utility of the production. It overcomes the instability problem of MaximumWeight Scheduling in SPNs.