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138
On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models
 Annals of Applied Probability
, 1995
"... It is now known that the usual traffic condition (the nominal load being less than one at each station) is not sufficient for stability for a multiclass open queueing network. Although there has been some progress in establishing the stability conditions for a multiclass network, there is no unified ..."
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Cited by 361 (29 self)
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It is now known that the usual traffic condition (the nominal load being less than one at each station) is not sufficient for stability for a multiclass open queueing network. Although there has been some progress in establishing the stability conditions for a multiclass network, there is no unified approach to this problem. In this paper, we prove that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the initial system configuration. As an application of the result, we prove that single class networks, multiclass feedforward networks and firstbufferfirstserved preemptive resume discipline in a reentrant line are positive Harris recurrent under the usual traffic condition. AMS 1991 subject classification: Primary 60K25, 90B22; Secondary 60K20, 90B35. Key words and phrases: multiclass queueing networks, Harris positive recurrent, stability, fluid approximation Running title: Stability of mu...
A tutorial on crosslayer optimization in wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2006
"... This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable my ..."
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Cited by 248 (30 self)
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This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channelaware) scheduling for cellular (singlehop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a cleanslate optimization based approach to the multihop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.
The linear programming approach to approximate dynamic programming
 Operations Research
, 2001
"... The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear ..."
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Cited by 225 (17 self)
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The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear combination of preselected basis functions to the dynamic programming costtogo function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and “staterelevance weights ” that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology. (Dynamic programming/optimal control: approximations/largescale problems. Queues, algorithms: control of queueing networks.)
Scheduling for Multiple Flows Sharing a TimeVarying Channel: The Exponential Rule
 American Mathematical Society Translations, Series
, 2000
"... We consider the following queueing system which arises as a model of a wireless link shared by multiple users. Multiple flows must be served by a "channel" (server). The channel capacity (service rate) changes in time randomly and asynchronously with respect to different flows. In each tim ..."
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Cited by 172 (15 self)
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We consider the following queueing system which arises as a model of a wireless link shared by multiple users. Multiple flows must be served by a "channel" (server). The channel capacity (service rate) changes in time randomly and asynchronously with respect to different flows. In each time slot, a scheduling discipline (rule) picks a flow for service based on the current state of the channel and the queues. We study a scheduling rule, which we call the exponential rule, and prove that this rule is throughputoptimal, i.e., it makes the queues stable if there exists any rule which can do so. In the proof we use the fluid limit technique, along with a separation of time scales argument. Namely, the proof of the desired property of a "conventional" fluid limit involves a study of a different fluid limit arising on a "finer" time scale. In our companion paper [12] it is demonstrated that the exponential rule can be used to provide Quality of Service guarantees over a shared wireless link.
Scheduling Algorithms for a Mixture of RealTime and NonRealTime Data in HDR
 in Proceedings of 17th International Teletraffic Congress (ITC17
"... High Data Rate (HDR) technologz has recently been proposed as an overlay to CDMA... In this paper, we study various scheduling algorithms for a mixture of realtime and nonrealtime data over HDR/CDMA and compare their performance. We study the performance with respect to packet delays and also ave ..."
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Cited by 138 (1 self)
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High Data Rate (HDR) technologz has recently been proposed as an overlay to CDMA... In this paper, we study various scheduling algorithms for a mixture of realtime and nonrealtime data over HDR/CDMA and compare their performance. We study the performance with respect to packet delays and also average throughput, where we use a token based mechanism to give minimum throughput guarantees. We nd that a rule which we call the exponential rule performs well with regard to both these criteria. (In a companion paper, we show that this rule is throughputoptimal, i.e., it makes the queues stable if it is feasible to do so with any other scheduling rule.) Our main conclusion is that intelligent scheduling algorithms in conjunction with token based rate control provide an ecient framework for supporting a mixture of realtime and nonrealtime data applications in a single carrier.
Stability Of Queueing Networks And Scheduling Policies
 IEEE Transactions on Automatic Control
, 1995
"... Usually, the stability of queueing networks is established by explicitly determining the invariant distribution. However, outside of the narrow class of queueing networks possessing a product form solution, such explicit solutions are rare, and consequently little is known concerning stability too. ..."
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Cited by 134 (16 self)
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Usually, the stability of queueing networks is established by explicitly determining the invariant distribution. However, outside of the narrow class of queueing networks possessing a product form solution, such explicit solutions are rare, and consequently little is known concerning stability too. We develop here a programmatic procedure for establishing the stability of queueing networks and scheduling policies. The method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a Lyapunov function. If the underlying system is Markovian, our method establishes not only positive recurrence and the existence of a steadystate probability distribution, but also the geometric convergence of an exponential moment. We illustrate this method on several example problems. For an example of an open reentrant line, we show that all stationary nonidling policies are stable for all load factors less than one. This includes the well known First Com...
Adversarial queueing theory
 In Proc. 28th ACM STOC
, 1996
"... We introduce a new approach to the study of dynamic (or continuous) packet routing, where packets are being continuously injected into a network. Our objective is to study what happens to packet routing under continuous injection ..."
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Cited by 113 (6 self)
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We introduce a new approach to the study of dynamic (or continuous) packet routing, where packets are being continuously injected into a network. Our objective is to study what happens to packet routing under continuous injection
Scheduling in a Queueing System with Asynchronously Varying Service Rates
 Probability in the Engineering and Informational Sciences
"... We consider the following queueing system which arises as a model of a wireless link shared by multiple users. There is a nite number N of input
ows served by a server. The system operates in discrete time t = 0; 1; 2; : : :. Each input
ow can be described as an irreducible countable Markov chain; ..."
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Cited by 94 (8 self)
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We consider the following queueing system which arises as a model of a wireless link shared by multiple users. There is a nite number N of input
ows served by a server. The system operates in discrete time t = 0; 1; 2; : : :. Each input
ow can be described as an irreducible countable Markov chain; waiting customers of each
ow are placed in a queue. The sequence of server states m(t); t = 0; 1; 2; : : : , is a Markov chain with nite number of states M. When server is in state m it can serve m i customers of ow i (in one time slot). The scheduling discipline is a rule that in each time slot chooses the
ow to serve based on the server state and the state of the queues. Our main result is that a simple online scheduling discipline, Modied Largest Weighted Delay First, along with its generalizations, is throughput optimal, namely it ensures that the queues are stable as long as the vector of average arrival rates is within the system maximum stability region. 1
Adversarial Queuing Theory
, 2001
"... We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on timeinvariant stochastic generation. We examine the stability of ..."
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Cited by 93 (0 self)
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We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on timeinvariant stochastic generation. We examine the stability of queuing networks and policies when the arrival process is adversarial, and provide some preliminary results in this direction. Our approach sheds light on various queuing policies in simple networks, and paves the way for a systematic study of queuing with few or no probabilistic assumptions.