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140
A generalized processor sharing approach to flow control in integrated services networks: The singlenode case
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1993
"... The problem of allocating network resources to the users of an integrated services network is investigated in the context of ratebased flow control. The network is assumed to be a virtual circuit, connectionbased packet network. We show that the use of Generalized processor Sharing (GPS), when co ..."
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Cited by 2010 (5 self)
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The problem of allocating network resources to the users of an integrated services network is investigated in the context of ratebased flow control. The network is assumed to be a virtual circuit, connectionbased packet network. We show that the use of Generalized processor Sharing (GPS), when combined with Leaky Bucket admission control, allows the network to make a wide range of worstcase performance guarantees on throughput and delay. The scheme is flexible in that different users may be given widely different performance guarantees, and is efficient in that each of the servers is work conserving. We present a practical packetbypacket service discipline, PGPS (first proposed by Deme5 Shenker, and Keshav [7] under the name of Weighted Fair Queueing), that closely approximates GPS. This allows us to relate ressdta for GPS to the packetbypacket scheme in a precise manner. In this paper, the performance of a singleserver GPS system is analyzed exactly from the standpoint of worstcase packet delay and burstiness when the sources are constrained by leaky buckets. The worstcase session backlogs are also determined. In the sequel to this paper, these results are extended to arbitrary topology networks with multiple nodes.
Supporting RealTime Applications in an Integrated Services Packet Network: Architecture and Mechanism
, 1992
"... This paper considers the support of realtime applications in an ..."
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Cited by 573 (26 self)
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This paper considers the support of realtime applications in an
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 357 (27 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...
Stability, queue length and delay of deterministic and stochastic queueing networks
 IEEE Transactions on Automatic Control
, 1994
"... Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of ..."
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Cited by 231 (21 self)
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Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate `. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and minimum envelope rate with respect to `. Based on these two new notions of traffic characterization, we develop a set of rules for network operations such as superposition, inputoutput relation of a single queue, and routing. Specifically, we show that (i) the MER of a superposition process is less than or equal to the sum of the MER of each process, (ii) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, (iii) the MER of a departure process from a stable queue is less than or equal to that of the input process (iv) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to ` under a further assumption of independence. These rules provide a natural way to analyze feedforward networks with multiple classes of customers. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the FCFS policy. Moreover, when restricting to the family of twostate Markov modulated arrival processes, the notion of MER with respect to ` is shown to be
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 132 (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...
Stability and Convergence of Moments for Multiclass Queueing Networks via Fluid Limit Models
 IEEE Transactions on Automatic Control
, 1995
"... The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on longrun average moments of the queue lengths at ..."
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Cited by 117 (37 self)
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The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on longrun average moments of the queue lengths at the various stations, and we bound the rate of convergence of the mean queue length to its steady state value. Our work provides a solid foundation for performance analysis either by analytical methods or by simulation. These results are applied to several examples including reentrant lines, generalized Jackson networks, and a general polling model as found in computer networks applications. Keywords: Multiclass queueing networks, ergodicity, general state space Markov processes, polling models, generalized Jackson networks, stability, performance analysis. 1 Introduction The subject of this paper is open multiclass queueing networks, which are models of complex systems such as wafer fabri...
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.
Fluid Approximations And Stability Of Multiclass Queueing Networks: WorkConserving Disciplines
, 1995
"... This paper studies the fluid approximation (also known as the functional strong lawoflargenumbers) and the stability (positive Harris recurrent) for a multiclass queueing network. Both of these are related to the stabilities of a linear fluid model, constructed from the firstorder parameters (i. ..."
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Cited by 87 (9 self)
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This paper studies the fluid approximation (also known as the functional strong lawoflargenumbers) and the stability (positive Harris recurrent) for a multiclass queueing network. Both of these are related to the stabilities of a linear fluid model, constructed from the firstorder parameters (i.e., longrun average arrivals, services and routings) of the queueing network. It is proved that the fluid approximation for the queueing network exists if the corresponding linear fluid model is weakly stable, and that the queueing network is stable if the corresponding linear fluid model is (strongly) stable. Sufficient conditions are found for the stabilities of a linear fluid model. Keywords and phrases: Multiclass queueing networks, fluid models, fluid approximations, stability, positive Harris recurrent, and workconserving service disciplines. Preliminary Versions: September 1993 Revisions: June 1994; September 1994; January 1995 To appear in Annals of Applied Probability AMS 1980 su...
Performance Bounds for Queueing Networks and Scheduling Policies
, 1994
"... Except for the class of queueing networks and scheduling policies admitting a product form solution for the steadystate distribution, little is known about the performance of such systems. For example, if the priority of a part depends on its class (e.g., the buffer that the part is located in), t ..."
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Cited by 82 (16 self)
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Except for the class of queueing networks and scheduling policies admitting a product form solution for the steadystate distribution, little is known about the performance of such systems. For example, if the priority of a part depends on its class (e.g., the buffer that the part is located in), then there are no existing results on performance, or even stability. However, in most applications such as manufacturing systems, one has to choose a control or scheduling policy, i.e., a priority discipline, that optimizes a performance objective. In this paper we introduce a new technique for obtaining upper and lower bounds on the performance of Markovian queueing networks and scheduling policies. Assuming stability, and examining the consequence of a steadystate for general quadratic forms, we obtain a set of linear equality constraints on the mean values of certain random variables that determine the performance of the system. Further, the conservation of time and material gives an au...
Lowcomplexity distributed scheduling algorithms for wireless networks
 IEEE/ACM Trans. on Netw
"... Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. ..."
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Cited by 81 (6 self)
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Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. The first algorithm requires each link to collect local queuelength information in its neighborhood, and its complexity is independent of the size and topology of the network. The second algorithm is presented for the nodeexclusive interference model, does not require nodes to collect queuelength information even in their local neighborhoods, and its complexity depends only on the maximum node degree in the network. I.