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442
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 110 (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 109 (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
Distributed Scheduling Based On Due Dates And Buffer Priorities
, 1991
"... We are motivated by the problem of scheduling a large semiconductor manufacturing facility, where jobs of wafers, each with a desired due date, follow essentially the same route through the manufacturing system, returning several times to many of the service centers for the processing of successi ..."
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Cited by 100 (16 self)
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We are motivated by the problem of scheduling a large semiconductor manufacturing facility, where jobs of wafers, each with a desired due date, follow essentially the same route through the manufacturing system, returning several times to many of the service centers for the processing of successive layers. Neglecting the randomness introduced by yield, such a system can be modeled as a nonacyclic ow line.
Distributed Admission Control
"... This paper describes a framework for admission control for a packetbased network where the decisions are taken by edge devices or endsystems, rather than resources within the network. The decisions are based on the results of probe packets that the endsystems send through the network, and requir ..."
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Cited by 94 (7 self)
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This paper describes a framework for admission control for a packetbased network where the decisions are taken by edge devices or endsystems, rather than resources within the network. The decisions are based on the results of probe packets that the endsystems send through the network, and require only that resources apply a mark to packets in a way that is load dependent. One application example is the Internet, where marking information is fed back via an ECN bit, and we show howthis approach allows a rich QoS framework for ows or streams. Our approach allows networks to be explicitly analysed, and consequently engineered.
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 75 (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.
On the existence of equilibria in noncooperative optimal flow control
 Journal of the ACM
, 1995
"... Abstract. The existence of Nash equilibria in noncooperative flow control in a general productform network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average timedelay. Previous attempts to study e ..."
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Cited by 71 (10 self)
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Abstract. The existence of Nash equilibria in noncooperative flow control in a general productform network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average timedelay. Previous attempts to study existence of equilibria for this flow control model were not successful, partly because the timedelay constraints couple the strategy spaces of the individual users in a way that does not allow the application of standard equilibrmm existence theorems from the game theory literature. To overcome this difficulty, a more general approach to study the existence of Nash equilibria for decentralized control schemes is introduced. This approach is based on directly proving the existence of a fixed point of the best reply correspondence of the underlying game. For the investigated flow control model, the best reply correspondence is shown to be a function, implicitly defined by means of K interdependent linear programs. Employing an appropriate definition for continuity of the set of optimal solutions of parametrized linear programs, it is shown that, under appropriate conditions, the best reply function is continuous. Brouwerâ€™s theorem implies, then, that the best reply function has a fixed point.
Algebraic Tools for the Performance Evaluation of Discrete Event Systems
 IEEE Proceedings: Special issue on Discrete Event Systems
, 1989
"... In this paper, it is shown that a certain class of Petri nets called event graphs can be represented as linear "timeinvariant" finitedimensional systems using some particular algebras. This sets the ground on which a theory of these systems can be developped in a manner which is very analogous to ..."
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Cited by 65 (6 self)
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In this paper, it is shown that a certain class of Petri nets called event graphs can be represented as linear "timeinvariant" finitedimensional systems using some particular algebras. This sets the ground on which a theory of these systems can be developped in a manner which is very analogous to that of conventional linear system theory. Part 2 of the paper is devoted to showing some preliminary basic developments in that direction. Indeed, there are several ways in which one can consider event graphs as linear systems: these ways correspond to approaches in the time domain, in the event domain and in a twodimensional domain. In each of these approaches, a di#erent algebra has to be used for models to remain linear. However, the common feature of these algebras is that they all fall into the axiomatic definition of "dioids". Therefore, Part 1 of the paper is devoted to a unified presentation of basic algebraic results on dioids. 1 Introduction Definitions and examples of Discrete ...
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 61 (14 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...
A Distributed CSMA Algorithm for Throughput and Utility Maximization in Wireless Networks
"... In multihop wireless networks, designing distributed scheduling algorithms to achieve the maximal throughput is a challenging problem because of the complex interference constraints among different links. Traditional maximalweight (MW) scheduling, although throughputoptimal, is difficult to imple ..."
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Cited by 56 (7 self)
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In multihop wireless networks, designing distributed scheduling algorithms to achieve the maximal throughput is a challenging problem because of the complex interference constraints among different links. Traditional maximalweight (MW) scheduling, although throughputoptimal, is difficult to implement in distributed networks; whereas a distributed greedy protocol similar to IEEE 802.11 does not guarantee the maximal throughput. In this paper, we introduce an adaptive CSMA scheduling algorithm that can achieve the maximal throughput distributedly under some assumptions. Major advantages of the algorithm include: (1) It applies to a very general interference model; (2) It is simple, distributed and asynchronous. Furthermore, we combine the algorithm with endtoend flow control to achieve the optimal utility and fairness of competing flows. The effectiveness of the algorithm is verified by simulations. Finally, we consider some implementation issues in the setting of 802.11 networks.
On the Analysis of Randomized Load Balancing Schemes
 IN PROCEEDINGS OF THE 9TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1998
"... It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends ..."
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Cited by 55 (7 self)
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It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends a previous analysis of the supermarket model, a model that abstracts a simple, efficient load balancing scheme in the setting where jobs arrive at a large system of parallel processors. In this model, customers arrive at a system of n servers as a Poisson stream of rate #n, # < 1, with service requirements exponentially distributed with mean 1. Each customer chooses d servers independently and uniformly at random from the n servers, and is served according to the First In First Out (FIFO) protocol at the choice with the fewest customers. For the supermarket model, it has been shown that using d = 2 choices yields an exponential improvement in the expected time a customer spends in the syst...