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Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions
 Annals of Applied Probability
, 2001
"... We study the distribution of steadystate queue lengths in multiclass queueing networks under a stable policy. We propose a general methodology based on Lyapunov functions, for the performance analysis of infinite state Markov chains and apply it specifically to Markovian multiclass queueing network ..."
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Cited by 35 (3 self)
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We study the distribution of steadystate queue lengths in multiclass queueing networks under a stable policy. We propose a general methodology based on Lyapunov functions, for the performance analysis of infinite state Markov chains and apply it specifically to Markovian multiclass queueing networks. We establish a deeper connection between stability and performance of such networks by showing that if there exist linear and piecewise linear Lyapunov functions that show stability, then these Lyapunov functions can be used to establish geometric type lower and upper bounds on the tail probabilities, and thus bounds on the expectation of the queue lengths. As an example of our results, for a reentrant line queueing network with two processing stations operating under a workconserving policy we showthat E[L] =O 1 (1; ) 2 � where L is the total number ofcustomers in the system, and is the maximal actual or virtual traffic intensity inthenetwork. In a Markovian setting, this extends a recent result by Daiand Vande Vate, which states that a reentrant line queueing network with two stations is globally stable if < 1: We also present several results on the
Stability and structural properties of stochastic storage networks
 J. Appl. Prob
, 1996
"... We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic ..."
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Cited by 25 (13 self)
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We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multidimensional content process is tight under the natural stability condition. The multidimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with nonzero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.
Queueing Network Models in the Design and Analysis of Semiconductor Wafer Fabs
 IEEE Transactions on Robotics and Automation
, 2001
"... We provide an introduction to the application of queueing network models to the design and analysis of semiconductor wafer fabs. We introduce the basic issues that confront the system manager and discuss a variety of queueing network based tools for addressing these issues. A representative collecti ..."
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Cited by 14 (0 self)
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We provide an introduction to the application of queueing network models to the design and analysis of semiconductor wafer fabs. We introduce the basic issues that confront the system manager and discuss a variety of queueing network based tools for addressing these issues. A representative collection of existing results in this area is also briey surveyed.
Stability and Instability of a TwoStation Queueing Network
 ANNALS OF APPLIED PROBABILITY
, 2001
"... This paper proves that the stability region of a 2station, 5class reentrant queueing network, operating under a nonpreemptive static bu#er priority service policy, depends on the distributions of the interarrival and service times. In particular, our result shows that conditions on the mean in ..."
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Cited by 9 (3 self)
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This paper proves that the stability region of a 2station, 5class reentrant queueing network, operating under a nonpreemptive static bu#er priority service policy, depends on the distributions of the interarrival and service times. In particular, our result shows that conditions on the mean interarrival and service times are not enough to determine the stability of a queueing network, under a particular policy. We prove that when all distributions are exponential, the network is unstable in the sense that, with probability one, the total number of jobs in the network goes to infinity with time. We show that the same network with all interarrival and service times being deterministic is stable. When all distributions are uniform with a given range, our simulation studies show that the stability of the network depends on the width of the uniform distribution. Finally, we show that the same network, with deterministic interarrival and service times, is unstable when the it is operated under the preemptive version of the static bu#er priority service policy. Thus, our examples also demonstrate that the stability region depends on the preemption mechanism used.
Transient Analysis of Manufacturing Systems Performance
, 1994
"... Studies in performance evaluation of automated manufacturing systems, using simulation or analytical models, have always emphasized steadystate or equilibrium performance in preference to transient performance. In this study, we present several situations in manufacturing systems where transient an ..."
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Cited by 8 (1 self)
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Studies in performance evaluation of automated manufacturing systems, using simulation or analytical models, have always emphasized steadystate or equilibrium performance in preference to transient performance. In this study, we present several situations in manufacturing systems where transient analysis is very important. Manufacturing systems and models in which such situations arise include: systems with failure states and deadlocks, unstable queueing systems, and systems with fluctuating or nonstationary workloads. Even in systems where equilibrium exists, transient analysis is important in studying issues such as accumulated performance rewards over finite intervals, first passage times, sensitivity analysis, settling time computation, and deriving the behavior of queueing models as they approach equilibrium. In certain systems, convergence to steadystate is so slow that only transient analysis can throw light on the system performance. In this paper, we focus on transient analysis of Markovian models of manufacturing systems. After presenting several illustrative manufacturing situations where transient analysis has significance, we discuss two problems for demonstrating the importance of transient analysis. The first problem is concerned with the computation of distribution of time to absorption in Markov models of manufacturing systems with deadlocks or failures, and the second problem shows the relevance of transient analysis to a multiclass manufacturing system with significant setup times. We also briefly discuss computational aspects of transient analysis.
Stability and performance for multiclass queueing networks with infinite virtual queues
"... infinite virtual queues ..."
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Capacity Planning In A Semiconductor Wafer Fabrication Facility With Time Constraints Between Process Steps
, 1998
"... Central to the advancement of the U.S. economy is the efficient production of semiconductors, which in turn depends upon having accurate methods of planning semiconductor wafer fabrication facility capacity. A characteristic of wafer fabrication that makes capacity planning particularly difficult i ..."
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Cited by 4 (1 self)
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Central to the advancement of the U.S. economy is the efficient production of semiconductors, which in turn depends upon having accurate methods of planning semiconductor wafer fabrication facility capacity. A characteristic of wafer fabrication that makes capacity planning particularly difficult is the presence of time constraints between process steps, also known as time bound sequences. In a time bound sequence, there exists a step that must be completed within some fixed time interval of an earlier step. An example in semiconductor manufacturing is a furnace operation that must be started within two hours of a prior clean operation. If more than two hours elapse before the furnace operation can begin, t...
Reducing the Variance of Sojourn Times in Queueing Networks with Overtaking
 Forschungsbericht, PreprintReihe Nr. 73, Universitat Wurzburg, Institut fur Informatik
, 1993
"... In a queueing network with overtaking, the probabilistic effects entailed by a customer propagate in such a manner that the sojourn time of the same customer in a node visited later is affected. The main effect of overtaking is the dependency of node sojourn times on nonovertakefree paths: the soj ..."
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Cited by 2 (1 self)
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In a queueing network with overtaking, the probabilistic effects entailed by a customer propagate in such a manner that the sojourn time of the same customer in a node visited later is affected. The main effect of overtaking is the dependency of node sojourn times on nonovertakefree paths: the sojourn time distribution of a nonovertakefree path is not simply the convolution of the sojourn time distributions of the nodes belonging to the considered path. Overtaking arises in manufacturing systems with rework, where defective parts are processed several times until the required quality is met or if sequences of processing steps of different product types intersect (reentrantlines).Since the influence of overtaking is limited to higher moments of sojourn time distributions (the mean is not affected), and since the influence increases with larger overtaking, the variability of sojourn times can be reduced by diminishing the magnitude of overtaking. For the purpose of reducing the variance of sojourn times, we investigate several queueing disciplines and derive analytical results for basic queueing networks with overtaking. Numerical results comparing the considered scheduling policies are presented and open problems are discussed. Revised: October 1994 1.
Reducing The Variance Of Cycle Times In Semiconductor Manufacturing Systems
 In International Conference on Improving Manufacturing Performance in a Distributed Enterprise: Advanced Systems and Tools
, 1995
"... : In semiconductor manufacturing, due to rework and reentrant flow, overtaking of wafers can occur. The effect of overtaking is that cycle times at successive service centers are not mutually independent. As far as the distribution of cycle times is concerned, only higher moments are affected, the ..."
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Cited by 1 (1 self)
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: In semiconductor manufacturing, due to rework and reentrant flow, overtaking of wafers can occur. The effect of overtaking is that cycle times at successive service centers are not mutually independent. As far as the distribution of cycle times is concerned, only higher moments are affected, the mean cycle time remaining unchanged by the influence of overtaking. Further, in the literature, it is conjectured that variance of cycle times increases when overtaking increases. Taking into account this conjecture, we attempt at reducing the variability of cycle times by diminishing the magnitude of overtaking. This can be done by reversing the overtaking through appropriate sequencing rules. In order to achieve this goal, we examine several sequencing rules by means of simulation studies based on real data sampled at four different semiconductor manufacturing facilities. Our results elucidate that there is no general correlation between the magnitude of overtaking and the variance of cycl...