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A Comparison of SenderInitiated and ReceiverInitiated Reliable Multicast Protocols
, 1994
"... Senderinitiated reliable multicast protocols based on the use of positive acknowledgments (ACKs) can suffer performance degradation as the number of receivers increases. This degradation is due to the fact that the sender must bear much of the complexity associated with reliable data transfer (e.g. ..."
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Cited by 227 (11 self)
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Senderinitiated reliable multicast protocols based on the use of positive acknowledgments (ACKs) can suffer performance degradation as the number of receivers increases. This degradation is due to the fact that the sender must bear much of the complexity associated with reliable data transfer (e.g., maintaining state information and timers for each of the receivers and responding to receivers' ACKs). A potential solution to this problem is to shift the burden of providing reliable data transfer to the receivers  thus resulting in receiverinitiated multicast error control protocols based on the use of negative acknowledgments (NAKs). In this paper we determine the maximum throughputs for generic senderinitiated and receiverinitiated protocols for two classes of applications: (i) onemany applications where one participant sends data to a set of receivers, and (ii) manymany applications where all participants simultaneously send and receive data to/from each other. We show that a receiverinitiated error control protocol which requires receivers to transmit NAKs pointtopoint to the sender provides higher throughput than a senderinitiated counterpart for both classes of applications. We further demonstrate that, in the case of a onemany application, replacing pointtopoint transfer of NAKs with multicasting of NAKs coupled with a random backoff procedure provides a substantial additional increase in the throughput of a receiverinitiated error control protocol over a senderinitiated protocol. We also find, however, that such a modification leads to a throughput degradation in the case of manymany applications.
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 171 (20 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
Towards a Theory of Negative Dependence
 J. Math. Phys
, 1999
"... : The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of positively dependent events. There is, as yet, no correspondi ..."
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Cited by 37 (1 self)
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: The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of positively dependent events. There is, as yet, no corresponding theory of negatively dependent events. There is, however, a need for such a theory. This paper, unfortunately, contains no substantial theorems. Its purpose is to present examples that motivate a need for such a theory, give plausibility arguments for the existence of such a theory, outline a few possible directions such a theory might take, and state a number of specific conjectures which pertain to the examples and to a wish list of theorems. Keywords: Associated, negatively associated, negatively dependent, FKG, negative correlations, lattice inequalities, stochastic domination, logconcave Subject classification: 60C05, 62H20, 05E05 1 Research supported in part by National Science F...
Networks in Labor Markets: Wage and Employment Dynamics and Inequality
 CALVÓARMENGOL, ANTONI AND YANNIS IOANNIDES (2005) “SOCIAL NETWORKS IN LABOR MARKETS,” IN THE NEW PALGRAVE, L. BLUME AND S. DURLAUF (EDS), LONDON: MACMILLAN PRESS (IN PRESS) GRANOVETTER, MARK
, 2003
"... We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and expected wage ..."
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Cited by 28 (2 self)
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We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and expected wages, in the sense of first order stochastic dominance. A similar effect results from an increase in the network contacts of an agent. In terms of dynamics and patterns, we show that both wages and employment are positively associated (a strong form of correlation) across time and agents. We also analyze the decisions of agents regarding staying in the labor market or dropping out. If there are costs to staying in the labor market, and we compare two networks of agents that are identical except that one group starts with a worse wage status, then that group's dropout rate will be higher than the other's and there will be a persistent di#erence in wages between the groups.
A New Ordering for Stochastic Majorization: Theory and Applications
 Advances in Applied Probability
, 1991
"... In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, Lsubadditive and convex in each variable. This ..."
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Cited by 19 (7 self)
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In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, Lsubadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differ for random vectors. Sample path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various forkjoin queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers. Keywords: load balancing, stochastic convexity, majorization ordering, routing, scheduling, forkjoin queues 0 1 Introduction Recently, stochastic comparison has received a great deal of attention. ...
How System Performance is Affected by the Interplay of Averages in a Fluid Queue with Long Range Dependence Induced by Heavy Tails
 Ann. Appl. Probab
, 1999
"... . We consider a fluid queue with sessions arriving according to a Poisson process. A longtailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonet ..."
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Cited by 17 (9 self)
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. We consider a fluid queue with sessions arriving according to a Poisson process. A longtailed distribution of session lengths induces long range dependence in the system and causes its performance to deteriorate. The deterioration is due to occurrence of load regimes far from average ones. Nonetheless, the extent of this performance deterioration is shown to depend crucially on the average values of the system parameters. 1. Introduction We consider the following fluid queuing model. Sessions (ON periods) are initiated at a network server or multiplexer according to a Poisson process with rate ? 0. Each session is active for a random length of time with distribution F and a finite mean ; during this time it generates network traffic at unit rate. We assume that the lengths of different sessions are independent, and they are also independent of the Poisson arrival process. The service rate is r ? 0 units of traffic per unit time. If X(t) denotes the amount of work (measured in unit...
Conditional Association, Essential Independence and Monotone Unidimensional Item Response Models
 Annals of Statistics
, 1993
"... We consider two recent approaches to characterizing the manifest probabilities of a strictly unidimensional latent variable representation (one satisfying local independence and response curve monotonicity with respect to a unidimensional latent variable) for binary response variables, such as those ..."
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Cited by 14 (8 self)
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We consider two recent approaches to characterizing the manifest probabilities of a strictly unidimensional latent variable representation (one satisfying local independence and response curve monotonicity with respect to a unidimensional latent variable) for binary response variables, such as those arising from the dichotomous scoring of items on standardized achievement and aptitude tests. Holland and Rosenbaum (1986) show that conditional association is a necessary condition for strict unidimensionality; and Stout (1990) treats the class of essentially unidimensional models, in which the latent variable may be consistently estimated as the length of the response sequence grows using the proportion of positive responses. Of particular concern are strictly unidimensional representations that are minimally useful in the sense that (1) the latent variable can be consistently estimated from the responses; (2) the regression of proportion of positive responses on the latent variable is mo...
A Law Of The Iterated Logarithm For Stable Processes In Random Scenery
 Stoch. Proc. Appl
, 1998
"... . We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit longrange dependence. Keywords. Brownian motion in stable scenery; law of the iterated logarithm; quasi association 1991 Mathe ..."
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Cited by 13 (3 self)
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. We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit longrange dependence. Keywords. Brownian motion in stable scenery; law of the iterated logarithm; quasi association 1991 Mathematics Subject Classification. Primary. 60G18; Secondary. 60E15, 60F15. * Research partially supported by grants from the National Science Foundation and National Security Agency x1. Introduction In this paper we study the sample paths of a family of stochastic processes called stable processes in random scenery. To place our results in context, first we will describe a result of Kesten and Spitzer (1979) which shows that a stable process in random scenery can be realized as the limit in distribution of a random walk in random scenery. Let Y = fy(i) : i 2 Zg denote a collection of independent, identicallydistributed, realvalued random variables and let X = fx i : i ? 1g denote a coll...
A heuristic for optimizing stochastic activity networks with applications to statistical digital circuit sizing
 IEEE Transactions on Circuits and SystemsI
, 2004
"... A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is th ..."
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Cited by 12 (4 self)
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A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is the minimum time required to complete all activities. In a stochastic activity network (SAN), the durations of the activities and the makespan are random variables. The analysis of SANs is quite involved, but can be carried out numerically by Monte Carlo analysis. This paper concerns the optimization of a SAN, i.e., the choice of some design variables that affect the probability distributions of the activity durations. We concentrate on the problem of minimizing a quantile (e.g., 95%) of the makespan, subject to constraints on the variables. This problem has many applications, ranging from project management to digital integrated circuit (IC) sizing (the latter being our motivation). While there are effective methods for optimizing DANs, the SAN optimization problem is much more difficult; the few existing methods cannot handle largescale problems.
TailMeasurability In Monotone Latent Variable Models
, 1996
"... We consider latent variable models for an infinite sequence (or universe) of manifest (observable) variables that may be discrete, continuous or some combination of these. The main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable model ..."
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Cited by 11 (3 self)
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We consider latent variable models for an infinite sequence (or universe) of manifest (observable) variables that may be discrete, continuous or some combination of these. The main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality, monotonicity, conditional independence, and tailmeasurability. Tailmeasurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed. The characterizing, necessary and sufficient, conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence (as one conditions upon successively more other manifest variables). Our main theorem considerably generalizes and sharpens earlier results of Ellis and Van den Wollenberg (1993), Holland and Rosenbaum (1986), and Junker (1993). It is also ...