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Monte Carlo Statistical Methods
, 1998
"... This paper is also the originator of the Markov Chain Monte Carlo methods developed in the following chapters. The potential of these two simultaneous innovations has been discovered much latter by statisticians (Hastings 1970; Geman and Geman 1984) than by of physicists (see also Kirkpatrick et al. ..."
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Cited by 1476 (29 self)
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This paper is also the originator of the Markov Chain Monte Carlo methods developed in the following chapters. The potential of these two simultaneous innovations has been discovered much latter by statisticians (Hastings 1970; Geman and Geman 1984) than by of physicists (see also Kirkpatrick et al. 1983). 5.5.5 ] PROBLEMS 211
Dynamic Power Allocation and Routing for Time Varying Wireless Networks
 IEEE Journal on Selected Areas in Communications
, 2003
"... We consider dynamic routing and power allocation for a wireless network with time varying channels. The network consists of power constrained nodes which transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be tran ..."
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Cited by 355 (73 self)
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We consider dynamic routing and power allocation for a wireless network with time varying channels. The network consists of power constrained nodes which transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (# ij ) that the system can stably supportwhere (# ij ) represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed which stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an adhoc wireless network where channel variations are due to user mobility, and compare its performance with the GrossglauserTse relay model developed in [13].
Dynamic Server Allocation to Parallel Queues with Randomly Varying Connectivity
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1993
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Impact of human mobility on opportunistic forwarding algorithms
 IEEE Trans. Mob. Comp
, 2007
"... Abstract — We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day]. T ..."
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Cited by 222 (21 self)
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Abstract — We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day]. This observation is confirmed using eight distinct experimental data sets. It is at odds with the exponential decay implied by the most commonly used mobility models. In this paper, we study how this newly uncovered characteristic of human mobility impacts one class of forwarding algorithms previously proposed. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the performance in terms of the delivery delay of these algorithms. We make recommendations for the design of well founded opportunistic forwarding algorithms, in the context of human carried devices. I.
Fitting Mixtures Of Exponentials To LongTail Distributions To Analyze Network Performance Models
, 1997
"... Traffic measurements from communication networks have shown that many quantities characterizing network performance have longtail probability distributions, i.e., with tails that decay more slowly than exponentially. File lengths, call holding times, scene lengths in MPEG video streams, and interva ..."
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Cited by 207 (14 self)
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Traffic measurements from communication networks have shown that many quantities characterizing network performance have longtail probability distributions, i.e., with tails that decay more slowly than exponentially. File lengths, call holding times, scene lengths in MPEG video streams, and intervals between connection requests in Internet traffic all have been found to have longtail distributions, being well described by distributions such as the Pareto and Weibull. It is known that longtail distributions can have a dramatic effect upon performance, e.g., longtail servicetime distributions cause longtail waitingtime distributions in queues, but it is often difficult to describe this effect in detail, because performance models with component longtail distributions tend to be difficult to analyze. We address this problem by developing an algorithm for approximating a longtail distribution by a hyperexponential distribution (a finite mixture of exponentials). We first prove tha...
Fair Resource Allocation in Wireless Networks using Queuelengthbased Scheduling and Congestion Control
"... We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be timevarying and different for different receivers. It is wellknown that appropriate ..."
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Cited by 203 (49 self)
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We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be timevarying and different for different receivers. It is wellknown that appropriately chosen queuelength based policies are throughputoptimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queuelengthbased scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queuelength stability.
General state space Markov chains and MCMC algorithm
 PROBABILITY SURVEYS
, 2004
"... This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform e ..."
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Cited by 190 (38 self)
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This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for MetropolisHastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.
Logarithmic Asymptotics For SteadyState Tail Probabilities In A SingleServer Queue
, 1993
"... We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asympt ..."
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Cited by 189 (15 self)
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We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asymptotics of the form x  1 logP(W > x)  q * as x for q * > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Ga .. rtnerEllis condition for the cumulant generating function of the associated partial sums, i.e., n  1 log Ee qS n y(q) as n , plus regularity conditions on the decay rate function y. The asymptotic decay rate q * is the root of the equation y(q) = 0. This result in turn implies a corresponding asymptotic result for the steadystate workload in a queue with general nondecreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.
EndtoEnd Congestion Control for the Internet: Delay and Stability
, 2001
"... Under the assumption that queueing delays will eventually become small relative to propagation delays, we derive stability results for a fluid flow model of endtoend Internet congestion control. The theoretical results of the paper are intended to be decentralized and locally implemented: each end ..."
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Cited by 168 (1 self)
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Under the assumption that queueing delays will eventually become small relative to propagation delays, we derive stability results for a fluid flow model of endtoend Internet congestion control. The theoretical results of the paper are intended to be decentralized and locally implemented: each end system needs knowledge only of its own roundtrip delay. Criteria for local stability and rate of convergence are completely characterized for a single resource, single user system. Stability criteria are also described for networks where aH users share the same roundtrip delay. Numerical experiments investigate extensions to more general networks. Through simulations, we are able to evaluate the relative importance of queueing delays and propagation delays on network stability. Finally, we suggest how these results may be used to design network resources.