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作者：Kruk, Lukasz; Lehoczky, John; Shreve, Steven
作者单位：Maria Curie-Sklodowska University; Carnegie Mellon University; Carnegie Mellon University
摘要：This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems, performance is measured by the fraction of customers who meet their deadline, rather than more traditional performance measures, such as customer delay, queue length or server utilization. To model such systems, one must keep track of customer lead times (the...
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作者：Goel, S
作者单位：Cornell University
摘要：A deck of n cards is shuffled by repeatedly moving the top card to one of the bottom k(n) positions uniformly at random, We give tipper and lower bounds on the total variation mixing time for this shuffle as k(n) ranges from a constant to n. We also consider a symmetric variant of this shuffle in which at each step either the top card is randomly inserted into the bottom k(n) positions or a random card from the bottom k(n) positions is moved to the top. For this reversible shuffle we derive bo...
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作者：Hansen, NR
作者单位：University of Copenhagen
摘要：We define the reflection of a random walk at a general barrier and derive, in case the increments are light tailed and have negative mean, a necessary and sufficient criterion for the global maximum of the reflected process to be finite a.s. If it is finite a.s., we show that the tail of the distribution of the global maximum decays exponentially fast and derive the precise rate of decay. Finally, we discuss an example from structural biology that motivated the interest in the reflection at a ...
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作者：Budhiraja, Amarjit; Ross, Kevin
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for Brownian control problems [14], associated with a broad family of stochastic networks, follows as a consequence.
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作者：Goergen, Laurent
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in this direction equals either zero or one. Combined with our results on the limiting velocity, this implies a strong law of large numbers in two dimensions.
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作者：Neal, Peter
作者单位：University of Manchester
摘要：We consider a multitype epidemic model which is a natural extension of the randomized Reed-Frost epidemic model. The main result is the derivation of an asymptotic Gaussian limit theorem for the final size of the epidemic. The method of proof is simpler, and more direct, than is used for similar results elsewhere in the epidemics literature. In particular, the results are specialized to epidemics upon extensions of the Bernoulli random graph.
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作者：Ekstrom, Erik; Villeneuve, Stephane
作者单位：University of Manchester; Universite PSL; Ecole des Hautes Etudes en Sciences Sociales (EHESS); Universite de Toulouse; Universite Toulouse 1 Capitole; Centre National de la Recherche Scientifique (CNRS)
摘要：We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time for the buyer is guaranteed. The results are illustrated explicitly in two examples.
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作者：Chazottes, Jean-Rene; Redig, Frank; Verbitskiy, Evgeny
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Leiden University; Leiden University - Excl LUMC; Philips; Philips Research
摘要：We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice Z(d), d >= 2. From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns.
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作者：Foley, RD; McDonald, DR
作者单位：University System of Georgia; Georgia Institute of Technology; University of Ottawa
摘要：Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion of time spent on the boundary, where server 2 is idle, may be zero. This is in sharp contrast to the ...
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作者：Grübel, R; Stefanoski, N
作者单位：Leibniz University Hannover
摘要：We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and compounded standard distributions, we derive approximations by Poisson and mixed Poisson distributions; these lead to asymptotic normality results. We are particularly interested in the influence of the key value on the distribution of the node depth. Methodol...
