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We study the problem of statistical model checking of probabilistic systems for <b>PCTL</b> unbounded until property <b>P</b>Join<sub>p</sub>(Æ<sub>1</sub><b>U</b>Æ<sub>2</sub>) (where Join |X| {<, d, >, e}) using the computation of <b>P</b> d <sub>0</sub>(Æ<sub>1</sub><b>U</b>Æ<sub>2</sub>). The approach is first proposed by Sen et… (More)

We consider a one dimensional stochastic control problem that arises from queueing network applications. The state process corresponding to the queue-length is given by a stochastic differential equation which reflects at the origin. The controller can choose the drift coefficient which represents the service rate and the buffer size b > 0. When the… (More)

A central question in pairwise sequence comparison is assessing the statistical significance of the alignment. The alignment score distribution is known to follow an extreme value distribution with analytically calculable parameters K and λ for ungapped alignments with one substitution matrix. But no statistical theory is currently available for the gapped… (More)

We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural non-anticipativity condition for admissibility of control policies is introduced. The condition is seen to hold for a broad class of… (More)

We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the… (More)

We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such networks with an ergodic cost criterion is studied. It is shown that the value function (i.e., optimum value of the cost) of… (More)

We have developed a new approximate probabilistic model-checking method for <i>untimed</i> properties in probabilistic systems, expressed in a probabilistic temporal logic (PCTL, CSL). This method, in contrast to the existing ones, does not require the untimed until properties to be <i>bounded</i> a priori, where the bound refers to the number of discrete… (More)

- Arka P Ghosh, Ranjan Maitra, Anna D Peterson
- 2010

We propose a separability index that quantifies the degree of difficulty in a hard clustering problem under assumptions of a multivariate Gaussian distribution for each cluster. A preliminary index is first defined and several of its properties are explored both theoretically and numerically. Adjustments are then made to this index so that the final… (More)

This paper studies a scheduling control problem for a single-server mul-ticlass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite-state Markov process that modulates the arrival and service rates in the system. Various cases are considered: fast changing environment, fixed environment,… (More)

In a number of applications, the underlying stochastic process is modeled as a finite-state discrete-time Markov chain that cannot be observed directly and is represented by an auxiliary process. The maximum a posteriori (MAP) estimator is widely used to estimate states of this hidden Markov model through available observations. The MAP path estimator based… (More)