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Machine Repair Problem in Production Systems with Spares and Server Vacations

Jau-Chuan Ke, Ssu-Lang Lee, Cheng-Hwai Liou (2009)

RAIRO - Operations Research

This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacation, and hybrid single/multiple vacation. The Markov process and the matrix-geometric approach are used...

Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment

Saba Amsalu, Heinrich Matzinger, Serguei Popov (2007)

ESAIM: Probability and Statistics

We investigate the optimal alignment of two independent random sequences of length n. We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness.

Maintenance policy under multiple unrevealed failure.

Francisco Germán Badía Blasco, M.ª Dolores Berrade Ursúa, Clemente A. Campos (2002)

Qüestiió

The unrevealed failures of a system are detected only by inspection. In this work, an inspection policy along with a maintenance procedure for multiunit systems with dependent times to failure is presented. The existence of an optimum policy is also discussed.

Marking (1, 2) points of the brownian web and applications

C. M. Newman, K. Ravishankar, E. Schertzer (2010)

Annales de l'I.H.P. Probabilités et statistiques

The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding...

Markovian perturbation, response and fluctuation dissipation theorem

Amir Dembo, Jean-Dominique Deuschel (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is,...

Maximal displacement for bridges of random walks in a random environment

Nina Gantert, Jonathon Peterson (2011)

Annales de l'I.H.P. Probabilités et statistiques

It is well known that the distribution of simple random walks on ℤ conditioned on returning to the origin after 2n steps does not depend on p=P(S1=1), the probability of moving to the right. Moreover, conditioned on {S2n=0} the maximal displacement maxk≤2n|Sk| converges in distribution when scaled by √n (diffusive scaling). We consider the analogous problem for transient random walks in random environments on ℤ. We show that under the quenched law Pω (conditioned on the environment ω), the maximal...

Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers

Kuo-Hsiung Wang, Sheau-Chyi Chen, Jau-Chuan Ke (2004)

RAIRO - Operations Research - Recherche Opérationnelle

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability ( 1 - b ) . We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter ρ , the...

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