Journal of Applied Probability

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On the optimality of static priority policies in stochastic scheduling on parallel machines
Journal of Applied Probability - Tập 24 Số 2 - Trang 430-448 - 1987
Thomas Kämpke
n jobs are to be preemptively scheduled for processing on n machines. The machines may have differing speeds and the jobs have processing requirements which are distributed as independent exponential random variables with different means. Holding cost g(U) is incurred per unit time t...... hiện toàn bộ
Limit theorem for continuous-time random walks with two time scales
Journal of Applied Probability - Tập 41 Số 2 - Trang 455-466 - 2004
Peter Becker–Kern, Mark M. Meerschaert, Hans‐Peter Scheffler
Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equat...... hiện toàn bộ
On New Classes of Extreme Shock Models and Some Generalizations
Journal of Applied Probability - Tập 48 Số 01 - Trang 258-270 - 2011
Ji Hwan, Maxim Finkelstein
In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. A shock model which combines these two types is called a ‘combined shock model’. In this paper we study new classes of extreme shock models and, based on the obtained results and model int...... hiện toàn bộ
Approximations in finite-capacity multi-server queues by Poisson arrivals
Journal of Applied Probability - Tập 15 Số 4 - Trang 826-834 - 1978
Shirley A. Nozaki, Sheldon M. Ross
An approximation for the average delay in queue of an entering customer is presented for the M/G/K queuing model with finite capacity. The approximation is obtained by means of an approximation relating a joint distribution of remaining service time to the equilibrium service distribution.
Advances in Complete Mixability
Journal of Applied Probability - Tập 49 Số 2 - Trang 430-440 - 2012
Giovanni Puccetti, Bin Wang, Ruodu Wang
The concept of complete mixability is relevant to some problems of optimal couplings with important applications in quantitative risk management. In this paper we prove new properties of the set of completely mixable distributions, including a completeness and a decomposition theorem. We also show that distributions with a concave density and radially symmetric distributions are completely...... hiện toàn bộ
Availability of periodically inspected systems with Markovian wear and shocks
Journal of Applied Probability - Tập 43 Số 02 - Trang 303-317 - 2006
Jeffrey P. Kharoufeh, Daniel E. Finkelstein, Dustin G. Mixon
We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.
Steady-state Markov chain models for the Heine and Euler distributions
Journal of Applied Probability - Tập 29 Số 4 - Trang 869-876 - 1992
Adrienne W. Kemp
The paper puts forward steady-state Markov chain models for the Heine and Euler distributions. The models for oil exploration strategies that were discussed by Benkherouf and Bather (1988) are reinterpreted as current-age models for discrete renewal processes. Steady-state success-runs processes with non-zero probabilities that a trial is abandoned, Foster processes, and equilibrium random...... hiện toàn bộ
The control of a finite dam with penalty cost function: Markov input rate
Journal of Applied Probability - Tập 24 Số 2 - Trang 457-465 - 1987
F. A. Attia
The long-run average cost per unit time of operating a finite dam controlled by a hiện toàn bộ
Rational Processes Related to Communicating Markov Processes
Journal of Applied Probability - Tập 49 Số 1 - Trang 40-59 - 2012
Peter Buchholz, Miklós Telek
We define a class of stochastic processes, denoted as marked rational arrival processes (MRAPs), which is an extension of matrix exponential distributions and rational arrival processes. Continuous-time Markov processes with labeled transitions are a subclass of this more general model class. New equivalence relations between processes are defined, and it is shown that these equivalence re...... hiện toàn bộ
Large deviations of heavy-tailed random sums with applications in insurance and finance
Journal of Applied Probability - Tập 34 Số 2 - Trang 293-308 - 1997
Claudia Klüppelberg, Thomas Mikosch
We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of hiện toàn bộ
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