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The exact probability distribution of a two-dimensional random walk
A calculation is made of the exact probability distribution of the two-dimensional displacement of a particle at timet that starts at the origin, moves in straight-line paths at constant speed, and
Optimal strategies for some repair replacement models
The problem of finding optimal replacement strategies for certain classes of failure systems is considered. These systems can be repaired upon failure, but are stochastically deteriorating, i.e., the
A generalized impulse control model of cash management
Abstract This paper presents a general model of cash management, viewed as an impulse control problem for a stochastic money flow process. Generalizing classical approaches, we represent this process
Applications of bulk queues to group testing models with incomplete identification
TLDR
This paper develops the generating function for the steady-state probabilities of the embedded Markov chain and compute the optimal values of the decision variables ( m,  M ) that maximize the expected profit.
Telegraph processes with random velocities
We study a one-dimensional telegraph process (M t ) t≥0 describing the position of a particle moving at constant speed between Poisson times at which new velocities are chosen randomly. The exact
Optimal repair policies with general degree of repair in two maintenance models
TLDR
Two maintenance models for repairable systems with exponential lifetimes are studied and optimal maintenance strategies (minimizing the expected discounted costs over an infinite horizon) are determined analytically.
Markov-modulated linear fluid networks with Markov additive input
We consider a network of dams to which the external input is a multivariate Markov additive process. For each state of the Markov chain modulating the Markov additive process, the release rates are
The busy period of the queueing system M / G /∞
For the queueing system M/G/oo some distributions connected with the associated busy periods are derived. QUEUES WITH UNLIMITED SERVICE
EXACT RESULTS FOR A FLUID MODEL WITH STATE-DEPENDENT FLOW RATES
  • O. Kella, W. Stadje
  • Mathematics
    Probability in the Engineering and Informational…
  • 1 October 2002
We consider a modulated fluid system with a finite state-space Markov chain Jt as modulating process and general state-dependent net input rates. We derive differential equations for the transient
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