Browsing by Subject "Stationary distribution"

Now showing 1 - 4 of 4

Open Access
Approximation of multiserver retrial queues by means of generalized truncated models
(Springer, 2002) Anisimov, V. V.; Artalejo, J. R.
It is well-known that an analytical solution of multiserver retrial queues is difficult and does not lead to numerical implementation. Thus, many papers approximate the original intractable system by the so-called generalized truncated systems which are simpler and converge to the original model. Most papers assume heuristically the convergence but do not provide a rigorous mathematical proof. In this paper, we present a proof based on a synchronization procedure. To this end, we concentrate on the M/M/c retrial queue and the approximation developed by Neuts and Rao (1990). However, the methodology can be employed to establish the convergence of several generalized truncated systems and a variety of Markovian multiserver retrial queues.
Open Access
Averaging in Markov models with fast Markov switches and applications to Queueing models
(Springer, 2002) Anisimov, V. V.
An approximation of Markov type queueing models with fast Markov switches by Markov models with averaged transition rates is studied. First, an averaging principle for two-component Markov process (x n (t),ζ n (t)) is proved in the following form: if a component x n (⋅) has fast switches, then under some asymptotic mixing conditions the component ζ n (⋅) weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by x n (⋅). The convergence of a stationary distribution of (x n (⋅),ζ n (⋅)) is studied as well. The approximation of state-dependent queueing systems of the type MM,Q/MM,Q/m/N with fast Markov switches is considered.
Open Access
Non-Boltzmann stationary distributions and non-equilibrium relations in active baths
(Optical Society of America, 2017) Argun, A.; Moradi, A. R.; Pinçe, E.; Bağcı, Gökhan Barış; Imparato, A.; Volpe, Giovanni
The presence of active noise generated by motile bacteria results in the violation of Boltzmann distribution. Therefore, non-equilibrium relations become invalid active baths. Yet these relations can be recovered by introducing effective potentials.
Open Access
Non-Boltzmann stationary distributions and nonequilibrium relations in active baths
(American Physical Society, 2016-12) Argun, A.; Moradi A.-R.; Pinçe, E.; Bagci, G. B.; Imparato, A.; Volpe, G.
Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments.