We derive novel upper and lower finite length bounds of the error probability in joint source-channel coding when the source is distributed according to an ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive channel. We show that these bounds are tight in the moderate deviations regime and for a certain interval of rates, also in the large ...

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an Ornstein-Uhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dep...

Providing probabilistic analysis of queueing models can be difficult when the input distributions are non-Markovian. In response, a plethora of methods have been developed to approximate a general renewal process by a process with the time between renewals being distributed as a phase type random variable, which allows the resulting queueing models to become analytically or numerically tractabl...

A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example...

The application of Queuing Theory to quantify the relationships between trajectory uncertainties due to aviation operations, precision of navigation and control, and traffic flow efficiency in the National Airspace System is discussed. This work builds on a previous research effort on Markovian queuing network models of the NAS. Two approaches for incorporating the trajectory uncertainties in t...

Discrete-time queueing models find a large number of applications as they are used in modeling systems arising digital platforms like telecommunication and computer networks. In this paper, we analyze an infinite-buffer model with discrete Markovian arrival process. The units on served batches by single server according to the general bulk-service rule, service time follows distribution rate de...

This paper studies a control problem for the multiclass G/G/1 queue for a risk-sensitive cost of the form n logE exp ∑ i ciX n i (T ), where ci > 0 and T > 0 are constants, X n i denotes the class-i queue length process, and the number of arrivals and service completions per unit time are of order n. The main result is the asymptotic optimality, as n → ∞, of a priority policy, provided that ci ...

We consider a single-server queueing system at which customers arrive according to a Poisson process. The service times of the customers are independent and follow a Coxian distribution of order r . The system is subject to costs per unit time for holding a customer in the system. We give a closed-form expression for the average cost and the corresponding value function. The result can be used ...

Abstract. We consider a tandem queueing system BMAP/G/1 → •/M/N/0. The input flow is described by the BMAP (Batch Markovian Arrival Process). After receiving service at the first stage a customer proceeds to the second stage. The service at the second stage requires a random number of servers. If a customer does not see the required number of free servers it leaves the system forever or waits t...

We consider an infinite-buffer single-server queue where inter-arrival times are phase-type (PH), the service is provided according to Markovian service process (MSP ), and the server may take single, exponentially distributed vacations when the queue is empty. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function (VGF) of system-len...