This paper introduces the retrial CPP/M/c queue, which is the generalization of the M/M/c retrial queue. The arrival process of jobs into the queue follows the Compound Poisson Process (CPP). We present an efficient and numerically stable computational algorithm for the steady state probabilities.

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice and state transition probabilities, (ii) the steady-state distribution, and (iii) the conditional state distribution given an initial state. In a Monte Carlo study we find that the test ...

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that data from distinct markets can be pooled. We formulate tests of (i) the conditional choice and state transition probabilities, (ii) the steady-state distribution, and (iii) the conditional state distribution given an initial state. If the null cannot be rejected, then the data across ...

A certain Markov chain which was encountered by T. L. Hill in the study of the kinetics of a linear array of enzymes is studied. An explicit formula for the steady state probabilities is given and some conjectures raised by T. L. Hill are proved.

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of pa...

Computation of steady-state probabilities is an important aspect of analysing biological systems modelled as probabilistic Boolean networks (PBNs). For small PBNs, efficient numerical methods can be successfully applied to perform the computation with the use of Markov chain state transition matrix underlying the studied networks. However, for large PBNs, numerical methods suffer from the state...

Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...

In order to obtain more accurate predicted dynamic steady-state performance with shorter computation time, an available mathematical model is modified and presented. Using this modified model, performance of a typical switched reluctance motor (SRM) under a wide range of variations of operating conditions is obtained and discussed. These include variations of speed, voltage, load and switching ...

This paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are nonexponentially distributed with means s and s...