This paper models a call center as a Markovian queue with multiple servers, where customer impatience, and retrials are modeled explicitly. The model is analyzed as a continuous time Markov chain. The retrial phenomenon is explored numerically using a real example, to demonstrate the magnitude it can take and to understand its sensitivity to various system parameters. The model is then used to ...

A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the resu...

A simple two-state Markov chain A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memoryless...

Markov chain sampling has recently received considerable attention in particular in the context of Bayesian computation and maximum likelihood estimation. This paper discusses the use of Markov chain splitting, originally developed for the theoretical analysis of general state space Markov chains, to introduce regeneration into Markov chain samplers. This allows the use of regenerative methods ...

Since the advent of Markovian Process Algebras, users have requested the ability to employ a greater variety of action distribution. We present a conservative extension to the popular Markovian process algebra, PEPA, which incorporates generally distributed sojourn-times for action duration. Just as a PEPA model generates a Markov chain for analysis purposes, so semi-Markov PEPA produces a semi...

We consider a threshold type control mechanism for dynamic setup/release of λ-channels in optical networks. There are two types of costs for the control mechanism: the setup/release cost and the operation cost. For such a control mechanism, there is a corresponding Markov model with high complexity. By state aggregation, we are able to identify a semi-Markov process that is simpler to analyze. ...

The Curveball algorithm is a variation on well-known switch-based Markov Chain Monte Carlo approaches for the uniform sampling of binary matrices with fixed row and column sums. We give a spectral gap comparison between switch chains and the Curveball chain using a decomposition of the switch chain based on Johnson graphs. In particular, this comparison allows us to prove that the Curveball Mar...

We address the batch arrival  systems with finite capacity under partial batch acceptance strategy where service times or rates oscillate between two forms according to the evolution of the number of customers in the system. Applying the theory of Markov regenerative processes and resorting to Markov chain embedding, we present a new algorithm for computing limit distributions of the number cus...

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...