A measure of the “mixing time” or “time to stationarity” in a finite irreducible discrete time Markov chain is considered. The statistic η π i ij j m j m = = ∑ 1 , where {πj} is the stationary distribution and mij is the mean first passage time from state i to state j of the Markov chain, is shown to be independent of the state i that the chain starts in (so that ηi = η for all i), is minimal i...

In this paper, based on probabilistic arguments, we obtain an explicit solution of the stationary distribution for a discrete time Markov chain with an upper Hessenberg time stationary transition probability matrix. Our solution then leads to a numerically stable and eecient algorithm for computing stationary probabilities. Two other expressions for the stationary distribution are also derived,...

It is well known that a simple closed-form formula exists for the stationary distribution of waiting times in the first-come, first-served (FCFS) M/GI/1 queue. In this paper, we extend this to the general stationary framework. Namely, we consider a work-conserving single-server queueing system, where the sequence of customers’ arrival epochs and their service times is described as a general sta...

In this paper, based on probabilistic arguments, we obtain an explicit solution of the stationary distribution for a discrete time Markov chain with an upper Hessenberg time stationary transition probability matrix. Our solution then leads to a numerically stable and efficient algorithm for computing stationary probabilities. Two other expressions for the stationary distribution are also derive...

This paper analyzes the stationary behavior of the TCP congestion window performing ideal congestion avoidance when the packet loss probability is not constant, but varies as a function of the window size. By neglecting the detailed window behavior during fast recovery, we are able to derive a Markov process that is then approximated by a continuous-time, continuous state-space process. The sta...

We consider population genetics models where selection acts at a set of unlinked loci. It is known that if the fitness of an individual is multiplicative across loci, then these loci are independent. We consider general selection models, but assume parent-independent mutation at each locus. For such a model, the joint stationary distribution of allele frequencies is proportional to the stationa...

We study a batch arrival M/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtain...

The seminal work of Huggett [“The risk-free rate in heterogeneous-agent incompleteinsurance economies”, Journal of Economic Dynamics and Control, 1993, 17(5-6), 953969] showed that there exists a unique stationary distribution of agent types, given by their individual states of asset and income endowment pairs. However, the question remains open if the equilibrium individual state space might t...

In this paper we extend the results of the research started in [6] and [7], in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of Koornwinder [5] to generate a large and interesting family of random walks whic...

The seminal work of Huggett [“The risk-free rate in heterogeneous-agent incomplete-insurance economies”, Journal of Economic Dynamics and Control, 1993, 17(5-6), 953-969] showed that in a stationary recursive equilibrium, there exists a unique stationary distribution of agent types. However, the question remains open if an equilibrium’s individual state space might turn out to be such that eith...