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I am currently working on a stochastic modelling problem in networks. I have a G/G/1 queue where the interarrival and inter-service times are iid the arrival and service time distributions are ind …

I considered the problem of a form of CTMC evolving in a graph: Consider a graph of $G(V,E)$ with $|V|=N$ nodes. Each node has a 1-0 CTMC associated with it: There is a vertex dependent rate $\mu_i …

I was reading this paper when I came across something called the edge-perspective degree distribution in a network. Consider a graph $G$, the degree distribution of whose nodes is $f(d)$. They say the …

I know that for a continuous-time Markov chain, the probability of transition from time $0$ to $t$ is given by $P(t)=e^{Q(t)t}$. I have a system of $N$ interdependent continuous-time Markov chains evo …

In the paper, Survival in a quasi-death process by van Doorn and Pollett, the quasi-stationary distribution of a transient CTMC is discussed and QSD for a simple death process is derived. Consider a …

I had to explain in informal terms what a Feller process was, to undergraduate students who understand Markov property, Poisson processes and such. It was easy to define Levy process as generalisation …

I was contemplating an epidemic model where infection and recovery rates are determined by links. Here node $i$ is infected first and recovers at a rate $\mu_i$. For all other nodes, the recovery is b …

Consider the SIS model of epidemic spreading. There is a finite graph $G(V,E)$, link infection rates $\lambda_{ij}$ and node recovery rates $\mu_i$. There are a few initial nodes which are infected at …