In this paper, we introduce a class of a directed acyclic graph on the assumption that the collection of random variables indexed by the vertices has a Markov property. We present a flexible approach for the study of the exact distributions of runs and scans on the directed acyclic graph by...

We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic...

In this paper, we illustrate that a power series technique can be used to derive explicit expressions for the transient state distribution of a queueing problem having “chemical” rules with an arbitrary number of customers present initially in the system. Based on generating function and...