The Z-Transform Applied to Birth-Death Markov Processes

The Z-transform Applied to a Birth-death Process Having Varying Birth and Death Rates

The analysis of a birth-death process using the z-transform was recently reported for processes having fixed transition probabilities between states. The current report extends that analysis to processes having transition probabilities that can differ from state to state. It is then shown that the model can be used to study practical queuing and birth-death systems where the arrival, birth, ser...

Spatial Birth-and-Death Markov Processes

Quasi - Birth - Death Processes

1 Description of the Model This case study is analog to the one described in [2]. We considered a system consisting of a fixed number of m processors and an infinite queue for storing job requests. The processing speed of a processor is described by the rate γ, while λ describes the incoming rate of new jobs. If a new job arrives while at least one processor is idle, the job will be processed d...

Birth-death processes

Integral functionals of Markov processes are widely used in stochastic modeling for applications in ecology, evolution, infectious disease epidemiology, and operations research. The integral of a stochastic process is often called the “cost” or “reward” accrued by the process. Many important stochastic counting models can be written as general birth-death processes (BDPs), which are continuous-...

Application of Markov Processes to the Machine Delays Analysis

Production and non-productive equipment and personnel delays are a critical element of any production system. The frequency and length of delays impact heavily on the production and economic efficiency of these systems. Machining processes in wood industry are particularly vulnerable to productive and non-productive delays. Whereas, traditional manufacturing industries usually operate on homoge...