Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [birth-death-process]

This tag is for questions about birth and death processes. These processes are a special case of the continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one and they are used to model the size of a population, queuing systems, the evolution of bacteria, the number of people with a disease within a population etc.

This tag is for questions about birth and death processes. These processes are a special case of the continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one and they are used to model the size of a population, queuing systems, the evolution of bacteria, the number of people with a disease within a population etc.

123 questions
1
vote
0 answers

Formula for $\pi_n$ for a Birth-Death Process Stationary Distribution

Consider a birth-death process with parameters $\lambda_n = 2 \cdot (6-n)$ and $\mu_n = 3.5 \cdot n$ where $n = 0,1,2,\dots,6$. Find the stationary distribution (as a function of n). My attempt is that by using the balance equation we…
waterr
  • 67
1
vote
1 answer

Stationary distribution of a birth-death process

Consider a birth-death process with constant parameters $\lambda_n = 4$ and $\mu_n = 5$ with $n = 0,1,2,\dots$. Find the stationary probability (as a function of n) My attempt so far is using the balance equations $\lambda_n\pi_n =…
waterr
  • 67
1
vote
0 answers

How do I prevent an individual from both a birth and death in a birth-death process?

In birth-death processes for populations, what are solutions for preventing the same individual from both giving birth and dying simultaneously (meaning the same time-step) in your model? I'll provide some context: Let's say the timestep is a year.…
youpddd
  • 11
1
vote
0 answers

Quasi birth death process with Erlang interarrival time distribution

I am struggling with modeling a system as a quasi birth death process, since the interarrival times are not Poisson but Erlang distributed with parameters $n = \lambda = 2$. Is this even possible? Could you help me out? Thank you in advance!
user675763
  • 45
  • 9