Birth and Death Process

Birth and Death Process

1. Model Probabilistic

   • Input
     • Birth
       • Random
         • λn
           • Average rate
         • μ n
           • Average rate of exit
   • Output
     • Death

2. Theory of queues

   • Pure birth process
     • Customers come but never leave
       • Poisson process
       • Erlang´s birth
       • Bernoulli process
       • Pascal process
   • Pure death process
     • New customers never come

3. System status

   • notation: N(t)
     • Represent customers in a while
       • Transitions
         • n + 1 (birth)
         • n - 1 (death)
   • Time is continuous
   • inputs & outputs
     • Random variables exponential
     • Independent

4. Applications

   • M/M/s/k finite capacity
     • Theory of queues
   • M/M/s/H infinite population
     • Demography
     • Biology

5. Considers

   • Input
     • Is exponential with parameter λ
   • Output
     • is exponential with parameter µ
   • The first and the second variable are independent

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