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6.1 In state (n, m), male i mates female j at rate , so male i mates at rate m. Since there are n males, mating occurs at rate v(n,m) = nm. Since any mating is equally likely to produce
 

Summary: Ross:
6.1 In state (n, m), male i mates female j at rate , so male i mates at rate m. Since there are
n males, mating occurs at rate v(n,m) = nm. Since any mating is equally likely to produce
a female or a male, we have P(n,m),(n+1,m) = P(n,m),(n,m+1) = 1/2.
6.3 Not a birth-death process, since we also need to know which machine is working. We can
analyze it by letting the states be:
b: both working
1: 1 is working, 2 is down
2: 2 is working, 1 is down
01: both are down, 1 is being serviced
02: both are down, 2 is being serviced
The parameters are then given by
vb = 1 + 2, v1 = 1 + , v2 = 2 + , v01
= v02
= .
Pb,1 =
2
2 + 1
= 1 - Pb,2, P1,b =

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente
Litvak, Nelly - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering