Question

. Consider two machines that are maintained by a two repairmen, with one assigned to each...

. Consider two machines that are maintained by a two repairmen, with one assigned to each machine. Machine i functions for an exponential time with rate µi before breaking down, for i = 1, 2. The repair times (for either machine) are exponential with rate µ. Model this as a continuous-time Markov chain, both in terms of a transition matrix with state-dependent rates, and as a rate matrix.

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his is not a birth and death process since we need more information than just the number working. We also must know which machine is working. We can analyze it by letting the states be
B: both machines are working
1: 1 is working, 2 is down and being repaired
2: 2 is working, 1 is down and being repaired
01: both are down, 1 is being repaired
02: both are down, 2 is being repaired

VB=
V1=

V2=

Pb,1=
PP1,b=

P2,b=

P01,1=p02,2=1

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