A barbershop has 2 servers (i.e. hair stylists) and no waiting room. Arrivals to the shop are \( P P(\lambda) \). Server \( i \) (for \( i=1,2 \) ) takes \( \exp \left(\mu_{i}\right) \) amount of time to serve a customer. Let \( \left(X_{1}(t), X_{2}(t)\right) \) be the state of the system at time \( t \), where \( X_{i}(t) \) is the number of customers at server \( i \). Assume that if there are more than one servers free, the arriving customer picks one of them at random with equal probabilities. Model the system as a CTMC.
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The state of the system can be represented as \( (X_1, X_2) \), where \( X_1 \) and \( X_2 \) are the number of customers being served by server 1 and server 2, respectively. Possible states are \( (0,0), (1,0), (0,1), (1,1) \). Show more…
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