Question: Consider an M/M/m/ system (this model is widely used in telephony or circuit switched networks). In this context, customers in the system correspond to active

Consider an M/M/m/ system (this model is widely used in telephony or circuit switched networks). In this context, customers in the system correspond to active telephone calls and the m servers represent a single transmission line consisting of m circuits. The principle quantity of interest is the steady-state probability that all circuits are busy, in which case an arriving call must wait in the queue. Given the call arrival rate is , and the duration of a call is exponentially distributed with mean 1/, what is the probability that all circuits are busy in this M/M/m/ system?

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