Consider a M M 1 queue system, that is a single server queue in which customers arrive in according to a Poisson process of rate X 0 and where service times are independent identically exponentially distributed with parameter pe 0 If the queue length is k 1, what is the probability that the next customer arrives before the current customer's service time ends Determine the distribution of the number of arrivals during one service period (recall that the service time is exponentially distributed with parameter 0)

Question: Consider a M/M/1 queue system, that is a single server queue in which customers arrive in according to a Poisson process of rate X >

Consider a M/M/1 queue system, that is a single server queue in which customers arrive in according to a Poisson process of rate X > 0 and where service times are independent identically exponentially distributed with parameter pe> 0

If the queue length is k > 1, what is the probability that the next customer arrives before the current customer's service time ends?
Determine the distribution of the number of arrivals during one service period (recall that the service time is exponentially distributed with parameter > 0).

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