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Number of ways arrival and departure events happen in a FIFO queue.

Answer: The number of ways this can happen is $$\binom{M+N}N-\binom{M+N}{U}$$ Proof: In the window, there are exactly $N$ departures and $M$ arrivals, so there are at most $\binom{M+N}{M}$ sequences. ...
Mike Earnest's user avatar
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Queuing theory - Probability of servers being busy when packets are discarded if all servers are busy

Assume service times are i.i.d. exponential $\mu$, and the raw arrivals are Poisson $\lambda$ and independent of service times. Then part (a) is a M/M/1/1 queue (which can be modeled by a 2 state CTMC)...
Michael's user avatar
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