a) Consider an M/M/1 queueing system with arrival rate , service rate µ, µ > λ. Assume that the queue is in steady state. Given that an arrival occurs at time t, find the probability that the system...

a) Consider an M/M/1 queueing system with arrival rate , service rate µ, µ > λ. Assume that the queue is in steady state. Given that an arrival occurs at time t, find the probability that the system is in state i immediately after time t.

b) Assuming FCFS service, and conditional on i customers in the system immediately after the above arrival, characterize the time until the above customer departs as a sum of random variables.

c) Find the unconditional probability density of the time until the above customer departs.