Consider a queuing system in which arrivals are Poisson with parameter for any state of the system and the departure rate for state k is k for each value

of k = 0, 1, .... Obtain the probability of having k customers in the system as a function of and , the average number of customers in the system, and the average time spent by a customer in the system.

2. (40 points) M/M/o Queue. Responsive Servers: Consider a queuing system in which arrivals are Poisson with parameter for any state of the system and the departure rate for state k is k for each value of k = 0, 1, . Obtain the probability of having k customers in the system as a function of and , the average number of customers in the system, and the average time spent by a customer in the system