Question: A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour.

A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour. Type 2 customers arrive according to a Poisson process at a mean rate of 3 per hour. The system has two servers, both of which serve both types of customers. All service times have an exponential distribution with a mean of 10 minutes. Service is provided on a first-come-first-served basis. a. What is the probability distribution of the time between consecutive arrivals of customers of any type, what is its mean? b. Assume that when a Type 2 customer arrives, he finds two Type 1 customers being served and no other customers in the system. What is the probability distribution of this Type 2 customers waiting time in the queue and it mean?

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