A queueing system serves two types of customers. Type 1customers arrive according to a Poisson process with a mean rate of5 per hour. Type 2 customers arrive according to aPoisson process at a mean rate of 3 per hour. Thesystem has two servers, both of which serve both types of customer.All service times have exponential distribution with a mean of 10minutes. Service is provided on a first-come-first-servedbasis.
a. What is the probability distribution of the time betweenconsecutive arrivals of customers of any type, what is itsmean?
b. Assume that when a Type 2 customer arrives, he finds two Type1 customers being served and no other customers in the system. Whatis the probability distribution of this Type 2 customer’s waitingtime in the queue and its mean?
