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Consider a queuing system with 2 types of customers. Type 1 customers arrive according to Poisson procedure with a mean rate of 5 per hour. Type 2 customers arrive according to Poisson procedure with a mean rate of 8 per hour.

a) Find the probability that a type 1 customer arrives before the type 2 does.

b) What is the probability distribution of time between consecutive arrivals of customers (independent of their types?)

c) Assume there is one server in system, which serves both types of customers and service times follow exponential distribution with the mean of 10 minutes. If a type 2 arrives and type 1 being served, what is the distribution of waiting time for this time 2 customer?

Project Management, Management Studies

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