[jacklam]

Consider an infinite server queue. Suppose customers arrive at service stations according to a Poisson process with rate λ. A customer is served upon arrival and the service distributions for all servers in the system is gamma (α, β) with mean αβ, and the service times of the servers are independent of each other. Find the expected number of customers who have not been served by time t. Compute the expected value for λ=3, α=1.2, β=4, t=10. You can use software for computation.