Your solution must include the code you use as well as the computed values. Provide the estimates only, not the random variables!

PLEASE INCLUDE R CODE

THANK YOU!

1. (Stat-461 only) Consider a singleserver queueing model where customers arrive according to a homogeneous Poisson process with rate AA = 10. Upon arrival a customer either enters service if the server is free at that moment or else joins the waiting queue if the server is busy. When the server completes serving a customer it then begins serving the customer that had been waiting the longest. If there are no waiting customers the server remains idle until the next customer arrives. The service times are i.i.d. exponential random variables with rate A3 = 5, independent of arrivals. Suppose that each cus- tomer will be lost, i.e., will leave after an exponential amount of time with rate AW = 2, from his/her arrival, if not served by then. Let N (T) = the number of customers that arrive by time T and L(T) = the number of customers, out of these N (T), that are lost. Estimate E[L(T)/N(T)] when T = 10 using 1000 simulation runs of the queue