Solution:(a)the expected number of customers in the system L=2np.=2 (b) The expected number of customers in the queue L,=2(n-2)P,=3/8 (c) The expected number of customers being served is E=L-L=2-378=13/8 (d) The expected waiting time in the system W L 2=1, the expected waiting time in the queue, Wa= 16 (e)This expected service time =W-_13 16 8. You are given an M/M/1 queueing system with mean arrival rate x and mean service rate u. An arriving customer receives n dollars if customers are already in the system Determine the expected cost in dollars per customer. (10 points) Solution: the expected cost in dollars per customer is E=n(l-Po)=n(5 Solution: (a) the expected number of customers in the system 2 4 0 = ∑ = n= L npn (b) The expected number of customers in the queue 8 ( 2) 3/ 4 2 = ∑ − = n= Lq n pn (c) The expected number of customers being served is E = L − Lq = 2 − 3/ 8 = 13/ 8 (d) The expected waiting time in the system 1 2 2 = = = q L W , the expected waiting time in the queue, 16 3 = = λ q q L W (e) This expected service time is 16 1 13 = W −Wq = μ 8. You are given an M/M/1 queueing system with mean arrival rate λ and mean service rate μ. An arriving customer receives n dollars if customers are already in the system. Determine the expected cost in dollars per customer. (10 points) Solution: the expected cost in dollars per customer is (1 ) (1 ) 0 μ λ E = n − p = n −