2. For a single-server queueing system (e.g. one-operator barbershop), define L(t) to be the total number of customers in the system at time t (including the queue and the customer in service at time t, if any). 1) Is it true that L(t) = number of customers in queue +1? Why or why not? 2) What are the state variables that we need to include in order to study L(t)? Make a plot of L(t) vs. t between times 0 and T(6). Note that T(6) is the time required to observe the 6th customer enter service in the system. In the initialization step, the interarrival times Ai of customers are assumed to be: A1=0.2, A2=1.0, A3=0.5, A4=1.5, A5= 0.2 A6=1.7, A7=0.2, A8=1.4, A9=1.9 The service time of customer i, denoted as Si, is initialized as: S1=1.8, S2=0.9, S3=0.2, S4=1.1, S5=3.5, S6=0.6 3) From your plot in (b), compute ???? (6)=the time-average number of customers in the system during the time interval [0,T(6)]. What is the estimated value of ???? (6)? 4) Explain how ???? (6) is computed during the simulation? (How the area under L(t) varies with the simulation clock?)