Examples are given, do number 3. Please submit original work. I don't want someones else's answers copy & pastes, where I can just search this question and find it myself.

Example 7-1 Single-channel - Drive through window in a bank Model: Rate of arrival Service rate 15 per hr 20 per hr line: system: in line includes serving time average utilization of the teller Lq=12/(-1) avarage no in waiting line Ls (-2) average no in the system Wq=Lq/ average waiting time in line Ws = Ls/ average waiting time in system Example Multiple-channel - No of servers Parts clerk fills a request while the mechanic works Mechanics arrive at a rate of 40 per hour (Poisson) Clerks fill requests at the rate of 20 per hour Poisson distribution Rate of arrival 40 per hr 2 Service rate 20 per hr cost of clerk $30 per hr cost of mechanic $60 per hr What is the optimum number of clerks to staff the counter? We need to reduce the cost of mechanics waiting! Determine that you need more than 2 Model: Assume 3 clerks first and work upwards Use s = 3 (1 or 2 may not work) (because 1 clerk can do 20 and two can do 40 per hour- but we have arrival rate at 40) Use Table Exhibit 7.12 average utilization of the customer p= / La mechanic Expected no of mechanics waiting Cost of waiting (for s=3) add another clerk mechanic Use S=4 Use Table Exhibit 7.12 La Expected no of mechanics waiting Cost of waiting (for s=4) Time saved in dollars (Difference of cost of waiting) Cost of the additional clerk Cost reduction by adding the 4th clerk hence, 4 clerks Problem 3: Model: Rate of arrival Service rate 10 per hr 12 per hr T> CONSTANT Lq=12/2u(avarage no in waiting line customers Ls=Lq + (average no in the system customers Wq=Lqa average waiting time in line hour 0 minutes Ws = Ls/d average waiting time in system hour 18 minutes