A computing system has a single printer attached to print out the output of the users. The operating system software sends an average of $20$ requests per hour to the printer. The printer is capable of printing out $35$ jobs per hour on the average. Assume that the job arrival rate and the printing rate are Poisson distributed.a$.$On the average, how many jobs are in the output queue waiting to be printed out?b$.$How many jobs are in the printer output system on the average?c$.$How long can a user expect to wait to have his or her job printed out once it has been sent to the printer?d$.$Once a job enters the output queue, how long does it take before printing begins on the job?e$.$What percentage of time will the printer be busy doing print jobs?f$.($Case $2)$ Assume that a second printer is added to the system. Answer questions $1\mathrm{.}1$ to $1\mathrm{.}5,$ assuming that the two printers are identical.