15-29 A computer center is equipped with three digital computers, all of the same type and capability. The number of users in the center at any time is equal to 10. For each user, the time for writing (and key punching) a program is exponential with mean rate .5 per hour. Once a program is completed, it is sent directly to the center for execution. The computer time per program is exponentially distributed with mean rate 2 per hour. Assuming that the center is in operation on a full-time basis, and neglecting the effect of computer down-time, find the following. a) The probability that a program is not executed immediately upon receipt at the center. b) The average time until a program is released from the center. c) The average number of programs awaiting execution. d) The expected number of idle computers. e) The percentage of time the computer center is idle. f) The average percentage of idle time per computer.

Fig: 1