Computer Architecture: I need some help with this problem. For the last part, these are the probability formulas I need to use.

5. 20 pts) Parts(a) and (b) of this problem concern an M/M/1 queueing system. Parts (c) and (d) concern M/M/1 queueing systems that are different from the system in parts (6) and (b). (6) How many tasks are in an M/M/I queueing system (either waiting or being served), on aver , if the average arrival rate is 8 per second and the average service time is 1/10 second? x=8 2 - 2 1 - 1 = 8.10=80 = to q=&= 90 180 (b) In part (a), how many tasks are being served, on average? (C) What is the utilization of an M/M/1 queue if the average number waiting is equal to W = 1 1 2 = 2 = 1 p = p = p + 3 8 - 12 (d) For an M/M/1 queueing system with utilization what is the minimum buffer length needed to ensure that the probability of buffer overflow is less than 1%? 2(1) ****014) Porcaxx)=1=phy w=24** In() in -2 We mooth 2 = -1 + 3 - 2 ory 2014 y 5 meth Pr(Q = L = (1-Pp Probability that the length of the queue Q is exactly L PrQ >L) = p1+1 Probability that Q is greater than the buffer length L 5. 20 pts) Parts(a) and (b) of this problem concern an M/M/1 queueing system. Parts (c) and (d) concern M/M/1 queueing systems that are different from the system in parts (6) and (b). (6) How many tasks are in an M/M/I queueing system (either waiting or being served), on aver , if the average arrival rate is 8 per second and the average service time is 1/10 second? x=8 2 - 2 1 - 1 = 8.10=80 = to q=&= 90 180 (b) In part (a), how many tasks are being served, on average? (C) What is the utilization of an M/M/1 queue if the average number waiting is equal to W = 1 1 2 = 2 = 1 p = p = p + 3 8 - 12 (d) For an M/M/1 queueing system with utilization what is the minimum buffer length needed to ensure that the probability of buffer overflow is less than 1%? 2(1) ****014) Porcaxx)=1=phy w=24** In() in -2 We mooth 2 = -1 + 3 - 2 ory 2014 y 5 meth Pr(Q = L = (1-Pp Probability that the length of the queue Q is exactly L PrQ >L) = p1+1 Probability that Q is greater than the buffer length L