# 4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maxi

4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy?
b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
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Nathalie Redfern

At most $$20/4 =5$$ processes can be active at any one point in time. Since, at most one of those drives can be idle in each process, at most 5 drives could be idle. It is also possible that no drives are idle, as all processes are using their full complement at that point in time.
(b) Allocate the last drive for each process “upon demond”, thus, each process would start with 3 drives. This means that $$20/3 =6$$ processes could be active at any time. The minimum number of drives available would still be 0, but the maximum would be 2.
Note that the fact that there could only be 2 drives indicates that a seventh process could not start, and there is no dead lock resulting.