Final examAnalytical Models of Operating SystemsCSC521Spring 2007Answer only five questions from belowDue date: April 28, 2007Modality: Take home. 1. Indicate how a system could ascertain its “Memory Utilization” rate dynamically. Why is it an important metric? Suggest a plausible scheme for the system to automatically recover memory dynamically without being prompted by the system user if it dips too low. 2. (a) A process is seemingly generating a large number of page faults. Argue both for and against giving the process high priority for the CPU. (b) Suppose you put a tap on an I/O channel and observe heavy page traffic. What conclusions can you then derive?3. In working set models, one has the option of going for (a) fixed size resident set or (b) a variable size resident set. Compare and contrast the two. Should one aim for a large resident size per process or a small one would be better? Discuss the pros and cons.4. Assume a task set },...,,{21 nTTTcomprising n tasks with the execution time foriTgiven by it i. Let minTbe the length of an optimum schedule for on m processors. Show that, in general, minT}{maxkktand  mtTi/min. Next show that for preemptive schedules on  comprising independent tasks, minTis given by a tighter bound  }/),(max{maxminmttTikk5. (a) Assume a page reference string for a process with m frames (initially all empty). The page reference string has length p with n distinct page numbers occurring in it. For any page-replacement algorithms, what is a lower bound on the number of page faults? And what is an upper bound on the number of page faults? (b) For each of the following page replacement algorithms, describe a case (a reference pattern) where the algorithm does a poor job in scheduling memory: LRU, LFU, FIFO, OPT. 6. Assume a process that accesses a single I/O device in two distinct modes: (a) Without buffering, and (b) with buffering. How does the performance of the second one compare with that of the first one? How does the scenario appear when the process needs to refer to ndevices instead?7. Consider an n-track disk system on which the target sectors are identically and uniformly distributed all over the platter. Compute the expected number of tracks the disk-head need to traverse to attempt a seek. 8. When a file is removed, its blocks are generally put back on the free list, but they are not erased. Do you think it would be a good idea to have the operating system erase each block before releasing it? Consider both security and the performance factors in your answer and explain the effect of each. Bonus question: (This has to be submitted separately as a group endeavor) Max mark perindividual contributor: 25Provide a system design and architecture layout of an Oxygen Administration System (OAS) that delivers oxygen to a needy toddler based on the oxygen output read from one of its fingers given a target reading (set externally) B. The system behavior is anticipated along the following general assumptions and observations (admittedly a rough sketch).a. The output is the oxygen reading from the finger. Assume this to be )(ty at a time t. b. System objective is to arrive at the goal  |)(| Btywithin an excursion period of , that is by tT the observed output )(tyBwithin an acceptable error .c. More oxygen input from the OAS tank elevates )(tyup. d. If no oxygen is delivered during an interval the oxygen output falls exponentially at a rate ydtdy within that interval. e. The system is predicated as a potential real-time negative feedback one as shown:f. The program logistic may treat both the sensor output )(ty and the target-deviation measurements as real-time processes to be appropriately synchronized if need be. The sensor readings are sampled inputs to the feedback process with a convenient sampling frequency. If possible, indicate what kind of motor-actuator (that would release oxygen tank valve) could be procured off-the-shelf to serve the system as designed.