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Jobs arrive to a computer system (consisting of a CPU and an I/O device) according to a Poisson process with rate 8 jobs per minute. Once in the system, a job requires on average 30 seconds of CPU time and six seconds of I/O time, in which the CPU and I/O time required by the jobs are exponentially distributed. i) What is the probability that a job will have to wait before being processed by the devices? (Hint: replace the CPU and I/O subsystem by an equivalent single server) ii) What proportion of time is the system busy iii) On average, how many jobs are waiting in line to be processed?

Jobs arrive to a computer system (consisting of a CPU and an I/O device) according to a Poisson process with rate 8 jobs per minute. Once in the system, a job requires on average 30 seconds of CPU time and six seconds of I/O time, in which the CPU and I/O time required by the jobs are exponentially distributed. i) What is the probability that a job will have to wait before being processed by the devices? (Hint: replace the CPU and I/O subsystem by an equivalent single server) ii) What proportion of time is the system busy iii) On average, how many jobs are waiting in line to be processed?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Jobs arrive to a computer system (consisting of a CPU and an I/O device) according to a Poisson process with rate 8 jobs per minute. Once in the system, a job requires on average 30 seconds of CPU time and six seconds of I/O time, in which the CPU and I/O time required by the jobs are exponentially distributed. i) What is the probability that a job will have to wait before being processed by the devices? (Hint: replace the CPU and I/O subsystem by an equivalent single server) ii) What proportion of time is the system busy iii) On average, how many jobs are waiting in line to be processed? 1 iv) On average, how long will a job spend in the system? v) What is the probability that exactly 10 jobs arrive to the system in one minute? vi) What is the probability that there are more than one jobs in the system? vii) What is the probability of exactly 1 job being in the system at a particular time? viii) What happens if the Average I/O time can (somehow) be reduced from 6 to 3 seconds?
Transcribed Image Text:Jobs arrive to a computer system (consisting of a CPU and an I/O device) according to a Poisson process with rate 8 jobs per minute. Once in the system, a job requires on average 30 seconds of CPU time and six seconds of I/O time, in which the CPU and I/O time required by the jobs are exponentially distributed. i) What is the probability that a job will have to wait before being processed by the devices? (Hint: replace the CPU and I/O subsystem by an equivalent single server) ii) What proportion of time is the system busy iii) On average, how many jobs are waiting in line to be processed? 1 iv) On average, how long will a job spend in the system? v) What is the probability that exactly 10 jobs arrive to the system in one minute? vi) What is the probability that there are more than one jobs in the system? vii) What is the probability of exactly 1 job being in the system at a particular time? viii) What happens if the Average I/O time can (somehow) be reduced from 6 to 3 seconds?
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