A system is composed of CPU, Disk and Network. The execution of a process proceeds as follows:The process uses the CPU and then with probability 0.2 proceeds to step 2, with probability 0.3 proceeds to step 3, and with probability 0.5 proceeds to step 4.The process performs Disk I/O and then with probability 0.3 proceeds to step 1, and with probability 0.7 proceeds to step 4.The process performs Network I/O and then with probability 0.4 proceeds to Step 1 and with probability 0.6 proceeds to step 4.The process leaves the system (perhaps due to an I/O error).The following information is known about this system:Processes (each process starts from step 1) arrive according to a Poisson process with an average rate of 40 processes per second.The service time of the CPU is exponentially distributed with an average of 15 msec.The service time of the Disk is exponentially distributed with an average of 50 msec.The service time of the Network is exponentially distributed with an average of 60 msec.All buffers are of infinite sizes.Answer the following questions.What is the average total turnaround time for a process submitted to the above system? What is the probability that a process would immediately begin its execution (i.e., without any waiting) on the CPU when it is submitted to the CPU? What arrival rate would render this system unstable?

We can use a Markov Chain to model the system and then examine its behavior to address this…

Answered: y 0.5 proceeds to step 4. The process…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.13: Closed Queuing Networks

Problem 1P

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A system is composed of CPU, Disk and Network. The execution of a process proceeds as follows:

The process uses the CPU and then with probability 0.2 proceeds to step 2, with probability 0.3 proceeds to step 3, and with probability 0.5 proceeds to step 4.
The process performs Disk I/O and then with probability 0.3 proceeds to step 1, and with probability 0.7 proceeds to step 4.
The process performs Network I/O and then with probability 0.4 proceeds to Step 1 and with probability 0.6 proceeds to step 4.
The process leaves the system (perhaps due to an I/O error).

The following information is known about this system:

Processes (each process starts from step 1) arrive according to a Poisson process with an average rate of 40 processes per second.
The service time of the CPU is exponentially distributed with an average of 15 msec.
The service time of the Disk is exponentially distributed with an average of 50 msec.
The service time of the Network is exponentially distributed with an average of 60 msec.
All buffers are of infinite sizes.

Answer the following questions.

What is the average total turnaround time for a process submitted to the above system?
What is the probability that a process would immediately begin its execution (i.e., without any waiting) on the CPU when it is submitted to the CPU?
What arrival rate would render this system unstable?

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