Question: the processing time per job is exponentially distributed with an average of 3 jobs per minute. Jobs arrive randomly at an average rate of one

the processing time per job is exponentially distributed with an average of 3 jobs per minute. Jobs arrive randomly at an average rate of one job every 4 jobs per minute and are processed on a first-come-first-served basis. The manager of the installation has the following concerns.this is a small batch computing system (M/M/1)

A queue of jobs waiting to be processed will form, occasionally.

What is the average number of jobs waiting in this queue?

What is the probability that an arriving job will require more than 20 minutes to be processed?

What is the actual utilization factor for the system?

The manager decides to enhance his utilization factor by 10%. What are the actions that should be taken?

What is the probability of having 0 jobs in the system?

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