Question

A computer processes jobs on a first-come, first served basis in a time-sharing environment. The jobs have Poisson arrival rates average 0.6 jobs per minute. The objective in processing these jobs is that they spend no more than 5 minutes, on average, in the system. Assuming exponential service times, how fast does the computer have to process jobs (in minutes), on average, to meet this objective

Answer 1

0.8 minutes

Explanation:

From the given information:

The arrival time for the jobs to the computer obeys a Poisson distribution;

Thus, the arrival rate is:

Assuming the average time spent on the jobs in the system is denoted by:

The average time a job process in the system can be expressed as follows:

From above formula:

service rate

arrival rate

replacing the values;

Open brackets

0.8 minutes