Advanced Research Computing Centre (ARCC) wants to improve the service time of their compute cluster Myriad which is designed for parallel multi-core batch- processing jobs. Myriad has 30 physical nodes on it. ARCC plans to use one of two options. In the first option, each submitted job will be run on 10 of the nodes. Accordingly, 3 jobs can be run simultaneously. In this option, the average run time follows an exponential distribution with mean 20 minutes. In the second option, each submitted job will be run on 15 of the nodes. The running time follows an exponential distribution with a mean of 14 minutes. As a side note, due to communication time between the nodes, the speed gain is not proportional to the increase in the number of nodes in the second option. The interarrival time between job submits is 10 minutes and arrivals follow a Poisson distribution. Grid Engine puts all submitted jobs into in a single queue according to their arrival times.

i) In order to achieve the shortest average time spent in queue which option should be used?

ii) To achieve the shortest total time spent in the system which system should be used?

iii) Assume that currently only 10 nodes work on Myriad and only a single job can be run on these 10 nodes. A PhD student wants to run his script on Myriad. He uses "qstat" function to see the current situation of jobs. He sees that there are two jobs in queue (excluding his) and that the currently running script has been running for 12 minutes. How much time do you expect it will take before the Grid Engine starts to run the student's job?