Example 7.10

Consider in IIT Kanpur computer centre (CC) where you have a cluster of computer servers, 6 in number, each of which processes the programs independently as and when the jobs/programs are input into the computer server system. By computer server system we mean the set of these 6 servers. The jobs are processed as per the queue, i.e., they are processed as and when their respective time comes. The arrival of jobs is Poisson distributed with an average rate of 10 per 30 minutes. The processing time is exponentially distributed with a mean of 45 minutes. Once jobs arrive they are made to wait in a queue and the temporary server (which holds the jobs in a queue) can hold maximum of 5 jobs considering its RAM and CPU capacity. From this set of information find

1. The probability, p_n, of n jobs in the system.
2. The effective arrival rate of programs/jobs that are actually held in the temporary server.
3. The average number of jobs in the temporary server.
4. The average time a job waits for being processed in the temporary server.
5. The average number of cluster servers which are busy.
6. The average utilization of the computer cluster server