Derivation of Residence Time

Response time for a task, t, at multiprogramming level, n, consists of the time spent servicing t, as well as the time t waits for service. The waiting time of t is the service time of all tasks in the queue before t arrives.

Thus, response time of server i can be obtained from adding the service time of each task before the current task enters the system, , and the service time of the new task, .

Since residence time is the total time a transaction is at a server during all of its visits, it is equal to the product of the response time and the visit ratio.