In a queuing system, new jobs must wait for a while before being served. While a job waits, its priority increases linearly with time from zero at a rate α. A job waits until its priority reaches the priority of the jobs in service; then, it begins to share the processor equally with other jobs in service using round robin while its priority continues to increase at a slower rate β. The algorithm is referred to as selfish round robin, because the jobs in service try (in vain) to monopolize the processor by increasing their priority continuously. 

Use Figure to show that the mean response time _Rx for a job of service time x is given by:

Where

Assuming that arrival and service times are exponentially distributed with means 1/λ and s, respectively. 

X' Departures Waiting jobs Served jobs 1/A' Time