Vacationing server model for M/G/1 queues for rebuild processing in RAID5 and threshold scheduling for readers and writers

We present two methods to obtain the mean delay cycle for the M/G/1 queueing system with the Vacationing Server Model - VSM, which starts with an arrival during a vacation and ends when the queue is emptied and a vacation starts. In the case of VSM with multiple vacations the server returning from a vacation takes another vacation if the queue is empty, otherwise it starts serving requests. The M/G/1 queue has arrivals with rate λ, mean service time x‾, so that its utilization factor is ρ=λx‾, and its mean busy period is g‾=x‾/(1−ρ). The VSM delay cycle starts with a requested whose mean service time is augmented by the mean residual vacation time: y‾=x‾+v‾r, so that the mean delay cycle is d‾v=y‾/(1−ρ). This is the method used to determine rebuild time in RAID5 disk arrays. In a second study which deals with threshold scheduling of readers and writers d‾v is obtained as the product of the mean number of requests arriving during the residual vacation time plus one (the request starting the residual vacation time) times g‾, which yields d‾v−v‾r=(1+λv‾r)×g‾ as before. The analysis of VSM for rebuild processing in RAID5 and threshold scheduling of readers and writers is provided.