By Dr. Samuel H. Fuller (auth.)
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Extra info for Analysis of drum and disk storage units
Poisson assumption implies that the probability of k arrivals in an arbitrary interval of time, t, is The 22 Pr[k arrivals in interval t] = ~ t ) k e - k t k and the interarrival intervals have the exponential Pr[interarrival density function time = t} = ke -~t In the more specific terms of I/O requests arriving at a drum, the Poisson assumption requires that the degree of multiprogramming is sufficiently large that the central processors generating requests to the drum are never idle and that the times between the generation of I/O requests can be modeled as independent~ random variables.
Lumping the latency and transmission servers into one server in the onestage model further over-approximates the coefficient of variation of service time 3 even though the mean is still exact, and hence the onestage model is a larger overestimate of the waiting time than the twostage model. Examination of Fig. e. 4~, shows several significant features of the SLTF file drum models. striking is the degradation of the one and two-stage models. 6 / drum for R = 1/8. 0 I0 CO 49 distributed over some integer number of drum revolutions, the finishing address of an I/O request is not independent of its starting address.
When we estimated the latency intervals by the exponential distribution with mean of T/(n+l), we slightly overestimated the coefficient of variation. It has been shown in other queueing models that the mean waiting time is positively related to the mean service time as well as the coefficient of variation of the service time. Therefore, it is not surprising that the two-stage model is an overestimate of the results found by simulation. Lumping the latency and transmission servers into one server in the onestage model further over-approximates the coefficient of variation of service time 3 even though the mean is still exact, and hence the onestage model is a larger overestimate of the waiting time than the twostage model.