Modelling and Validation of Response Times in Zoned RAID

Abstract

vious measures can be easily derived. Analytical queueing network models of RAID performance [4,9, 12, 18, 19] deWe present and validate an enhanced analytical queueing veloped prior to [10] approximate only the mean response network model ofzoned RAID. The modelfocuses on RAID time of the system. We note that RAID performance can levels 01 and 5, and yields the distribution ofI/O request also be modelled using other techniques including simularesponse time. Whereas our previous work could only suption [4, 12], table-based [2] and black-box modelling [13]. port arrival streams ofI/O requests of the same type, the Our RAID model is developed in a bottom-up hierarchimodelpresented here supports heterogeneous streams with cal fashion. We begin by modelling each disk drive in the a mixture ofread and write requests. This improved realism array as a single M/G/1 queue. We then abstract the RAID is made possible through multiclass extensions to our exas a fork-join queueing network [3] in which each disk in isting model. When combined with priority queueing, this the array is represented by an M/G/1 queue. In an N-queue development also enables more accurate modelling of the fork-join network (see Fig. 1) each incoming job is split way subtasks ofRAID 5 write requests are scheduled. In into N subtasks at the fork point. Each of these subtasks all cases we derive analytical results for calculating not queues for service at a parallel service node before joining only the mean but also higher moments and the full distria queue for the join point. When all N subtasks in the job bution ofI/O request response time. We validate our model are at the head of their respective join queues, they rejoin against measurements from a real RAID system.(synchronise) at the join point.Pi Q

Modelling Zoned RAID Systems Using Fork-Join Queueing Simulation

“…[5][6][7][8][9]). In [4,10,11] we have developed approximate analytical queueing models of RAID 01 and 5. Simulations are often used to validate the results of analytical models.…”

Using bulk arrivals to model I/O request response time distributions in zoned disks and RAID systems

“…Some progress has been made on reflecting variable sized I/O requests [4,18], but to the best of our knowledge all existing models of RAID assume a simple non-bursty Markovian I/O request arrival stream (e.g. [5,11,12,13,15,25,26]). We also note that prior to [12] and [13], all previous analytical studies focused only on mean I/O request response time; however, modern Service Level Agreements demand the ability to reason about higher moments and percentiles of response time.…”

“…[5,11,12,13,15,25,26]). We also note that prior to [12] and [13], all previous analytical studies focused only on mean I/O request response time; however, modern Service Level Agreements demand the ability to reason about higher moments and percentiles of response time. For certain highly constrained Markovian arrival streams, [12,13] derive the full cumulative distribution function of I/O request response time, from which all of the previous measures can be easily obtained.…”