A Cost Model for DBaaS Storage

Abstract

Cloud infrastructures employ hybrid storage systems that incorporate various types of devices (flash memory solid-state and hard disk drives). Dealing with such heterogeneity makes the use of data placements strategies necessary. These strategies generally rely on cost modeling techniques. In this paper, we propose a cost model for the storage of database objects in a Cloud infrastructure. Our cost model increments the existing work by including: (1) storage cost, which comprises the occupation, the energy and the endurance costs, (2) the penalty cost that could arise from the SLA (Service Level Agreement) violation, and (3) the migration cost resulting from the object movement between storage systems. We also evaluate the relevance of our model and its usability throughout examples.

Appendix A: Notations

Variable	Description
Customers
$\varvec{U}$,$\varvec{u}_{\varvec{k}}$	The set of customer in cloud, kth customer in cloud ${\text{k}} \in \{1,{\text{K}}\}$
$\varvec{w}_{{\varvec{u}_{\varvec{k}} }}$	The workload of customer $u_{k}$
$\varvec{pn}_{{\varvec{u}_{\varvec{k}} }}$	The penalty of customer $u_{k}$
$\varvec{iops}_{sla,u_{k}}$	The IOPS SLA of customer $u_{k}$
$\varvec{iops}_{offered,u} (\varvec{u}_{\varvec{k}} )$	The IOPS offered to customer ${\text{u}}_{\text{k}}$ in the period $T$
$\varvec{t}_{exe,u} (\varvec{u}_{\varvec{k}} )$	The time need to handle the I/O workload of customer ${\text{u}}_{\text{k}}$
$\varvec{io}_{req,u} (\varvec{u}_{\varvec{k}} )$	The total number of the IO requests issued from customer ${\text{u}}_{\text{k}}$
Objects
$O , O_{{u_{k} }}$	The set of cloud objects, The set of objects of customer $u_{k}$
$O_{{d_{j} }}$	The set of objects hosted in device $d_{j}$
$o_{{i,u_{k} }}$, $s_{{o_{{i,u_{k} }} }}$	The $i th$ object of customer $u_{k} i \in \{1,I\}$, its size
$req_{{op,o_{{i,u_{k} }} }}$	The average IOPS of type $op$ issued to the object $o_{i,k}$
Migration
$O_{mv} ,o_{{mv_{m} ,d_{s} ,d_{d} }}$	The set of objects to move, the $m th$ objects to move
$pr_{{o_{{mv_{m} }} }}$	The priorty of $m th$ objects to move
Devices
$D$, $d_{j}$	The set of device, The $j th$ device $j \in \{1,J\}$
$p_{{d_{j} }}$,$c_{{d_{j} }}$,$wo_{{d_{j} }}$	The price, The capacity, The wear out of device $d_{j}$
$iops_{{op,d_{j} }}$	The max throughput of device $d_{j}$ for operation type $op$
$t_{{op,d_{j} }}$	The response time of device $d_{j}$ for operation type $op$
$t_{atv} (d_{j} )$,$t_{idl} (d_{j} )$	The active time, the idle time of device
$seek_{{d_{j} }}$	The average seek distance of device $dj$
$msr_{{op,d_{j} }}$	The set of experimental measures taken for the device $d_{j}$ and I/O operations of type $op$
$wo_{w}$	The impact of workload on the lifetime of device
$E_{ss,t}$,$E_{d,t}$,$E_{up}$	storage system energy, device energy, energy unit price
$P,P_{{atv,d_{j} }}$,$P_{{idl,d_{j} }}$	The power, the active power, the idle power of device $d_{j}$
General
$io_{size}$	The size of I/O block (database block)
$T$	Period of time
$op$	$op \subseteq OP, OP = \{rr,sr,rw,sw\}$,$rr$ :random read. $sr$: sequential read,$rw$ :random write, and $sw$ :sequential write.
Cost notations
$Cost_{pl,T}$	The placment cost for given period $T$
$Cost_{stg,T}$	The storage cost for given period $T$
$Cost_{pnl,T}$	The penalty cost for given period $T$
$Cost_{pnl,u,T} (u_{k})$	The penalty cost of customer $u_{k}$ for given period $T$
$Cost_{mgr,T}$	The Migration Cost for given period $T$
$Cost_{mng,T}$	The Management Cost for given period $T$
$Cost_{occp,T}$	The occupation cost for given period $T$
$Cost_{w,T}$	The workload cost for given period $T$
$Cost_{amz,T}$	The amortized cost for given period $T$
$Cost_{amz,1}$	The amortized cost for one unite of time
$Cost_{erg,T}$	The energy cost for given period $T$
$Cost_{edr,T}$	The Endurance cost of stotage system for given period $T$
$Cost_{edr,d,T} (d_{j})$	The endurence cost of device $d_{j}$ for given period $T$