A Comprehensive Analytical Performance Model for Disk Devices under Random Workloads.
AbstractOur goal with this paper is to contribute a common theoretical framework for studying the performance of disk-storage devices. Understanding the performance behavior of these devices will allow prediction of the I/O cost in modern applications. Current disk technologies differ in terms of the fundamental modeling characteristics, which include the magnetic/optical nature, angular and linear velocities, storage capacities, and transfer rates. Angular and linear velocities, storage capacities, and transfer rates are made constant or variable in different existing disk products. Related work in this area has studied Constant Angular Velocity (CAV) magnetic disks and Constant Linear Velocity (CLV) optical disks. In this work, we present a comprehensive analytical model, validated through simulations, for the random retrieval performance of disk devices which takes into account all the above-mentioned fundamental characteristics and includes, as special cases, all the known disk-storage devices. Such an analytical model can be used, for example, in the query optimizer of large traditional databases as well as in an admission controller of multimedia storage servers. Besides the known models for magnetic CAV and optical CLV disks, our unifying model is also reducible to a model for a more recent disk technology, called zoned disks, the retrieval performance of which has not been modeled in detail before. The model can also be used to study the performance retrieval of possible future technologies which combine a number of the above characteristics and in environments containing different types of disks (e.g., magnetic-disk-based secondary storage and optical-disk-based tertiary storage). Using our model, we contribute an analysis of the performance behavior of zoned disks and we compare it against that for the traditional CAV disks, as well as against that of some possible/future technologies. This allows us to gain insights into the fundamental performance trade-offs.
Introduction
The performance modeling of direct-access storage devices is concerned with expressing mathematically
the technology behind them and the way their components cooperate in order to perform
a task and is used to predict the performance of those devices. Such a modeling can be useful in
estimating the expected retrieval cost, in optimal data placement determination, in estimating the
average time spent on specific operations such as disk seek and rotational latency, etc.
In general, analytical as well as simulation-based modeling have been used in the literature.
The benefit of the analytical models over simulation is its generality, ease of use, understanding, and
update. The drawback is that analytical models have to usually make simplifying assumptions for
the system which are not necessary when using simulation. In this paper, we contribute to the field
of analytical modeling for disk retrieval performance without having to resort to over-simplifying
assumptions.
1.1 Overview of Available Disk Technologies
In order to model the performance of storage devices, we need to fully understand their tech-
nology. We should be aware of the disk products currently available, the data placement strategies,
details regarding their functionality and features (i.e., the exact behavior of the disk when servicing
various requests etc).
There are two kinds of disk devices: magnetic and optical. The properties that affect mostly
the performance of these devices are the surface format and the operational characteristics of the
device. A magnetic disk drive typically consists of several disk platters, each of which has two
writable/readable surfaces. On the other hand, many optical disks typically have a single platter.
The geometry of a disk drive partitions each platter's surface into either a set of concentric tracks,
or a single spiral track, which are in turn partitioned into a number of sectors. Sectors are the
minimum unit of data that can be read and recorded from/onto a disk. Also, consecutive tracks
from all the platters of the drive are grouped to form cylinders. Information is read and written onto
the platter surfaces using a per-platter-surface read/write head. Each read/write head is attached
to a head-arm mechanical assembly which positions all the read/write heads onto the cylinder and
its tracks which will be accessed. Finally, the disk pack is constantly revolving with the help of a
spindle at a constant or variable velocity.
Older technology of magnetic disks is based on the Constant Angular Velocity (CAV) format.
In this format, data are read or written while keeping constant the angular velocity of the disk.
The tracks of a magnetic CAV disk are concentric and the revolution axis passes through the center
of the tracks and is perpendicular to the disk surface. The sectors become more elongated as we
move away from the revolution axis, resulting in a smaller recording density (bits/inch). Thus, the
outer tracks contain the same number of sectors as the inner ones do. This results in a waste of
storage space, since the potential for additional storage capacity of the longer outer tracks is not
exploited. Therefore, the storage capacity and the time to read a sector (transfer rate) remains
constant throughout the platter.
Recently, a new technology of magnetic disks emerged, which we call the Zoned CAV (ZCAV)
disk. In this format, the cylinders are divided into successive groups of cylinders, called zones.
Within each zone, the number of sectors per track as well as the transfer rate (i.e., time to read
a sector) is constant. However, a track in a given zone, contains more sectors than the track in
the neighboring zone closer to the platter center. As a result, since the angular velocity remains
constant, the transfer rate of the outer zones is higher than the transfer rate of the inner ones. This
happens because outer tracks observe higher linear velocities meaning that more sectors per unit
of time pass beneath the disk head in the case of the outer zones.
For optical disks, besides the CAV recording format, another recording format is popular. In
this format the recording density (bits/inch) remains constant throughout the disk platter. This
format is a Constant Linear Velocity (CLV) format and is used in CD-ROM devices. In CLV
disks, the constant linear velocity results in a constant transfer rate. This is achieved by adjusting
their angular velocity, decreasing it as we move to outer tracks. This adjustment impacts on the
speed of access, making these disks generally slower than the CAV ones. Some optical disks have
a single spiral track. However, even in this case, we can still define tracks. This can be done by
considering a radial line of the disk. A "track" is lying between two successive intersections of the
spiral track with the radial line. The set of the successive tracks which all have the same capacity
(in number of sectors) can be viewed as forming a zone, similarly to ZCAV disks.
The ZCAV recording format tries to combine the benefits of CAV and CLV formats and form
disks with larger storage capacities and lower access times. There are many other possibilities for
disk products, each resulting from combinations of the above mentioned fundamental characteris-
tics. For example, there can be CLV magnetic disks, optical disks with no spiral tracks, disks which
are partitioned into CAV and CLV partitions, etc. Most of these possible technologies currently
remain in the sphere of theory. The following table summarizes some of the existing disk-device
technologies in terms of their fundamental characteristics presented earlier.
Technology Type Constant Variable
CAV magnetic angular velocity linear velocity
storage capacity sector length
transfer rate
CLV optical linear velocity angular velocity
transfer rate storage capacity
sector length
ZCAV magnetic angular velocity linear velocity
storage capacity
sector length
transfer rate
1.2 Target Applications
The performance of the I/O subsystem is one of the most critical factors that will determine
the success of systems which are built to support the demanding workload of emerging applications.
We mention two "champion" applications that can benefit from the comprehensive model proposed
in this paper. The first application is the query optimizer of large databases of traditional data.
In these environments, storage hierarchies of secondary storage devices (magnetic disks) and near-line
tertiary storage devices (such as jukeboxes of optical disks) are typically employed, given the
great storage space requirements. A small portion of the data is kept on-line, i.e., in the secondary
storage devices which are mainly composed by magnetic disks, and the rest of them are stored
in the tertiary storage layer. When a user query is submitted to the system (often concurrently
with others), it is decomposed into a number of requests for blocks that need to be retrieved from
disk (seconday and/or tertiary). Typically, these blocks are randomly distributed over the various
storage devices ([6, 7]). Some of the requested blocks may already reside in primary memory. For
the rest of the cache-missed blocks, the query optimizer needs to know what is the expected retrieval
cost. Such an information will then be used in order to compute the best access plan in serving
the query, which typically is the one that minimizes the overall I/O cost. Our model estimates the
expected I/O cost for retrieving a number of randomly distributed blocks from the disk surface,
and, therefore, it can be used by such query optimizers.
A second application involves the admission controller component of multimedia database
systems. Typically, in a multimedia (e.g., video) database server, several video blocks, one per each
video display, are being retrieved in parallel from the disks ([10, 15]). The admission controller is
unaware of low-level details, such as exact position of video blocks on the disk surface. Typically,
video streams are striped over the secondary storage disks, using a coarse-grained striping technique,
such as that suggested in [22, 21]. With such striping, a video's blocks are stored in round-robin
fashion at consecutive disks, distributing the video to all disks. With respect to the workload
received by a single disk, this striping has a randomizing effect. In addition to this, VCR-type user
interactions have also the tendency to create random workloads for each disk. Therefore, there
appears to be a random access distribution of requests to disk blocks. In addition, an admission
controller should make a quick decision of whether a new request will be accepted by the system
or not. One way of making such a decision is the probabilistic approach which tries to predict the
available I/O bandwidth of the system based on stochastic models ([13]). The model presented in
this paper can be used as the basis of such a probabilistic admission controller when the disk access
pattern is assumed to be random.
The balance of the paper is organized as follows. In section 2, we present a brief overview of
related work in the modeling of the performance of retrieval operations of disk devices. In section
3, we present our comprehensive model, which combines all the essential features of current disk
technologies and characterizes the performance of the disk operations. In section 4, we derive the
formulas for calculating the expected cost of operations in the comprehensive disk technology model
derived earlier. In section 5, we show how our unifying model can be reduced to models for the
existing disk technologies and for possible future technologies. Section 6, first presents the validation
of the analytical results derived in the previous sections by comparing them with simulation-based
results. Subsequently, we show some performance results concentrating on the performance of
zoned magnetic CAV disks (a popular recent disk device technology, the performance of which has
not been analytically modeled before). In addition, this section also compares the performance
of ZCAV disks against CAV disks and some theoretical disks, such as CLV magnetic disks and
CLV/CAV magnetic disks. Finally, section 7 contains concluding remarks.
Related Work
In the bibliography, two kinds of disks have been studied extensively: the magnetic CAV and
the optical CLV disks. In the following, a notion widely used, will be the qualifying sector. We say
that a sector qualifies if and only if that sector has been specifically asked to be retrieved by a user
request.
2.1 CAV Magnetic Disks
For CAV magnetic disks, the researchers' attention has been focused on modeling the performance
of the fundamental disk operations and estimating the seek cost and rotational delay.
The seek operation (during which the disk head moves from the current track to the target track),
depends on the distance d traveled by the head. The seek operation mainly consists of three phases
namely the acceleration, the linear and the settle phases. In the acceleration phase, the head speeds
up until it reaches a certain threshold velocity. In the linear phase, the head travels with this constant
velocity. After the linear phase, the head slows down and lands on the destination track.
This is called the settle cost. If the distance to be traveled is short enough, then there is no linear
phase.
The seek cost in the past has been modeled as a square root function or as a linear function
of the distance ([24, 25]) or a bi-linear equation (one line for each type of seek, short or long).
Recently, the best modeling is based on a combination of the above: i.e., on a square root function,
when the seek distance d is short enough (d ! Q), and by a linear function of d, if the distance
is long enough (d  Q) ([16, 26]). Experimental studies have also determined the value for Q
for different disk products. For example, for the HP 97560 and HP C2200A models Q= 383 and
Q=686 respectively. Notice that if the distance of the destination cylinder is such that d ! Q then
there is no linear phase. So, the cost for a single seek access at distance d is:
Cost seek
a 1
a
Seeks at distance less than Q are termed short seeks and seeks at distance greater than Q are
termed long seeks. The a 1 , a 2 , b 1 , b 2 and Q parameters are dependent on the characteristics of each
device. These parameters differ from product to product and can be very accurately estimated
experimentally.
After reaching the target track and paying a head settle cost, we must wait for the first
qualifying sector of this track to pass beneath the head. The duration of this operation, is called
rotational delay. The rotational delay has been modeled by one half of a full platter revolution
because, on average, the targeted sector will be lying one half of a track away after the seek
operation. Therefore, the rotational delay of a single access is given by
Delay rot =2 s t \Delta h (1)
where s t is the track capacity (in number of sectors) and h is the read sector time.
2.2 CLV Optical Disks
The seek cost and the rotational delay models for the case of the CLV optical disks are the
same as the ones above 1 . There is also a qualitative difference, namely that unlike magnetic disks,
the (expensive) seek operation is not always necessary. In optical disk drives, the target track can
sometimes be accessed by simply diverting the laser beam directly on it. This diversion can be
done by tilting the objective lens. The time consumed for this operation is practically negligible.
Unfortunately, there is a maximum angle that the optic assembly can be diverted. Thus, there is a
maximum number of tracks that can be reached without a seek operation. These tracks occupy a
portion of the disk platter, on the left or on the right of the current head position. This portion is
called the proximal window. In the remainder of this section, we survey the analysis for proximal
window accesses as found in ([3, 4, 5, 8]).
1 However, there is a significant quantitative difference; although the models are the same, CLV optical disks have
smaller average angular velocities, which result in worse transfer and rotational delays, and more expensive seek
operations.
Because storage densities of optical disks are very high, the laser diversion might lose the
target track. This is why the drive must be resynchronized and verify the identity of the landing
track. This resynchronization cost is denoted by SY NC and is measured in terms of the number of
the sectors which have passed under the head during the SY NC operation. Usually, the position
is verified by scanning a single sector.
As soon as the laser beam finds the target track, the drive waits for the target sector to pass
beneath the laser focus spot. After reaching the qualifying sector, data transfer can begin. The
head starts moving (seeking) towards the target track as soon as the laser finds the target track.
In this way, the drive does not have to wait until the head is positioned to read a sector; instead
the laser finds the track, data transfer begins and the head moves in parallel to the data transfer.
Another feature that complicates accesses within the proximal window is the command processing
time. This is the time it takes for the drive to examine the next retrieval request. During
this time the disk platter keeps rotating, so the disk head has scanned a number of sectors before
the processing is over. Thus, since optical CLV disks have a single spiral track, the longer the
command processing time is, the further the head will have moved by the end of the command
processing time. Generally, command processing time depends on the distance of the target sector.
The proximal window is divided into three regions. The regions are termed backward-access,
middle and forward-access (figure 1). Within each region the command processing time is different.
In the middle region, the command processing time is optimized (it is the minimum of the command
processing times of all regions). The limit sector between the middle and the forward-access region
is denoted by LIMIT F while the limit sector between the middle and the backward-access region is
denoted by LIMITB . We index with a 0 the sector just scanned at the moment the request arrived.
The sectors lying to the left (right) of sector 0 are indexed with -1, -2 (+1, +2) etc (figure 1).
region
current track (i th zone)
backward-access forward-access region
middle region
head position when request arrives
head reads in this direction (forwards)

Figure

1: Proximal window access regions.
The middle access region is also termed the jump back region. This is because the LIMIT F
sector is calculated based on the command processing time. After the command processing time,
the head will be lying at the starting track of the forward access region. Therefore, the access to
any target track in the middle access region, is made by diverting the laser focus one track back
each time. If it is determined that the track on which the laser landed is not the target one, then
the laser diverts once more jumping back one track and paying a synchronization and a verification
cost for a second time. If the target track is not in the middle region and is missed, then the laser
does not jump back, but diverts once more. In the following, it is assumed that laser diversions
out of the middle region are accurate, thus paying once the resynchronization and verification cost
As stated previously, the number of sectors scanned during command processing time depends
on the offset index I of the next qualifying sector (expressed as the number of sectors that lie
between the source and the target sectors) and is analogous to the command processing time. Let
CS F , CSB and CSM be the number of sectors scanned by the disk head during command processing
time when the next target sector lies in the forward-access, the backward-access and the middle
region respectively (CSM
Track of i th zone
Here arrives the command
If request is in the middle region
If request is in the forward-access region
If request is in the backward-access region

Figure

2: Sectors scanned during command processing.
It can be shown that the proximal window cost when accessing a sector indexed by I is given
by the following formula ([8]):
Cost proxW in
I \Gamma(CS F +SY NC+1)
(2)
where h i is the time needed for a sector to be scanned in the i th zone, C i is the track capacity in
the i th zone, W is the proximal window size in number of tracks and JumpBacks(I
the number of jump backs in the case of accessing the middle region:
2.3 Motivations and Goals
We can see from the above overview of the related work in the area of disk-device performance
modeling that only a few possible technologies have been modeled. There are existing disk
technologies which are not covered by the above modeling efforts. As an example, we mention the
zoned magnetic, ZCAV, disks. These disks have dominated, due to their higher storage capacities
and transfer rates ([1, 9, 12, 13, 14, 19]). Another example, also recently produced, is the Hitachi
(which behaves as a CAV optical disk when reading from the
innermost half part with a speed varying from 8X to 16X, and as a CLV disk when reading from
the outermost part with a speed of 16X).
Thus, understanding the performance behavior of the disk-based devices is important for of our
"champion" applications (see section 1.2). Furthermore, even if models for all currently available
technologies were developed, new models will be needed for future products. This constituted the
driving force behind the work described in this paper. Therefore, we have developed a comprehensive
performance model for disk device technologies. Our comprehensive model can be reduced to
known models and to models for previously unmodeled existing disk technologies. In addition, because
our model is based on the fundamental features of disk technology, it can be used to model the
performance of future/possible disk technologies. This may enable manufacturers to measure the
performance of "theoretical" technologies and compare them against existing technologies before
their production.
Our unifying performance model accounts for the fundamental characteristics of disk-storage
device technologies, namely the optical/magnetic nature and their constant or variable angular
velocities, transfer rates and storage capacities. Thus, it constitutes a common framework for
analyzing the performance of all disk-storage technologies characterized by any combination of the
above features.
Moreover, one can observe that important factors in determining the disk access costs, either
have not been modeled at all, or have not been modeled in detail in related work. As an example of
the former, we mention the significant cost for head switching, which occurs when a different platter
surface of the same cylinder must be accessed. Although it has been found that head switching
contributes significantly to disk access costs ([16]), it has not been modeled analytically. As an
example of the latter we mention the simplistic modeling of rotational delays, as presented above.
Currently, disk controllers can operate on a batch of requests for sectors of the same cylinder (a
feature that is termed command queuing). This can have a beneficial impact in minimizing the
rotational delay, since the disk controller can retrieve the blocks in the optimal order given the
current position of the head. Thus, modeling the above features can help improve the performance
predictions based on our model considerably.
3 A Comprehensive Model
The device parameters that will be used in order to develop the comprehensive device model
are depicted in the following table:
number of platters D
number of recordable surfaces per platter S
number of cylinders L
maximum number of cylinders in short seeks Q
number of tracks T
number of sectors M
number of zones Z
number of cylinders of zone Z i kZ i k
number of sectors per track (track capacity) of zone Z i C i
time to read a sector of zone Z i h i
block size (in number of sectors)
proximal window size W
settle constant constant settle
head switch constant constant headSwitch
The following equations generally hold:
Z
Z
Our unifying device model will account for all the features of magnetic and optical disks. It will
incorporate all the functionality which has been found to significantly influence the performance of
disks such as the seek cost, the rotational delay, the transfer cost, the settle cost, the head switch
cost and the proximal window cost.
In our comprehensive model we make the following conventions:
1. The time a CLV drive needs to adjust its rotational speed is encapsulated in the seek cost
component.
2. We believe that a cache cost analysis is out of the scope of this paper in which we mainly
focus on the data not found in the cache memory, i.e., cache misses. The interested reader
can find an analytical and validated cache model in [11, 17]. Also, we stress that for the
random workloads typically found in our "champion" applications, caching would introduce
only marginal benefits. In [17], all the crucial performance parameters, such as the hit ratio,
are derived and validated.
3. We selected a block size equal to 1. The expansion of the model to an arbitrary block size is
straightforward but this would make much more complex and hard to read our equations. On
the other hand, a block size which equals 1 sector, preserves the essence of our disk technology
modeling.
4. We selected the SCAN policy to schedule the disk arm, because this is a very widely used
(and well studied) policy.
3.1 Proximal Window Cost for Concentric Tracks
The proximal window cost in our comprehensive model is two-branched. The first branch
corresponds to those disks having a single spiral track and the second to those disks having a set
of concentric tracks. In the former case, the proximal window cost is given by equation (2). In the
latter case, we have to develop a new cost expression. The reason is that, in the single spiral track
model, after the command processing time, the head might be a few "tracks" away from the source
track. In the concentric track model, however, the head will always be lying on the departure track.
Recall that the proximal window cost is dependent only on the number of sectors which must
pass underneath the disk's head, after the laser beam has been diverted to the target track. (This
is so since the laser beam diversion has a negligible cost). Thus, in essence, the proximal window
cost is a "rotational delay" type cost. To compute the proximal window cost we first develop a
sector indexing which will allow us to determine the aforementioned rotational delay. Again we
index with a 0 the sector just scanned by the head when the next retrieval command arrived. The
departure track, as well as the tracks closer to the disk edge, are termed forward tracks, while the
rest are termed backward tracks. We draw a radial line to the left of sector 0, which can be used
to define the desired sector indexing. The first sector of the k th forward track is on the right of
the radial line, indexed by k C i and the last sector is on the left of the radial line, indexed by
1. Similarly, the first sector of the k th backward track is on the right of the radial line,
indexed by \Gammak C i , and the last sector is on the left of the radial line, indexed by \Gamma(k
The indexing scheme is illustrated in figure 3.
Departure
track
Tracks of zone i
Head is lying here when command arrives
Radial line

Figure

3: Index scheme for concentric tracks.
Suppose that the target sector has an index I (as modeled above) and is in some forward
track of the i th zone. The number of the sectors scanned during the command processing time
and during the synchronization and verification procedure is (CS F 1). After diversion
(and synchronization/verification), we must wait until the target sector, which is lying on the
landing track, is brought beneath the head. Given that we are focusing on the i th zone, the relative
position of the qualifying sector is I rel while the relative position of the head
(after synchronization and verification) is H rel (CS Therefore,
for forward accesses, the number of the sectors needed to be scanned, before reaching the target
sector, is:
I rel
The number of the sectors scanned, in the case of a backward access is derived from
the previous expression by considering the absolute value of the index of the target sector (jI j):
I rel (jI j; C
Let CS be equal to CS F in the case of forward accesses and equal to CSB in the case of backward
accesses:
CSB , for backward accesses
Finally, the proximal window cost for the concentric track model, takes the following form:
Cost proxW in
As an example, consider that suppose that a
forward access is about to be performed. Then I
sectors are needed to be scanned, before reaching the target sector.
3.2 Seek Cost
A unifying seek cost function has the form shown in the graphs of figure 4. Notice that, in
accelaration
cost
Cost seek
Cost seektime
distance
time
distance
a) d >= Q b) d < 2Q
linear phase
d

Figure

4: Seek cost.
the general case, seeks at distance less than the proximal window size, are never performed since a
proximal window access is invoked instead. So, the cost for a single seek access at distance d is:
Cost seek
a 1
a
Note that we set in the case of magnetic disks 2 .
3.3 Settle Cost
When the head reaches the destination cylinder, a procedure is triggered in order to verify the
current cylinder and correct any head mispositioning. The time paid for this settling operation is
called the settle cost. In our model, the settle cost is constant:
Cost
Typical values of the settle cost range from 1 ms to 3 ms.
3.4 Rotational Delay
Normally, the rotational delay depends on the rotational speed and on the number of the
sectors that must be passed and is a fraction of the time of a full platter revolution. Since the
rotational speed depends on the zone index, the rotational delay for scanning s sectors in i th zone
before the first qualifying sector is brought beneath the head, is
Delay rot (s;
3.5 Transfer Cost
The transfer of data can begin at the moment the first sector of the block has been brought
beneath the head. The transfer cost is determined by the time to read a sector and is analogous
2 For CLV disks, the rotational speed adjustment time is enclosed in the seek cost.
to the block size and the underlying zone Z
Cost transfer
3.6 Head Switch Cost
Magnetic disks are composed of a number of vertically-aligned platters forming cylinders.
Usually, the platters are two sided, meaning that data can be read and written on both platter
surfaces. For each readable/recordable surface there is a single head for reading and writing this
All heads are moved together and at any time all reside in a single cylinder only. One
head is active each time sending/receiving data to/from the disk's read/write channel. When data
have been accessed from a platter surface and some other data are next to be accessed on another
surface, a head switch must take place. Due to the fact that the tracks of modern disks are almost-
concentric (as opposed to exactly-concentric tracks) the newly activated head may not be above
the track of the cylinder. In this case, a repositioning cost is paid. The time for a head switch is
termed head switch cost and is considered constant:
Cost headSwitch = constant headSwitch
Typical values of the head switch cost constant range from 0.5 ms to 1.5 ms.
4 Average Cost Analysis
In this section, we will model the performance of retrieving N cache-missed sectors. These
sectors are randomly distributed on the disk and are termed qualifying sectors. The tracks/cylinders
that contain at least one qualifying sector are termed qualifying tracks/cylinders. Using the above,
we will derive analytical models for the average retrieval cost of the N sectors.
The average retrieval cost of the N cache-missed sectors randomly distributed on the disk, is
the sum of the average costs previously described. Therefore, the total expected retrieval cost, is:
Cost disk Cost proxW in (N) Cost seek (N) Cost settle (N)
+Delay rot (N) Cost transfer (N) Cost headSwitch (N)
4.1 Average Seek Cost
To estimate the average seek cost of the N sectors, we determine the number of seeks at each
possible distance and multiply it with the seek cost for that distance. Thus, we get:
Cost seek
expected # seeks at distance j ? seek cost at distance j ?)
probability of seek at distance j ?) \Delta ! seek cost at distance j ?)
where Q c is the expected number of qualifying cylinders.
The expected number of seeks at distance j is equal to the expected number of qualifying
cylinders times the probability that a seek at distance j will occur. The expected number of qualifying
cylinders is equal to the total number of cylinders times the probability that a cylinder will
qualify 3 .
In turn, the probability that a cylinder qualifies depends on the zone in which the cylinder belongs,
since larger cylinders have a higher access probability. Thus,
Z
Z
does not qualifyjY 2 Z i
Z
# ways we can pick N sectors from
# ways we can pick N sectors from M ones
Z
Z
where kZ i k is the number of cylinders contained in i th zone.
The probability that a seek at distance j depends on the number of the qualifying
cylinders Q c and the total number of cylinders L:
ways we can pick a pair of successive qualifying cylinders with distance
ways we can pick a pair of successive qualifying cylinders ?
Consider a pair of successive qualifying cylinders with a gap of j cylinders between them. This
pair can be found in (L different positions. Given this pair, there are
combinations of the remaining Q qualifying cylinders. Therefore, the number of possible pairs
of successive qualifying cylinders with distance
1). On the other
hand, the number of ways we can choose the Q c cylinders is
and for each of these we can
pick a pair of qualifying cylinders with (Q ways. Thus, the number of pairs of successive
qualifying cylinders is
1). Finally, the probability P gap (j; L; Q c ) takes the form:
Eng is a sampling space with n mutually exclusive events E i , then the occurrence probability
of an event A is:
The average seek cost is
Cost seek
4.2 Average Proximal Window Cost
The proximal window cost is dependent upon the direction of the head travel. For this reason
we will develop two expressions for the average proximal window cost; one for forward accesses and
one for backward accesses.
The average cost for a single forward access in the proximal window, given that the window
is lying in zone Z i , is the sum, over every position in the window, of the product of the access
probability at a position of the window and the cost for that access:
Cost proxW in (j
Note that for every j  W \Delta C i , the proximal window access cost is zero because a seek access is
invoked instead. P gap (j; M;N) is the probability that j non-qualifying sectors are lying between
two successive qualifying sectors (equation (6)). Although the P gap expression was developed to
estimate the probability that two successive qualifying tracks are lying at a certain distance, the
same expression holds for the probability that two successive qualifying sectors are lying at a certain
distance. Also note that when the access is made at sector j then the gap between the current
and the next sector to be retrieved is j. The total average proximal window cost is:
Cost proxW inforwards
Z
expected # accesses in Z access cost for Z i ?
The expected number of proximal window accesses in zone Z i is the product of the probability
that a proximal window access will occur and the expected number of the sectors accessed in zone
Z i . For the former we have:
D) is the expected number of qualifying cylinders (equation (5)). The
latter is proportional to the number of tracks of zone Z
sectors of Z i ? \DeltaP rob(! a sector qualifies
So, the expression for the expected proximal window cost for the forward accesses takes the form:
Cost proxW inforwards
Z
Cost proxW in (j
Z
Cost proxW in (j
The expression for backward accesses is almost identical with the one just developed. The
difference stems from the fact that sectors are read forwards and the retrieval is made backwards.
So, after reading one sector forwards, the head has to travel backwards and to bypass the sector
just read, the gap j, and finally the sector to be retrieved next (figure 5).
head here after 1st read
head reads forward
. gap j .
next sector to be retrieved

Figure

5: Backward access in proximal window.
The total average cost for backward retrievals is:
Cost proxW inbackwards
Z
expected # accesses in Z access cost for Z i ?
Z
Cost proxW in (\Gamma(j
Z
Cost proxW in (\Gamma(j
4.3 Average Settle Cost
The settle cost is paid every time a seek operation is performed. Thus, to calculate the average
settle time, we only need to know the expected number of qualifying cylinders (equation (5)). So,
the total expected settle cost for all N sectors for the Q c (M; N; C; Z ; cylinders is:
Cost settle
4.4 Average Rotational Delay
With current technology (e.g., SCSI), controllers can operate on a queue of requests. Thus,
requests for the same track can be queued in the controller and it is up to the controller to determine
the best way of retrieving the appropriate sectors. This way, detailed information about the disk's
rotation can be used in order to reduce the rotational delay. One way to achieve this goal is for
the controller to arrange the requests in an order consistent with the order with which the desired
sectors will pass underneath the head.
In the case of magnetic disks consisting of a set of concentric tracks, the total rotational delay
paid for all sectors on the same track is the sum of the delay to reach the first sector plus the delays
to bypass the sectors between the qualifying sectors. Considering the expected positions of the j
qualifying sectors of a track of the i th zone, the disk head could be lying anywhere at the end of the
seek operation. The expected position of the head is the middle of the beginnings of two successive
qualifying sectors. Because the number of the sectors between the beginnings of two successive
qualifying sectors is C i
j , the expected number of sectors scanned before reaching the first sector
that qualifies on average is C i
(figure 6b). The expected positions of j qualifying sectors on the
same track is such that the distance, in number of sectors, between any two sectors that qualify,
is the same. This means that if the number of sectors per track is C i , then the above intersector
distance is C i \Gammaj
(figure 6a) 4 . Summing up, the number of sectors bypassed, for a single track of
expected
head position
expected
head position
distance
intersector
a) Intersector distance
beginning of 1st sector
beginning of 2nd sector
head reads this way
Expected head position

Figure

Expected sector and head positions.
the i th zone which has j qualifying sectors randomly distributed over it, is
reach cost for 1 st sector reach cost for 2 nd sector reach cost for j th sector ?
For the case of optical disks, we assume that the first qualifying sector is reached by a seek operation
(as opposed to a proximal window access). Therefore, we only need to calculate the rotational delay
required to reach the first of the qualifying sectors of the track. The rotational delay for the rest of
the sectors of the track will be taken into account in the average proximal window cost (as these
will be accessed via a proximal window access). The expected number of sectors scanned until the
first qualifying sector is brought under the head, if we are in zone Z i , is
So the non-qualifying sectors passed by the disk head is given by:
where  is equal to 1 for magnetic disks and 0 for optical disks. The average rotational latency for
that track is
then the intersector distance cannot be equal to C i \Gammaj
j for every successive pair of qualifying
sectors. However, in our analysis we assume, without any noticeable impacts, that C i mod
where Delay rot (s; i) is the rotational cost for scanning s sectors in zone Z i (equation (3)) and
is the probability that a track contains j qualifying sectors:
sectors from another track ? sectors in the track ?
ways we can distribute the N sectors ?
Finally, the expected rotational delay is the summation over all zones of the partial rotational
delays and depends on the total number of tracks per zone:
Delay rot
Z
D) is the number of tracks in zone i and  is the probability that an access is a
proximal window access.
4.5 Average Transfer Cost
Every operating system adopts the notion of block to deal with data transfers from and to the
disk. The size of a block may be variable but definitely is multiple of the smallest physical storage
unit which is the sector. The cost depends on the zones and is the product of the expected number
of block accesses and a weighted cost sum over the set of the zones.
Cost transfer
Z
(Prob(Z i is cost in Z i ?)
Z
sectors in Z i ?
Z
Z
M is the probability of accessing the i th zone and Cost transfer (i) is the cost for
block transfer (equation (4)).
4.6 Average Head Switch Cost
This cost is equal to the average number of head switches times the cost paid for each such
switch. The average number of head switches is equal to the expected number of qualifying tracks
minus the expected number of qualifying cylinders. This is because once the set of heads reaches
a cylinder, a head switch is performed for all the qualifying tracks of the cylinder except the first
one. So, the total average head switch cost is:
Cost headSwitch
D) is the expected number of qualifying cylinders (see equation (5)) and
D) is the expected number of qualifying tracks. The expected number of qualifying
tracks is sum of the expected number of qualifying tracks in each zone:
Z
and
#tracks of Z i ? \DeltaP rob(a track of Z i qualifies)
track of Z i does not qualify))
# ways one can pick N sectors from
# ways one can pick N sectors from M ones
Remember that all the qualifying tracks of the same cylinder are accessed before moving to another
cylinder (since we assume a SCAN-like scheduling algorithm).
5 Reductions of the Comprehensive Model
In this section, we show how one can derive the performance models for the currently known
disk technologies from our comprehensive performance model. Additionally, we show how one can
derive the performance models for some disk technologies that might appear in the future (see
figure 7).
CAV/CLV Multi-spiral
optical disks
h C <> const
=const
const
Generalized Disk Model
transfer transfer

Figure

7: Reductions of the comprehensive disk model.
ffl CAV model
We can derive a model for CAV optical disks from the comprehensive model. This can be
done if we set the number of the zones to 1 1). If we, additionally, consider that there
is no proximal window cost (i.e., W =0), then we get the model for CAV magnetic disks.
ffl CLV model
The difference between the CLV optical disk model and the unifying model stems from the
fact that the read sector time is constant throughout a CLV disk, i.e., h 1 =h
constant. The track capacity (per zone) increases as we move towards the outer disk edge.
Additionally, there is no head switch cost since optical disks are single plattered 5 . If we set
W =0, then the comprehensive model is further reduced to that for CLV magnetic disks.
ffl ZCAV model
In the model for ZCAV disks, the read sector time decreases as we get closer to the disk edge,
thus, increasing the transfer rate. A full disk revolution takes constant time, independently
of the zone in which the head is lying. This means that the product
throughout the disk.
ffl ZCLV model
In the zoned CLV disk model, the transfer rate increases near the outer edge, as is the case
with the ZCAV disks. However, the product (i.e., the angular velocity) does not,
necessarily, remain constant across the disk.
ffl CLV/CAV and CAV/CLV model
When we started the development of this unifying disk performance model both of CLV/CAV
and CAV/CLV did not exist. Since then, optical CAV/CLV appeared as a product (Hitachi
12-16X CD-ROM drive [2]). They are divided into two major parts: the CLV (CAV) part is
the innermost and the CAV (CLV) part is the outermost. The reason for their existence could
be to strike a balance between low rotational delays and high storage capacities. Having a part
as CLV results in large storage capacities. At the same time, a CAV part insures low access
times (since there are no angular velocity adjustments) and maximum angular velocity which
implies low rotational delays. We obtain the CAV/CLV model from the comprehensive model
as follows: if the innermost part has Z 1 zones, then we simply set h 1 =h
=constant
and C 1
constant. On the other hand, if the outermost part has Z 2 zones,
we should set hZ 1
constant and CZ 1
The CLV/CAV model can be obtained similarly.
ffl Optical multi-spiral model
This is also an optical model that already exists. In this disk, n spirals are wrapped up in
parallel as shown in figure 8. The single head of the drive splits the laser beam into n distinct
beams, each headed on a separate spiral. This way the transfer rate is multiplied by a factor
of n since n spirals can be read simultaneously and, thus, the transfer cost is down scaled by
a factor of n. Our model reduces to the optical multi-spiral model, if we replace our transfer
cost expression of equation (4) with a new one:
Cost 0
For all the above models, we can derive the corresponding magnetic model if we set
Otherwise, if we assign a nonzero value to the proximal window size, we get the corresponding
optical model.
5 Even if the optical has two readable surfaces, there is only one optical head.
Disk surface
Sectors
1st spiral
2nd spiral

Figure

8: Multi-Spiral Disk.
6 Performance Results
The purpose of this section is threefold. First, we show the validation of our analytical results
by comparing them with results we obtained from simulations of disk accesses. Second, we wish
to present the performance behavior we obtain from our comprehensive model after reducing it to
the model for the ZCAV disk technology (whose performance has not been analytically modeled
previously). Third, we show the performance behavior of some possible future disk technologies.
The reader can compare the performance of CAV and CLV disks against that of ZCAV disks
and CLV/CAV disks, with respect to the total seek, rotational, transfer and head switch cost of
retrieving N qualifying sectors (which have missed the cache). The qualifying sectors are randomly
distributed and retrieved using the SCAN scheduling algorithm. For our performance comparisons
we choose to include the models for two existent products (magnetic CAV and ZCAV disks). In
addition, we included the models for two theoretical disks (magnetic CLV and CLV/CAV) in order
to corroborate our intuitive explanations of (and gain insights into) the fundamental performance
behavior.
The ZCAV disk has 8 zones. The number of cylinders in the zones (moving towards the disk
are: 252, 268, 318, 138, 144, 136, 192 and 533 respectively. Using a sector size of 1 KB,
the number of sectors per track for these zones are: 28, 32, 36, 40, 42, 44, 46 and 48 respectively.
For all disks, the track capacity of the innermost tracks are 28 sectors, each with size of 1KB, so
to correspond to real disk products, such as the HP C2240, which have a total of 56KB in the
innermost track. For the CLV disk the track capacity increases with constant rate so to reach
the maximum track capacity of 48 sectors/track in order to meaningfully compare it against the
ZCAV disk. The CAV disk has 28 sectors per track for all its tracks. The CLV part of the hybrid
disk (CLV/CAV) starts with innermost track capacity of 28 sectors, increasing uniformly to the
maximum capacity of the outermost track of 38 sectors. The CAV part of the same disk has 39
sectors per track and 1150 cylinders.
All disks with constant angular velocity rotate with the same speed of 7200 r.p.m. In addition,
the angular velocity of the CLV and the CLV/CAV disks is also equal to 7200 r.p.m. The average
angular velocity of the CLV disk is 11.3 ms per revolution, which amounts to 5305 r.p.m. The
average angular velocity for the CLV part of the hybrid disk is 6109 r.p.m. and for the CAV part
is 5169 r.p.m.
This rotational speed for the ZCAV disk results in a read sector time of 8:33=C i ms, where
8.33 ms is the full revolution time and C i is the number of the sectors of a track in the i th zone.
The read sector time for the CAV disk is constant and equal to 8:33=28 ms. For the CLV disk and
the CLV part of the hybrid disk the read sector time is constant and equal to 8:33=28 ms. (Note
that although the track capacity in CLV disks increases, the angular velocity decreases in a way
that results in a constant read sector time). Finally, the read sector time for the CAV part of the
hybrid disk is 11:6=39 ms, where 11:6 ms is the full revolution time. Observe that the read sector
times for the CLV, CLV/CAV and CAV disks are equal by construction.
All disks are single plattered (S =1), have the same number of platters (D=13) and the same
seek cost parameters (a 1 =0:4; b 1 =3:24; a 2 =0:008; b 2 =8; Q=383) and they have (almost) the same
storage capacity, e.g., 1052090 KB for the ZCAV disk, 1052100 KB for the CAV disk, 1051830 KB
for the CLV disk and 1051973 KB for the CLV/CAV disk. The head switch constant is 0.5 ms for
all disks. The ZCAV disk has a total of 1981 cylinders, the CAV disk has 2890 cylinders, the CLV
disk has 2145 cylinders and the CLV/CAV disk has 2232 cylinders.
6.1 Model Validation
In this section, we report on the results of our efforts to validate the analytical performance
model derived earlier. Specifically, we simulated accesses to a ZCAV disk and validated the empirical
results against those obtained analytically for ZCAV disks. We focused on ZCAV disks since they
incorporate most of the additional essential features of our model (e.g., variable transfer rates and
storage capacities) and can validate all of the mathematical expressions derived earlier (except for
that of the proximal window access cost).
Our simulation model uses the same disk configuration as the one of the ZCAV disk described in
the previous section. This means that the disk layout (i.e., Z, C i , S, D), the seek cost parameters
(i.e., a 1 , b 1 , a 2 , b 2 , Q), the rotational speed (i.e., 8:33 ms per full revolution), the block size
1), the settle cost constant (i.e., constant settle ) and the head switch cost constant (i.e.,
constant headSwitch ) are the same for both simulation and analytical models. Note that the above
disk configuration is a mixture of the products HP C2240 and HP 97560.
Our simulation model is based on the simulation model developed in [16] which was proved
to be accurate and validated. We use the same seek cost model which is a two branched function
of the distance (a root function for the short seeks and a linear function for the long seeks), the
rotational delay is calculated keeping track of the head while the platter rotates and optimizing the
retrieval of the qualifying sectors when more than one reside in the same track (so that they are
retrieved at most in a full revolution). Additionally, the head switch and the settle costs have been
incorporated in our simulator in the same way they have been embedded in the simulation model
of [16]. Thus, we managed, first, to match our analytical results with the results of our simulator
and second, to match our simulator's basic characteristics (i.e., takes into account settle phase,
head switch, command queuing, etc) with the one of [16].
In figure 9, we plot the empirical and analytical measurements for the total average seek cost,
rotational delay, transfer cost and head switch cost. In the figure, we can see that there is a very
close match between the analytical and the simulation results for all four metrics. The following
table shows the offness, which is defined to be the percentage deviation between our simulation
measurements and the analytical expressions.
Total
Average
Cost
(ms)
Number of Cache-Missed Qualifying Sectors (N)
ZCAV disk
Simulated
Analytical50001500025000
Total
Average
Rotational
Delay
(ms)
Number of Cache-Missed Qualifying Sectors (N)
ZCAV disk
Simulated
Analytical200600100014001800
Total
Average
Head
Switch
Cost
(ms)
Number of Cache-Missed Qualifying Sectors (N)
ZCAV disk
Simulated
Analytical20060010001400
Total
Average
Transfer
Cost
(ms)
Number of Cache-Missed Qualifying Sectors (N)
ZCAV disk
Simulated
Analytical

Figure

9: Validation
(a) (b)
(c) (d)
Metric Offness %
Rotational 0:852259
Head switch 0:544137
Transfer 0:396091
6.2 Comparison of Different Technologies
In figure 10a, we can see the total expected seek cost for the ZCAV, CAV, CLV and CLV/CAV
disks with respect to the number of the qualifying sectors. The seek cost for the CAV disk is always
higher than the seek cost of the ZCAV disk. This occurs because the CAV disk has more cylinders
than the ZCAV disk, which in turn is attributed to the fact that both disks have the same storage
Total
Average
Cost
(ms)
Number of Cache-Missed Qualifying Sectors (N)
ZCAV50000150000250000
Total
Average
Rotational
Delay
(ms)
Number of Cache-Missed Qualifying Sectors (N) (x1000)
ZCAV20006000100001400018000
Total
Average
Head
Switch
(ms)
Number of Cache-Missed Qualifying Sectors (N) (x1000)
Total
Average
Transfer
Cost
(ms)
Number of Cache-Missed Qualifying Sectors (N)

Figure

10: Total average costs.
(a) (b)
(c) (d)
capacity while the ZCAV disk has a higher average track capacity. The more the cylinders, the
more the qualifying cylinders and the more the expected distance between two successive qualifying
cylinders. The longest this distance, the higher the seek cost. There is an upper bound for the
total seek cost for both disks and this is reached when all the disk cylinders are qualifying. The
same explanation holds for the performance differencies between the other disk models.
The total average rotational delay of the ZCAV disk is lower than the rotational delay of the
CAV disk (see figure 10b). The reason is that the expected number of the qualifying sectors per
track is greater in the case of the ZCAV disk (because ZCAV has fewer but "larger" tracks (i.e.,
with higher average storage capacities)). The more the qualifying sectors per track, the lower is
the rotational delay. The CLV and CLV/CAV disk models have higher rotational latencies (despite
the fewer and larger tracks) because of the decreasing angular velocity when moving towards the
outer edge. This is evidenced by the better rotational delay of the CLV/CAV disk compared to
that of the CLV disk.
In figure 10c, we can see how the total head switch cost is affected by the number of the
qualifying sectors (N ). For small values of N , a qualifying cylinder has very few qualifying sectors.
For the cylinders with one qualifying sector we pay no head switch cost and, therefore, the CAV
head switch cost is lower (although not shown clearly in the figure) since it has more cylinders.
When the number of the sectors to be retrieved becomes large enough, the ZCAV disk provides
lower head switch cost. This happens because, for large values of N , all the cylinders are qualifying
for both disks and the key point becomes the expected number of the qualifying tracks. The greater
the number of the qualifying tracks, the greater the number of head switches. And since the CAV
disk has more and "smaller" tracks than the ZCAV disk, it has also more qualifying tracks. For
the same reason, CLV/CAV disk performs worse than the CLV disk.
Finally, in figure 10d, we can see that the total transfer cost of the ZCAV disk is lower than
the one of the CAV disk. The explanation is based on the "larger" tracks of the ZCAV disk, which
in turn imply shorter sectors (in inches). This coupled with the fact that the two disks have the
same angular velocity implies shorter average sector transfer time for the ZCAV disk. Notice also
that the transfer cost is the same for the CLV and the CLV/CAV disks. Recall that, by their
construction, these disks have the same transfer rate.
7 Contribution and Concluding Remarks
This paper presents an attempt to provide a common framework for studying the performance
behavior of retrieval operations in disk-storage device technologies under random workloads found
in several applications. To do this, we identify the fundamental characteristics of disk-storage device
technology which are the optical/magnetic nature and the constant or variable angular/linear
velocity, transfer rate and storage capacity. Based on these characteristics, we derived a comprehensive
analytical model which can be used in important system components such as the query
optimizer in a large-scale traditional database and in an admission controller in a multimedia storage
server. The comprehensive nature of our model makes it useful for studying the performance
of existing and possible future disk-drive products and is important for estimating the retrieval
cost in large database systems containing different types of disk drives (such as magnetic disks in
secondary storage and optical disk jukeboxes in tertiary storage).
For optical disks our model accounts for proximal window accesses. In doing this, we augmented
related work by providing an expected cost formula for proximal window accesses in the
case of optical disks with concentric tracks.
For magnetic disks, we derived expected costs for the traditionally-studied operations (e.g.,
seek and rotational delays). Our expected cost formulas accounted for the possibility of constant
or variable angular/linear velocities, transfer rates and storage capacities. In addition, we included
a more detailed analytical characterization of modern disk behavior, such as command queuing
(which allows disks controllers to minimize rotational delay). Also, we contributed expected cost
analysis of disk functionalities such as head switching which has not, to our knowledge, been
modeled before, although is has been found to contribute to disk access cost.
After deriving the unifying formulas for the expected disk retrieval cost, we reduced our formulas
to model costs for existing disk products and for theoretical disks. This allowed us to gain
insights into the fundamental performance trade-offs. It also gave us the opportunity to contribute
an analysis of the performance of the recently-produced zoned magnetic disks.
Our analytical results were validated against detailed simulation studies. The models for our
simulations are similar to models in the literature which have been found to very closely approximate
the performance of real disks [16], with the exception of cache modeling (which is not needed for
our target applications) and of detailed modeling of the controller's internals and bus contention
which are dependent on particular system configurations (such as the number of drives attached to
I/O buses, the size of drive-level speed-matching buffers and caches) and which change with time.
The same model can form a basis to develop a model to predict the performance of write disk
operations as well. Write operations, in general, are costlier. The exact cost model depends on
whether a written block can be read and checked for consistency without having to wait for an
additional revolution (a feature typically unavailable in optical disks), whether the disk block needs
to be erased before written (as is typically the case in optical disks) and depends also on the disk's
reliability (i.e., how many write operations must on average be repeated). Finally, the cost model
for write operations must also take into account the fact that many disks require data blocks to be
written on the disk's surface, whereas reads can be satisfied directly from the controller's cache. In
the future, we plan to extend this model to account for write operations as well.



--R

"Track-Pairing: a Novel Data Layout for VOD Servers with Multi-Zone- Recording Disks"
"Comparison: All 12X CD-ROM Drives Are Not Equal"
"Analysis of Retrieval Performance for Records and Objects Using Optical Disk Technology"
"Performance Analysis and Fundamental Trade Offs for Optical Disks"
"Optical Mass Storage Systems and their Performance"
"Estimating Block Selectivities for Physical Database Design"
"Estimating Block Accesses in Database Organizations"
"Performance Optimizations for Optical Discs Architectures"
"Placement of Continuous Media in Multi-Zone Disks"
"Tutorial on Multimedia Storage Servers"
"Hit-Ratio of Caching Disk Buffer"
"Magnetic Disk Drives Evaluation"
"Stochastic Service Guarantees for Continuous Data on Multi-Zone Disks"
"Observing the Effects of Multi-Zone Disks"
"Disk Scheduling for Mixed-Media Workloads in Multimedia Servers"
"An Introduction to Disk Drive Modeling"
"Performance Modeling for Realistic Storage Devices"
"Multimedia: Computing, Communications and Appli- cations"
"Placement of Multimedia Blocks on Zoned Disks"
"Optimal Data Placement on Disks: A Comprehensive Solution for Different Disk Technologies"
"Overlay striping and optimal parallel I/O for modern applications"
"Video striping in video server environments"
"An Exact Analysis of Expected Seeks in Shadowed Disks"
"Minimizing Expected Head Movement in One-Dimensional and Two-Dimensional Mass Storage Systems"
"Algorithmic Studies In Mass Storage Systems"
"A Tight Upper Bound of the Lumped Disk Seek Time for the SCAN Disk Scheduling Policy"
--TR

--CTR
Zhenghong Deng , Wei Zheng , Fang Wang , Zhengguo Hu, Research and implementation of management software for SAN based on clustering technology, Proceedings of the 2004 ACM SIGGRAPH international conference on Virtual Reality continuum and its applications in industry, June 16-18, 2004, Singapore
Daniel Ellard , Margo Seltzer, NFS tricks and benchmarking traps, Proceedings of the USENIX Annual Technical Conference on USENIX Annual Technical Conference, p.16-16, June 09-14, 2003, San Antonio, Texas
Athena Vakali , Evimaria Terzi , Elisa Bertino , Ahmed Elmagarmid, Hierarchical data placement for navigational multimedia applications, Data & Knowledge Engineering, v.44 n.1, p.49-80, January
performance modeling and prediction;disk technologies;zoned disks