Dynamic cache reconfiguration strategies for cluster-based streaming proxy

Abstract

The high bandwidth and the relatively long-lived characteristics of digital video are key limiting factors in the wide-spread usage of streaming content over the Internet. The problem is further complicated by the fact that video popularity changes over time. In this paper, we study caching issues for a cluster-based streaming proxy in the face of changing video popularity. We show that the cache placement problem for a given video popularity is NP-complete, and propose a series of techniques to address the problem. We first introduce the dynamic first fit (DFF) algorithm that give the results close to the optimal cache placement (OCP). We then propose minimum weight perfect matching (MWPM) and swapping-based techniques that can dynamically reconfigure the cache placement to adapt to changing video popularity with minimum copying overhead. Our simulation results show that MWPM reconfiguration can reduce the copying overhead by a factor of more than two, and that swapping-based reconfiguration can further reduce the copying overhead compared to MWPM, and allow for the tradeoffs between the reconfiguration copying overhead and the proxy bandwidth utilization.

Full text

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Dynamic Cache Reconfiguration Strategies for A
Cluster-Based Streaming Proxy
Yang Guo, Zihui Ge, Bhuvan Urgaonkar, Prashant Shenoy, and Don Towsley
Department of Computer Science
University of Massachusetts at Amherst
Amherst, MA 01002
?yguo,gezihui,bhuvan,shenoy,towsley
? @cs.umass.edu
Abstract—The high bandwidth and the relatively long-
lived characteristics of digital video are key limiting fac-
tors in the wide-spread usage of streaming content over
the Internet. The problem is further complicated by the
fact that video popularity changes over time. In this pa-
per, we study caching issues for a cluster-based streaming
proxy in the face of changing video popularity. We show
that the cache placement problem for a given video pop-
ularity is NP-complete, and propose the dynamic first fit
(DFF) algorithm that give the results close to the optimal
cache placement. We then propose minimum weight perfect
matching(MWPM) and swapping-based techniques that
can dynamicallyreconfigurethe cache placementtoadapt
tochangingvideopopularitywithminimum copyingover-
head. Our simulation results show that MWPM recon-
figuration can reduce the copying overhead by a factor
of more than two, and that swapping-based reconfigura-
tion can further reduce the copying overhead compared
to MWPM, and allow for the tradeoffs between the re-
configuration copying overhead and the proxy bandwidth
utilization.
I. INTRODUCTION
The high bandwidth and the relatively long-lived
characteristics of digital video are key limiting factors
in the wide-spread usage of streaming content over the
Internet. The problem is further complicated by the fact
that video popularity changes over time. The use of a
content distribution network (CDN) is one technique to
alleviate these problems. CDNs cache partial or entire
videos at proxies deployed close to clients, and thereby
reduce network and server load and provide better qual-
ity of service to end-clients [1–3]. Due to the relatively
This research was supported in part by the National Science
Foundation under NSF grants EIA-0080119, ANI-0085848, CCR-
9984030, ANI-9973092, ANI9977635, ANI-9977555, and CDA-
9502639. Any opinions, findings, and conclusions or recomenda-
tions expressed in this material are those of the authors and do not
necessarily reflect the views of the funding agencies.
large storage space and bandwidth needs of streaming
media, a streaming CDN typically employs a cluster of
proxies at each physical location. Each such cluster can
collectively cache a larger number of objects and also
serve clients with larger aggregate bandwidth needs. In
this paper, we study caching issues for such a streaming
proxy cluster in the face of changing video popularity.
Each proxy within the cluster contains two important
resources: storage (cache) space and bandwidth. Each
video file requires a certain amount of storage and band-
width determined by its popularity. Assuming that video
files are divided into objects, we study the cache place-
ment problem, i.e., whether to cache an object, and if
we do, which component proxy to place it on so that the
aggregate bandwidth requirement posed on the servers
and the network is minimized. Furthermore, since video
popularities vary over time (e.g., many people wanted
to watch the movie The Matrix again in preparation of
the release of its sequel The Matrix Reloaded causing it
to be very popular for a few weeks), the optimal cache
placement also changes with time. The proxy must be
able to deal with dynamically varying popularities of
videos and reconfigure the placement accordingly.
In this paper, we first consider the offline version of
the cache placement problem. We show that it is an
NP-complete problem and draw parallels with a closely
related packing problem, the
knapsack problem (
from heuristics for
static first-fit (SFF) and dynamic first-fit (DFF)—to map
objects to proxies based on their storage and bandwidth
needs. We then propose two techniques to dynamically
adjust the placement to accommodate changing video
popularities. Our techniques attempt to minimize the
copying overheads incurred when adjusting the place-
ment. The minimum weight perfect match (MWPM)
? -dimensional multiple
Taking inspiration
? -MKP) [4].
? -MKP, we propose two heuristics—

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reconfiguration method minimize the copying overhead
associated with such a placement reconfiguration by
solving a bipartite matching problem. In order to further
reduce the copying overhead, we propose swapping-
based reconfiguration, which mimics the hill climbing
approach [5] used in solving optimization problems.
The swapping-based reconfiguration also naturally al-
lows us to trade off proxy bandwidth utilization against
copying overhead.
We evaluate our techniques using simulation.
find that DFF gives a placement that is very close to
the optimal cache placement, and that both DFF and
SFF outperform a placement method that does not take
bandwidth and storage requirements into account. We
then examine the performance of MWPM reconfigu-
ration, and show that it can reduce the copying over-
head by a factor of more than two. Finally, we show
that swapping-based reconfiguration can further reduce
copying overhead relative to MWPM, and that further
copying overhead reduction can be achieved by decreas-
ing the proxy bandwidth utilization.
In summary, we study the dynamic cache reconfigura-
tion problem for a cluster-based streaming proxy in the
face of changing video popularities. Our contributions
are twofold:
We
?We show that the cache placement problem is NP-
complete, and propose DFF algorithm that is found
to give the results close to the optimal cache place-
ment.
?We propose MWPM and swapping-based tech-
niques that can reconfigure the cache placement
dynamically to adapt to changing video popularity
with minimum copying overhead.
The remainder of the paper is organized as follows.
In Section II, we describe the architecture of a cluster-
based streaming proxy. We formulate the optimal cache
placement problem and present the baseline strategies in
Section III. The techniques for dynamic reconfiguration
of cache placement are presented in Section IV. Section
V is dedicated to performance evaluation. Section VI
includes the related work, and Section VII concludes the
paper.
II. ARCHITECTURE OF CLUSTER-BASED
STREAMING PROXY
A cluster-based streaming proxy consists of a set of
component proxies as shown in Fig. 1. These individ-
ual proxies are connected through a LAN or SAN, and
are controlled by a coordinator residing on one of the
machines.
The coordinator provides an interface for clients and
servers so that the cluster-based streaming proxy acts as
a single machine proxy from the perspective of clients
and servers. In addition, the coordinator provides the
following functionalities to the component proxies in-
side a cluster-based proxy.
?Coordinate component proxies to serve client re-
quests.A client request may require multiple
cached objects from different component proxies
with a certain timing relationship. The coordina-
tor needs to orchestrate the component proxies to
serve these requests.
?Monitor and estimate the popularity (access fre-
quency) of multimedia objects.
?Compute the optimal cache placement based on the
current content popularity, and conduct dynamic
cache reconfiguration if the degree of the popularity
change demands cache reconfiguration.
LAN/SAN
Storage spaceComponent proxy
... ...
?????????
??????
?????????
??????
Coordinator
Fig. 1. A cluster-based streaming proxy
In this paper we focus on the dynamic cache reconfig-
uration issues for such a cluster-based streaming proxy.
We assume perfect knowledge of client access informa-
tion. Accurately monitoring the popularity of streaming
objects and efficiently coordinating component proxies
to provide requested service are significant problems in
their own right, and lie beyond the scope of this paper.
III. OPTIMAL CACHE PLACEMENT
Inthis section, weinvestigate the optimal cache place-
ment problem for a cluster-based streaming proxy for a
given video popularity. We formulate this problem as an
integer linear programming problem, and show that the
problem is NP-complete. We then present two baseline
heuristics for it. In Section IV, we will show how these
baseline heuristics can be enhanced to realize dynamic
cache reconfiguration with minimum copying overhead.

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A. Optimal Cache Placement: Problem Formulation
Consider a cluster-based proxy with
proxies. Let
space and bandwidth at the
pose that the cluster-based proxy services a set of videos
that are divided intodistinct objects. Let
denote the storage space and bandwidth requirement of
object
reduce the network bandwidth consumption on the path
from remote servers to the proxy cluster. We focus on
the problem of which objects to cache and where.
Let
object
holds a copy of object
ther, let
for object
gregate demand for the object is handled by component
proxy
to minimize the bandwidth consumption on the network
path from the remote servers to the proxy, or equiva-
lently, to maximize the share of the aggregate client re-
quests that can be serviced using cached videos. The re-
sulting optimal cache placement (O.C.P.) problem can
be formulated as follows:
?
component
?! and
"# denote the available storage
$ -th component proxy. Sup-
%&(' and
objects to
)?'
* . The proxy caches a subset of the
%
+
', be a selection parameter that denotes whether
* is cached at proxy
$ —
+-'. equals 1 if proxy
$
* and is zero otherwise. Fur-
/0', denote the amount of bandwidth reserved
* at proxy
$ (
/1', indicates how much of the ag-
$ ). Theobjective ofcaching objects attheproxy is
24365798
/!:?+<;>=@?

?
'
/0', A+?'.
(1)
subject to:
?
'
&B'C+?', EDF?G
(2)
?
'
/H', A+?', EDI">
(3)
?

+
',
/
',
DF)
'
(4)
where
+J'. LKMONP:-Q6R ,
*SKMHQT:AUAUAUO:??VR , and
$K
MHQT:AUAUAU6:?%WR .
The solution to this problem yields values of
798?X
; denotes the allocated proxy band-
width.
+O', and
/H', that completely describe the placement of objects
The solution may involve object replication across com-
ponent proxies to meet bandwidth needs. Further, some
objects may not be cached at any proxy, if it is not ad-
vantageous to do so.
Proposition III.1: The
ment (O.C.P) problem is NP-complete. The problem is
NP-complete even if all objects are of the same size.
The proof is included in the Appendix.
and the bandwidth reserved for that object at a proxy.
optimalcacheplace-
B. Cache Placement Heuristics
We note that O.C.P. is similar to the
multiple knapsack problem (
one ormoreknapsacks that have capacities along twodi-
mensions, and a number of items that have requirements
along two dimensions. Each item has a profit associated
with it. The goal is to pack items into the knapsacks so
as to maximize the profit yielded by the packed items,
while the capacity constraints along both dimensions are
maintained. The component proxies and video objects
in O.C.P. may be viewed as akin to the knapsacks and
the items in
with the video objects are their bandwidth requirements.
However there is an important difference between the
two problems—the requirements of an item along both
directions in
may be packed in exactly one knapsack; the bandwidth
requirement of a video object in O.C.P. is divisible and
may be met by replicating the object on multiple com-
ponent proxies.
Heuristics based on per-unit weight are frequently
used for knapsack problems. Consequently, we define
the bandwidth-space ratio of object
ratio of the required bandwidth and the object size), and
the bandwidth-space ratio of proxy
Static First-fit algorithm (SFF). Static first-fit
sorts proxies and objects in descending order of their
bandwidth-space ratios. Each object (in descending or-
der) is assigned to the first proxy (also in descending or-
der) that has sufficient space to cache this object. If this
proxy has sufficient bandwidth to service this object, the
corresponding amount of bandwidth is reserved at the
proxy, and the object is removed from the uncached ob-
ject pool. On the other hand, if the proxy does not have
sufficient bandwidth to service the object, the available
bandwidth at the proxy is reserved for this object. The
object is returned back into the un-cached object pool
withthe reserved bandwidth subtracted from its required
bandwidth. The proxy is removed from the proxy pool
since all of its bandwidth has been consumed. The algo-
rithm is illustrated in Fig. 2.
Dynamic first-fit algorithm (DFF). DFF is simi-
lar to SFF, except that the bandwidth-space ratio of a
component proxy is recomputed after an object is placed
onto that proxy and proxies are resorted by their new
bandwidth-space ratios (in SFF, the ratio is computed
only once, at the beginning). The intuition behind DFF
is that the effective bandwidth-space ratio of a proxy
changes after an object is cached, and recomputing this
? -dimensional
? -MKP) [4].
? -MKP has
? -MKP respectively; the profits associated
? -MKP are indivisible meaning the item
* to be
)-'ZY6&B' (the
$ to be
"[ OY\?G .
]
]

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STATIC-FIRST-FIT (
1. sort in descending order of bandwidth-space
ratio
2. while (is not empty)
3.object with highest bandwidth-space ratio
4.
for (proxyin the sorted order)
5.
if (
6.// cache object
7.
8.
if (
9.
10.
11.remove object
12.
else
13.
14.remove proxy
15.
16.return modified obj.
17. break;
18.
19.
20.
^ ,
_ )
^
_M
*`=
$aKb^M
&!'cDI?G )
M
+
'.
=dQ ;
*
?G e=@?B gfh&B' ;
)
'
DF"
)
/H', e=@)?'
"> e=i"> gfW)?'
* from
_
/
',
=@"

$ from
^
)?'j=@)?'jfk"# ;
* into
_
R //end of if
R //end of for loop
R //end of while loop
Fig. 2.Static First-fit Placement Algorithm. Denote by
the collection of proxies that have bandwidth and space
resources to provide caching service, and by
lection of objects that have not been cached, or need ad-
ditional bandwidth.
l
m
the col-
ratio may result in a better overall placement. In fact,
as we will see in Section V, DFF does perform better
than SFF, and gives results close to the optimal cache
placement.
So far we have focused on the optimal cache place-
ment with fixed storage and bandwidth needs of a set
of objects.In practice, bandwidth needs of objects
vary over time due to changes in object popularities.
The cache placement needs to be dynamically reconfig-
ured in order to adapt to the changing popularities, e.g.,
newly popular objects may need to brought in from the
servers, and cold objects may need to be ejected. We
denote the number of objects that need to be transmitted
among component proxies and from servers to proxy as
the copying overhead of cache reconfiguration. In the
following section, we study how to realize the cache re-
configuration with the minimum copying overhead.
IV. DYNAMIC CACHE RECONFIGURATION
A straightforward technique for dynamic cache re-
configuration is to recompute the entire placement from
scratch using DFF or SFF based on the newly measured
popularities, and bring in the objects from neighbor-
ing component proxies or remote servers. We denote
such cache reconfiguration approaches as simple DFF
reconfiguration or simple SFF reconfiguration. These
approaches may yield close-to-optimal bandwidth uti-
lization. However, they may cause many objects to be
moved across proxies, resulting in excessive copying
overhead as indicated by the simulation experiments in
Section V.
In the following, we propose two cache reconfigura-
tion techniques that can reduce the copying overhead
by exploring the existing cache placement.
present the minimum weight perfect matching reconfigu-
ration method (MWPM reconfiguration) by formulating
the minimum copying overhead reconfiguration prob-
lem as a minimum weight perfect matching on a bi-
partite graph. We then describe the swapping-based re-
configuration method that mimics the hill-climbing ap-
proach [5] used in solving optimization problems. The
swapping-based reconfiguration naturally allows us to
trade the proxy bandwidth utilization for the copying
overhead.
We first
A. MWPM cache reconfiguration
Let
^>n<:?^poT:AUAUAU?^cq
denote the
?
proxies in the clus-
ter. Let
the proxy cluster and let
ment that is desired. There can be as many as
to reconfigure the placement. Ideally, we would like to
reconfigure the placement such that the cost of moving
(copying) objects from one proxy to another or from the
server to a proxy is minimized.
Theabove problem is identical to the problem of com-
puting the minimum weight perfect matching on a bipar-
tite graph. To see why, we model the reconfiguration
problem using a bipartite graph with two sets of
tices. The first set of of
rent placement
the new placement
tex
if
all the objects placed on
an edge represents the cost of transforming the current
placement on the proxy represented by
placement represented by
r
denote the current placement of objects onto
denote the new place-
rEs<tvu
?Vw ways
?
ver-
?
vertices represents the cur-
r . The second set of vertices represent
r
s6txu . We add an edge between ver-
^`y of the first set and vertex
^pz of the second set
^
y has enough space and bandwidth to accommodate
^pz in
r
s6txu . The weight of
^>y to the new
^
z (the cost is governed by

Page 5

the number of new objects that must be fetched from an-
other proxy or a remote server to obtain the new place-
ment).
To illustrate this process, consider the example in Fig-
ure 3 with two identical proxies and five objects. In the
current placement
on
placement
and
identical, we add edges between both pairs of vertices
in the bipartite graph. This is because either proxy can
accommodate all the objects placed on the other proxy
by the new placement. The weights on the edges indi-
cate the cost of transforming each proxy’s cache to one
of these sets (e.g., transforming
to
r , the first three objects are placed
^
n and the remaining two objects on
^
o . The new
r
s<tvu involves placing
MHQT:??1:?{0R on one proxy
MHQT:?|0R on the other proxy. Since the two proxies are
^>o ’s cache from
M-}G:?|0R
MHQT:?|0R involves one copy whereas transforming it to
to incur zero overhead). It can be shown that finding a
minimum weight perfect match (MWPM) for this bipar-
tite graph yields a transformation with minimum copy-
ing cost. A perfect match is one where there is a one-
to-one mapping from vertices in the former set to the
latter; a minimum weight perfect match minimizes the
weights on the edges for this one-one mapping.
in Fig. 3, leaving
MHQT:??1:?{0R involves three copies; deletions are assumed
n
Thus,
^#n ’s cache as is, and transforming
^po ’s cache from
M-}G:?|0R to
MHQT:?|0R is the minimum weight
perfect matching with a copying cost of 1.
1,2,3
4,5
1,2,3
1,5
0
1
3
1
Fig. 3. An example of using the minimum weight perfect
matching to find the placement which minimizes object
movement in a 2 node proxy.
B. Swapping-based cache reconfiguration
MWPM cache reconfiguration can significantly re-
duce the copying overhead, as indicated by the simu-
lation experiments in Section V. In this section, we de-
scribe a swapping-based reconfiguration technique that
can further reduce the reconfiguration overhead. The
swapping-based reconfiguration takes the current place-
~
The bipartite graph can be constructed in
the minimum weight perfect matching is polynomial-time solvable
with complexity
€ƒ‚F„†…ˆ‡ time and
€‰…bŠ?‡ .
ment as the initial point, and use the well-known hill-
climbing method [5] to solve the optimal cache place-
ment (O.C.P.) problem. The reconfiguration cost in-
curred in MWPM is used as a control parameter to limit
the overhead incurred by the swapping-based technique.
The hill-climbing method is characterized by an iter-
ative algorithm that makes a small modification to the
current solution at each step to come closer to the op-
timal solution. To apply the hill-climbing method to
the cache reconfiguration problem, two issues need to
be properly addressed: (1) how to modify the existing
cache placement at each step to improve the proxy band-
width utilization, and (2) when to stop. In the following,
we address the above two issues.
B.1 Object swapping
Wepropose to swapthe position oftwoobjects ateach
step to modify the current placement. Our approach is
to select a pair of objects such that the utilized proxy
bandwidth increases after swapping. In fact, we select
the pair that maximally increases the bandwidth utiliza-
tion so as to minimize the copying overhead of recon-
figuration.
Proxies are classified into two categories: overloaded
proxies and under-loaded proxies, as shown in Fig. 4.
A proxy is said to be overloaded if the total bandwidth
needs of objects currently stored at the proxy exceed
capacity; under-loaded proxies have spare bandwidth.
All objects not currently stored on any proxy are as-
sumed to be stored on a virtual proxy with bandwidth
capacity zero (thus, the virtual proxy isalso overloaded).
The abstraction of a virtual proxy enables us to treat
cached and uncached objects in a uniform manner. Intu-
itively, a“cold” object from an under-loaded proxy is se-
lected and swapped with a“hot” object on an overloaded
proxy, so that the total bandwidth utilization increases.
We apply the following rules in selecting object:
?Cold object selection: Randomly select an under-
loaded component proxy with probability propor-
tional to the amount of spare bandwidth, and then
choose the least frequently accessed object in this
proxy.
?Hot object selection: Select the object with the
highest bandwidth requirement cached in the over-
loaded proxies or the virtual proxy.
These two objects are then swapped, and the corre-
sponding proxies are relabeled as under-loaded or over-
loaded based on the new cache contents.
o
Randomiza-
‹
No objects are physically moved at this time. Actual movement