[IEEE Fifth IEEE International Symposium on Network Computing and Applications (NCA'06) - Cambridge,...

Video-on-demand Equipment Allocation

Frederic Thouin and Mark CoatesMcGill University

Dept Elec. and Comp. Eng.3480 University, Montreal, Quebec, Canada H3A 2A7

{fthoui,coates}@ece.mcgill.ca

Dominic GoodwillNortel Networks

3500 Carling AvenueOttawa, ON, Canada K2H 8E9

[email protected]

Abstract

Video-on-demand (VoD) service providers are intenselyinterested in transport, storage, streaming and caching incontent delivery networks. Today’s 5,000-hour library maygrow toward the 750,000-hour “Long Tail” movie and TV-series catalog. We propose a method to calculate how muchof a library should be cached. Much previous work focusedon theoretical caching concepts, or the dynamics of cachefilling and reclamation. Our method explicitly considers theimpact of the available video server equipment; we presenta VoD design tool comprising a novel cost function, hit ratioestimation and heuristic.

1. Introduction

Network-based video-on-demand (VoD) deploymentsare today very limited in scope. The largest deployed li-braries are just 0.7% (5,000 hours) of the global movie andTV-series catalog and peak utilization of VoD targets are10-15% of broadcast TV peak viewing numbers. Recogniz-ing that libraries and usage may grow, service providers areintensely interested in the scalability of content delivery net-works that provide content propagation, storage, streaming,and transport. Three dominant factors must be consideredwhen planning scalable deployments for VoD: library size,peak concurrent streams and rate of ingest of new content.Each could increase by one or more orders of magnitudeafter the deployment. In this paper we describe a methodand design tool for the planning of VoD systems; our workstrives to address the future 750,000-hour global movie andTV-series catalog, to better exploit the heavy tail of the pop-ularity distribution, called the “Long Tail” of content [6].

Content delivery networks (CDNs) are designed to dis-tribute content to a set of clients, as streams or as files [4, 5,11, 14, 15]. Through approaches such as replication of con-tent at multiple servers (replicas, proxies or caches), CDNsattempt to minimize latency at the end-user while reducingbandwidth consumption and load at the origin server. This

paper deals primarily with the case of a streaming CDN,in that the client is assumed to have buffering capabilitybut not caching capability. Nonetheless, the mathematicsand the model are easily extended to the client-cached sce-nario. The CDN delivery of streaming media causes newproblems that did not apply to the distribution of HTTP ob-jects: streaming objects are much larger than web objectsand hence create much more traffic [10]. Furthermore, itis no longer possible to assume infinite storage size at thereplica locations [15].

The design of a CDN consists of making resource plan-ning decisions and the development of in-service intelligentrequest routing, resource control policies, and performancemonitoring. In this paper, we focus on the first challenge:the allocation of resources during network planning, gen-erally performed when planning greenfield and incrementaldeployments. Of particular interest is VoD delivery acrossmetropolitan area networks (MANs). A well-known for-mulation of this task is the replica (or cache) placementproblem. This consists of determining a subset of N po-tential locations in a given topology (Fig. 1(a)) to place kreplicas, such that the total network cost is minimized for agiven quality of experience (QoE) impairment, such as de-lay, packet loss, frame loss, or packet jitter. Bandwidth re-quirements and transmission distances have generally beenconsidered as the important resource parameters. Storagecapacity also plays a role. The location of the replicas is im-portant, but very different designs and costs are achieved de-pending on the capabilities of the available network equip-ment. We define the VoD equipment allocation problem aschoosing the number of streaming and storage devices foreach of the replica locations, such that the deployment costof the VoD system is minimized. Referring to Fig. 1(b), themethod is implemented by determining the number of VoDservers present at each replica site. As part of this analy-sis, we also determine the fraction of the total library thatshould optimally be stored at each location.

The remainder of this paper is organized as follows. Sec-tion 2 introduces related previous work. In Section 3, we ex-

Fifth IEEE International Symposium on Network Computing and Applications (NCA'06)0-7695-2640-3/06 $20.00 © 2006

(a) Requests from a group of clients are routed to the associatedreplica or to the origin in case of a cache miss.

(b) A VoD server has storage capacity of Gi TB and streamingcapacity of Fi Gbps. The total streaming capacity niFi must begreater or equal to hiMi where hi is the hit ratio and Mi is theworst-case demand at site i.

Figure 1. (a) Logical connectivity betweenclients, replicas and origin. (b) Replica withni = 3 VoD servers.

press the equipment allocation problem as an optimizationproblem, and we state our assumptions. In Section 4, wepresent our solution to this problem, developing a novel costfunction, hit ratio estimation function and heuristic. In Sec-tion 5, we apply our heuristic to three scenarios with differ-ent demand, equipment capabilities, and topologies (or ge-ographies). We also compare the optimal cost, as generatedby our heuristic, to a scenario where no replicas are installedat the available locations in the topology. Thus, we illustrateour method of determining when a centralized VoD deploy-ment should be evolved to a hierarchical-distributed VoDdeployment. In section 6, we summarize our observations.

2. Related work and Contribution

Many techniques have been proposed to place repli-cas or allocate storage in CDNs in a near-optimal man-ner [3–5, 12, 15]. They differ primarily according to thenature of the cost function, which specifies the optimizationparameters (distance, demand, storage, etc.). The simplerapproaches consider only the aggregate user demand; thespecific objects requested are not important [3, 4, 15]. An-other avenue is to treat objects individually, associating witheach a different popularity (user demand) [5, 12]. Althoughmost of these functions account for transport costs and somefor storage costs, none of them explicitly includes the num-ber and cost of the equipment installed at each location. Weextend the cost function proposed in [15], which is based ontopology, demand and hit ratio, by also considering the costincurred through installation of the VoD servers. These costfunctions are often complex and minimizing them to deter-mine the optimal design is NP-hard. A popular heuristicthat offers near-optimal performance, considered by manyauthors, is greedy selection [5, 7, 15]. It consists of itera-tively adding replicas to the design to achieve the lowestcost at every step.

It is not always possible to have complete replicas of theorigin server because the large size of multimedia objectsleads to a high storage cost. An alternative is to store onlyspecific objects from the origin at the surrogate servers [12].The empirical study performed in [7] indicates that approx-imately 80% of requests for Web objects are for 10% ofthe objects. This suggests that a relatively small amount ofstorage can achieve a high hit ratio if the cached contentis carefully chosen. Previous studies in the distribution ofmultimedia files in CDNs or in VoD applications have usedZipf’s Law to characterize the popularity of the differentfiles [2, 12, 13]. However, empirical data indicates that aZipf model is not a good fit for the most popular files [1,9].Contributions: Most previous work on content distribu-tion considered replica placement or content allocation. Incontrast, we address the VoD equipment allocation problem,which focuses on identifying the optimal number of VoDservers at a set of locations. We present four main contribu-tions to solving this problem. We design a parametric func-tion for estimating the worst-case hit ratio for given systemparameters (cache size, library size and file arrival rate) us-ing discrete-time simulations based on an extension of thefile access model proposed in [9]. We propose a cost func-tion based on the hit ratio, the distributed demand and thenumber of VoD servers at each location. We develop a two-step heuristic to generate a solution to the problem, whichfirst relaxes the integer constraint and then searches for aninteger solution in the neighborhood of this initial solution.Finally, we develop an interactive design tool that imple-ments our cost function, hit ratio function and heuristic.


3. Problem statement

We address the problem of determining the number ofstorage and streaming devices needed at each potentialreplica location. We require a topology of a metro-area net-work (MAN) indicating the set of inter-nodal distances andthe specifications (cost and capacity) of network elementsand available equipment. We consider the case where onlyone type of equipment (VoD server) is installed at each sitebut allow this equipment type to vary from site to site. Wedefine the VoD equipment allocation problem as choosingthe equipment for each of these replicas such that the de-ployment cost of the network is minimized.

As illustrated in Fig. 1(a), this topology contains one ori-gin server and a maximum of N replicas. Each replica isresponsible for a group of clients representing a fraction ofthe population; any request made by a client in that group isrouted to that replica. The origin server hosting the entire li-brary (the complete set of objects) can be located anywhereand serves all the requests that replicas are unable to fill.

This paper does not consider the management of the con-tent at the replicas. We suppose that there exists an externalmechanism to maintain the most popular files at the repli-cas, which can be executed during off-peak hours whenmore bandwidth is available. Because content delivery it-self is also out of the scope of this paper, we are assumingunicast delivery to the user-end.

3.1. Mathematical formulation

Let S = {si : i = 1, ..., N} and T = {ti : i = 1, ..., N}where si is the number of streaming devices with capacityFi (Gbps) and ti the number of storage devices with capac-ity Gi (TB) of replica site i. Let CTOT(S, T ) be a positivefunction that maps the number of devices installed at eachlocation to the total network cost. The objective is to deter-mine S and T to minimize total system cost:

{S∗, T ∗} = arg minS,T

CTOT(S, T ) (1)

This formulation is only valid when the streaming andstorage devices can be deployed independently (si doesnot need to be equal to ti). However, in practice, the twodevices are often deployed as a joint unit called a VoDserver, so that si = ti (Fig. 1(b)). In that case, we letN = {ni : i = 1, ..., N} and define ni as the numberof VoD servers with streaming capacity Fi and storage ca-pacity Gi at location i. The objective in this second formu-lation (used in the rest of this paper) is to choose the numberof VoD servers at each replica that minimizes the total cost:

Nopt = arg minN

CTOT(N ) (2)

We denote the worst-case demand Mi at replica i as thetotal bandwidth required to serve all client requests using

unicast streaming during the peak utilization hours. We as-sume that we either know Mi or can approximate it from agiven population size and peak usage ratio. We define thehit ratio hi as the smallest fraction of requests satisfied byreplica i at any given time (worst-case). If the desired ob-ject is not present at the replica or the replica does not haveenough streaming capacity, the request is unsatisfied (cachemiss) and routed to the origin server. Although the hit ratiocould be used as a measure of service quality, we decidednot to add this constraint to the optimization problem be-cause of the imperceptible difference in quality of streamingvideo between the origin and a replica in a MAN.

4. Proposed solution

In this section, we present the three components of oursolution: the hit ratio function, the cost function and theheuristic. The first step of the heuristic produces an initialsolution X that represents the fraction of the library thatshould be stored at every replica i to minimize our costfunction. This value is then mapped to an estimate of thehit ratio, which allows us to calculate the number of serversneeded, Nini. The second step of the heuristic consists ofsearching the neighborhood of Nini to determine a near-optimal integer solution Nopt. By feeding these values intoour cost function, we generate the infrastructure and trans-port cost for the entire network.

4.1. Hit ratio function

The purpose of a file popularity model is to predict theaccess frequency of a given file, which can be estimatedby dividing the number of requests for this file by the totalnumber of requests. The authors of [9] propose a file accessmodel that is driven by Zipf’s Law, but takes into accountthe “fetch-at-most-once” and “new arrivals” factors. VoDsystem users rarely access the same file twice because thefiles are not modified (fetch-at-most-once). Also, new filesare periodically added to the system and since the popular-ity of a titles diminishes in time, these objects become themost popular titles. Although it is possible to estimate theworst-case hit ratio through simulations, for the purpose ofan interactive design process where we need to modify pa-rameters repetitively, it is impractical and time-consuming.Our objective is to train a parametric function that providesan estimate of the worst-case hit ratio based on specifiedsystem parameters in a few seconds compared to the tens ofminutes simulations would take.

We designed a simulation environment with a library ofsize Y and a cache of size X · Y where files are accessedaccording to the model described by Gummadi [9]. We cal-culate the hit ratio by dividing the number of requests forobjects in the cache by the total number of requests. Leteach client’s library Lj be a subset of the complete library


−1 −0.8 −0.6 −0.4 −0.2 0

0.55

0.65

0.75

0.85

0.951

log(X)

Hit

ratio

Y=1000, Z=100Y=2500, Z=10Y=5000, Z=25Y=6500, Z=0

(a) H as a function of log(X) for different pairs Y, Z. The linear curvesindicate that H = A + B log(X) achieves an adequate fit.

0 0.2 0.4 0.6 0.8 10.8

0.85

0.9

0.95

1

Z

A

Y=1000Y=2500Y=5000Y=10000

(b) Markers show values of A as a function of Z for different values of Y .Dashed lines (–) show the linear fits.

Figure 2. Plots showing data fitting curves toconstruct the form of H, A and B.

L that excludes all files client j has selected in the previousweeks. During each iteration (one week) of the discrete-time simulation, the following sequence of events occurs:

1. Clients are added to the population at a specified rate.2. New files are added to the library L at a specified rate.3. The cache is filled with the most popular files.4. Each client j selects an object from his library Lj .5. The weekly hit ratio is calculated.

The users’ requests are generated using a Zipf distributionwith coefficient α = 1. The probability of selecting the fileat rank i in library Lj is given by pj(i):

pj(i) =i−α∑

i∈Lji−α

Files that have already been fetched by the user cannotbe selected again (fetch-at-most-once-model). After everyrequest a user makes, the selected file is removed from hislibrary Lj and file selection probabilities are recalculated.New files are introduced in the library L and each library Lj

at a specified rate. The insert position of a file is determinedusing a Zipf distribution (with α = 1); the ranks of exist-ing files which are less popular are decreased and selectionprobabilities are recalculated. We ran extensive simulationswith different values for the following parameters:

0

200

400

600

Num

ber

of p

oint

s

−0.02 0 0.02 0.04 0.060

200

400

600

Error

Num

ber

of p

oint

s

Figure 3. Histograms of the error H − H be-tween our function estimate H and the valueobserved during simulations H. Top: entiredataset (1000 ≤ Y ≤ 10000). Bottom: reduceddataset 2500 ≤ Y ≤ 10000.

1. Number of weeks (length of the simulation).2. Size of the client population.3. Number of new clients every week.4. Size of the initial library of objects Y .5. Number of files added to the library every week Z.6. Size of the cache as a fraction (X) of the library size.

From our simulation results, we determined that the onlyparameters that have a significant impact on the hit ratiowere the library size Y , the number of files added everyweek Z and the cache size ratio X . We generated 864 pointsfor the hit ratio H by running the simulation four times for216 possible combinations of X , Y and Z. In Fig. 2(a), weobserve the linear behavior of H as a function of log(X)for different values of Y and Z and propose the form in (3)for our estimate H , where 0 ≤ X ≤ 1, 1000 ≤ Y ≤ 10000and 0 ≤ Z ≤ 100. We construct the bilinear functionalform for A and B represented respectively by (4) and (5)based on the linear relationship between A and Z observedin Fig. 2(b) and similar observations made for B. Perform-ing further plot analysis, we observed that using log(Y ) in(4) and Y in (5) generated the best fit for A and B.

H = A + B · log(X) = f3(X) (3)

A = K1 + K2Z + K3 log(Y ) + K4Z log(Y ) (4)

B = K5 + K6Z + K7Y + K8ZY (5)

We determine the values of the coefficients K1 toK8 by solving in the least squares sense the systemKV (X, Y, Z) ∼= H obtained by substituting (4) and (5) into(3). Our resulting function for hi is quite accurate, showing


less than 2% error eighty-five percent of the time and lessthan 5% error ninety-nine percent of time. In the top plotof Fig. 3, we show the histogram of the error distributionfor the entire dataset used (1000 ≤ Y ≤ 10000) for oursimulations where the error is less than 5% ninety-nine per-cent of the time. In the bottom plot we show the histogramof a reduced dataset where the values for library size below2500 are discarded. The accuracy of this reduced dataset ismuch higher (less than 1.5% error ninety-eight percent ofthe time) because Y = 1000 did not fit the proposed formsas well as the other data points (see Fig. 2(b)).

4.2. Cost function

We can express the total cost, CTOT, as the sum of thecost of infrastructure, CT , and the cost of transport, CS .

CTOT = CT + CS (6)

The cost of infrastructure, CT , includes the software andstart-up cost of a location (Ai) and the cost of VoD servers(Bi) for every replica site i and the origin server. In (7),we express CT as a function of the number of VoD serversinstalled at location i, ni, and the origin, no.

CT =N∑

i=0

Ai + Bini = f1(no) +N∑

i=1

f1(ni) (7)

The cost of transport consists of two components: trans-port from the origin to replicas and clients, CSORi

, andtransport from replica i to client i, CSRCi

. It includes thecost of node interfaces (CIF ) and of fiber (Cf ). The trans-port from replicas to the user-end (small distances) uses di-rect fiber whereas the transport from the origin to the repli-cas uses DWDM connections.

CS =N∑

i=1

CSORi+ CSRCi

(8)

CSRCi= nRCi · (2 · CIF + dRCi · Cf ) (9)

CSORi= nORi

(2 · CIF ) +nORi

dwmax

[2CDWDM +

dORi· Cf +

(dORi

maxamp

)· CLA

](10)

nORi: Num. of interfaces (fibers) toward the origin.

nRCi: Num. of interfaces (fibers) toward the user-end.

c: Fiber capacity. (Gbps)CIF : Node switch interface cost. ($)Cf : Cost of fiber. ($/km)CDWDM : Cost of DWDM equipment ($)wmax: Number of fibers supported by DWDM equipment.CLA: Cost of line amplifier. ($)

damp: Max. distance between two amplifiers. (km)

The number of fibers at each node depends on the amountof traffic on the various links, the hit ratio at the replica andthe fiber capacity. On the link between location i and theclients (RCi), the traffic is equal to the demand from theuser, Mi. On the link between the origin and a location i(ORi), all the requests that cannot be served by the replica(cache misses) are handled by the origin server and gener-ate a traffic equal to (1− hi) ·Mi. Notice that we are usingnon-integer values for the network components because weassume that the unused fraction can be used for other appli-cations and does not need to be included in the cost.

nORi=

(1 − hi) · Mi

cnRCi

=Mi

c(11)

Because the worst-case demand between location i andthe group of clients is fixed, CSRCi

does not depend on anyof the optimization variables. However, CSORi

indirectlydepends on ni because the hit ratio hi changes with thenumber of VoD servers installed. We express the cost oftransport CS as follows, where f2(hi,Mi) is obtained bysubstituting (11) into (10) and (9):

CS =N∑

i=1

CSORi+ CSRCi

=N∑

i=1

f(nORi) + f(nRCi

)

=N∑

i=1

f2(hi,Mi) (12)

By substituting (7) and (12) in (6), we can express the to-tal cost as a function of the number of VoD servers installed(ni), the hit ratio (hi) and the demand (Mi) at each location:

CTOT = f1(no) +N∑

i=1

f1(ni) + f2(hi,Mi) (13)

The required number of VoD servers is determinedby either the streaming or storage requirement (ni =max(si, ti)), expressed as functions of Xi:

si =hi · Mi

Fi=

f3(Xi) · Mi

Fiti =

Xi · YGi

(14)

so =∑

i(1 − f3(Xi)) · Mi

Foto =

Y

Go(15)

Define f4(Xi) � max so, to and f5(Xi) � max si, ti.By substituting (3), (14) and (15) into (13) and assumingthat the demand Mi is known, we express CTOT as a func-tion of the optimizing variable Xi:

CTOT = f1(f4(Xo))+N∑

i=1

f1(f5(Xi))+f2(f3(Xi)) (16)


Figure 4. Screenshot of our design tool.

4.3. The heuristic

Step 1: The first step of the heuristic is to provide an ini-tial solution, X = {Xi : i = 1, ..., N}, representing theoptimal fraction of the library to store at each replica. Weobtain X by performing a constrained nonlinear optimiza-tion on CTOT (as expressed in (16)) where 0 ≤ X ≤ 1,which is solved using a sequential quadratic programming(SQP) method [8]. From X , we calculate Nini, the set offractional number of VoD servers, by expressing si, ti, so

and to as functions of Xi. From this initial solution Nini

we can calculate the lower-bound of CTOT and upper-boundby rounding Nini up to the nearest integer.Step 2: The second step of the heuristic consists of search-ing the surroundings of Nini for a near-optimal integer so-lution. For each replica, we calculate the cost for integervalues of ni near the initial value calculated (ni±2) lookingfor a lower cost. We repeat this procedure until no changesin Nopt can decrease the total cost. For each value of ni wemaximize the hit ratio to decrease the transport cost fromthe replica to the origin:

Xstorage =niG

YXstreaming = f−1

3 (hi) = f−13

(niF

Mi

)

Xi = min(Xstorage, Xstreaming)

5. Results

In this section we examine the results obtained fromapplying our heuristic to three scenarios using our designtool. The tool, shown in Fig. 4, allows the quick creationof topologies, easy modification of system parameters and

0

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2

x 104

Tot

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ost (

k$)

0 2 4 6 8 10 12 14 16 18 200

20

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Index of Network Configuration

Impr

ovem

ent (

%)

NoReplicaHeuristic (Step 1)Heuristic (Step 2)

NoReplica to Heuristic (Step 2)Heuristic (Step 1) to Heuristic (Step 2)

Figure 5. Scenario 1. Impact of each step ofthe heuristic on total network cost (top) andcost improvement (bottom). In both plots,20 different cases are displayed in increasingorder of cost of NoReplica.

visualization of the resulting design. In the figure, we cansee the topology of a MAN (small squares represent inter-connected locations) and the object editing window whichallows the user to create and edit objects in the topology;for example, the user can edit a replica object by changingthe type of VoD servers available.

Scenario1 20 different sets of inputs where the number oflocations N in the topology is between 1 and 100,files in the library between 1000 and 10000 and filearrival rate per week between 0 and 100. System pa-rameters are all uniformly distributed within specifiedranges: demand M (1-20Gbps), startup cost A (6-37k$), VoD server cost B (1-53k$), streaming capacityF (1-5Gbps), storage capacity G (1-10TB), distanceto the origin dOR (0-50km), average distance to theclient dRC (0-5km), cost of bandwidth (0-4k$/Gbps)and cost of storage (0-3k$/TB);

Scenario2 Topology of 25 locations with the system para-meters uniformly distributed within the same ranges asin Scenario1. For each trial, demand Mi = M at eachreplica, where M varies from 2.5Gbps to 50Gbps;

Scenario3 Topology of 14 locations with the system para-meters uniformly distributed within the same ranges asin Scenario1. The specifications of the equipment anddemand at each node appear in Table 1.

The top panel of Fig. 5 shows three different total net-work costs CTOT for Scenario1: cost without any equip-ment installed at the replicas (ni = 0 for all i) and costafter the first and second step of the heuristic. The bottompanel of Fig. 5 shows the percentage reduction of the costachieved by the two-step heuristic. Our two-step heuristic


0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

100

120

Demand per location (Gbps)

Cos

t (k$

)

0

2000

4000

6000

8000

Tot

al C

ost (

k$)

Heuristic (Step 2)NoReplica

Cost of replica (Heuristic)Cost of transport (Heuristic)Cost of transport (NoReplica)Cost of 1 VoD server

Figure 6. Scenario 2. Total network cost(top) and individual location cost (bottom) forMi = M at each replica, where M varies from2.5Gbps to 50Gbps.

yields average improvements of 17% over the case whereno equipment is deployed. The majority of the heuristic im-provement comes from the first step.

In Scenario2 we illustrate the impact of the demand Mon the deployment cost. Fig. 6 illustrates that as the de-mand increases, the cost differential between the designgenerated by our tool and a design in which no equip-ment is installed grows substantially. Below a certain de-mand (≈ 7 − 8Gbps), both designs are of equal cost, whichmeans that if the demand is too low, it is no longer cost-efficient to deploy equipment. The bottom panel of Fig. 6compares costs of transport and infrastructure of a single lo-cation i, which has a startup cost A = 19k$ and where VoDservers with 3Gbps and 2TB capacity are available at 2k$.As long as “Cost of 1 VoD server” is lower than “Cost oftransport (NoReplica)”, it is beneficial to cache content ati. If the equipment installed at the origin and i is identicaland “Cost of transport (NoReplica)” is smaller than “Costof 1 VoD server”, then it is cheaper not to install any replicaand carry the entire demand up to the origin. In the ana-lyzed scenario, equipment is cheaper at i than at the origin,so there is one point (M = 8.3Gbps) where the heuristic in-dicates that a replica should be installed even though thecost of transport is less than the minimum deployment cost.Therefore, the demand and type of equipment not only havean impact on the fraction of the library to cache, but also de-termine whether or not caching content is even profitable.

Table 1 displays the values for ni, si and ti calculatedwith our tool for Scenario3. The total network cost forthis equipment is 1,810k$. Looking at the table, we no-tice significant discrepancies between the values of si1 andti1 , which signifies that resources are wasted because of

poorly chosen equipment. For example, at location 3, therequired number of streaming devices is almost twice thenumber of storage devices, whereas the streaming capacityof the equipment is half of the storage capacity. We considerthe effect of making equipment available at these locationswith specifications that better match storage and streamingneeds. For example, we change the value of F3 from 1 to3 in order to have a closer match for s3 and t3. We repeatfor the other three locations where ni �= 0 (7, 10 and 11)and adjust the value of B accordingly; for example, B3 in-creases from 9k$ to 15k$ to support an extra 2Gbps. All themodifications (Bi2 , Fi2 and Gi2) and new results (ni2 , si2 ,ti2) are also shown in Table 1. We notice that the four loca-tions where we modified the hardware now have si2 = ti2 ,which indicate a better usage of resources. Moreover, be-cause of the savings at these locations, it is now beneficialto install more equipment at locations 1 and 14 to achievea minimal network cost. We also note that even though thevalue of n5 has not changed, the streaming and storage re-quirements have increased from 0 to 1.7. The new total net-work cost for this setup is 1,580k$, a 12.5% improvement.It is important to stress that the prices and capacity usedin these scenarios are not intended to reflect the real valuesused in practice. However, this simple example shows theimpact of modifying the type of equipment installed at eachlocation on the total deployment cost.

6. Conclusion

Network cost is affected not only by where replicas arelocated, but also what equipment comprises a replica. Wedeveloped a design tool to address the VoD equipment al-location problem. There are three principal contributionsfrom the development of this tool. We used extensive simu-lations to train a parametric function that generates accurateestimates of the hit ratio for given cache size, library sizeand file arrival rate. We constructed a cost function basedon the hit ratio hi, the demand Mi, and the number of VoDservers ni at each location. We designed a two-step heuris-tic that relaxes the integer constraint to produce an initial so-lution and then identifies a near-optimal integer solution inthe reduced search space. The tool that implements our costfunction, hit ratio function and two-step heuristic is trulyinteractive because it allows designers to create and changenetwork models to generate optimal designs in an efficientand timely manner.

Our key conclusions are: (i) the nature of the availableserver equipment has a major impact on the design and costof a VoD network; and (ii) it is not always beneficial tocache content. It is profitable to install VoD servers (regard-less of the library size) if the demand at the given locationis significant. On the other hand, even if the library has tensof thousands of assets, if the demand is too low, no amountof caching can reduce the network cost. Accounting for the


Table 1. Scenario 3. Initial specifications of 14 locations (left). On the right, specifications of thelocations after modifying equipment (modified values are highlighted with the surrounding box).

Mi Ai Bi1 Fi1 Gi1 ni1 si1 ti1 Bi2 Fi2 Gi2 ni2 si2 ti210 19 12 2 2 0 0 0 12 2 2 3 4.3 4.313 8 29 1 9 0 0 0 29 1 9 0 0 018 12 9 1 2 18 17.8 11 15 3 2 6 5.5 5.55 13 16 4 1 0 0 0 16 4 1 0 0 09 15 19 4 2 2 0 0 19 4 2 2 1.7 1.72 15 22 4 3 0 0 0 22 4 3 0 0 0

19 10 30 4 6 4 4.5 3.6 22 4 3 4 4.2 4.21 15 12 1 3 0 0 0 12 1 3 0 0 09 18 24 2 6 0 0 0 24 2 6 0 0 019 16 27 3 6 5 6.3 3.6 16 3 2 6 5.8 5.819 19 24 3 5 5 6.1 4.4 16 3 2 6 5.6 5.610 6 29 2 8 0 0 0 29 2 8 0 0 08 13 35 2 10 0 0 0 35 2 10 0 0 014 14 22 4 3 1 0 0 22 4 3 4 3.1 3.1

available equipment during the VoD network design is crit-ical as the choice of equipment has a direct impact on theminimum demand that makes caching profitable. Moreover,selecting equipment that jointly matches streaming and stor-age requirements at each location can result in substantialreductions in network cost; we showed in Scenario3 thatonly a few equipment changes can have a major impact.

We are extending the design tool to support more thanone type of equipment per location, and determine not onlythe number of servers at each site, but also select which typeof equipment yields the best solution. We are modifying thetool to include usage and maintenance costs for the networkcomponents subsequent to deployment.

References

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