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Cost Comparison of E-Learning SolutionsCherkaoui LEGHRIS

cleghris@tourisme.gov.maRadouane MRABET, Ph.D.

mrabet@ensias.maUniversité Mohammed V - Souissi

Ecole Nationale Supérieure d’Informatique et d’Analyse des SystèmesB.P. 713 Agdal – Rabat - Maroc

Summary

The e-learning applications continue to be developed following the emergence of new communicationtechniques. They became able to adapt their behaviors to the requirements of the new generation of users, in particular those mobiles. Therefore, a variety of sophisticated e-learning solutions appears on the teaching market.

In addition, the training operators, public and private, are more and more interested in these new methods of teaching with the principal objective to attract the maximum of learners. They are invited to choose a solution among those that fulfill their technical and budgetary constraints.

The choice of a best E-learning solution remains a difficult task because it depends on several factors. It must combine the objective and strategic needs of the training operators to the technical requirements of the e-learning environments as the transport networks, the used equipments, the learner’s features and the security [1].

Considering the multitude of these factors and the complexity to combine them, the decision makers find difficulties to evaluate the e-learning applications and to estimate their cost, in particular, when several environments meet the same needs.

To solve this problem, we design an E-learning Decision Making System (EDMS) that helps the decision-makersin the choice process of the right e-learning solution. This system is based upon two components: e-learningapplications classifier and e-learning application cost assessment.

The EDMS is conceived as a system that receives in input, the objectives and the features expected of the e-learning application and provide, in output, an e-learning class that includes one or several most suitable applications. If several classes have to be considered, EDMS will order them according to their relative costs. This paper will present more thoroughly the “e-learning application cost assessment” component of EDMS.

Key words : Decision-Making System, E-learning, Users’ mobility, Application cost.

Introduction

The choice of an e-learning environment passes, initially, by the classification of the e-learning applications according to an appropriate taxonomy , an objective well filled by [2].

Based on this classification, an e-learning solution is associated with a combination of subclasses related on the transmission networks, the used equipments, the user group, collaboration and security. Consequently, the cost of a given solution is the sum of the costs of its subclasses, in other words:

ζ(Solution i) = ζ(Nj) + ζ(Ek) + ζ(Up) + x *ζ(Lm) + y*ζ(Sn)With j ∈ [1..11] ; k∈ [1..8] ; p ∈ [1..6] ; m ∈ [1..10] ; n ∈ [1..6]

x ∈ [0..1] ; y ∈ [0..1](1)

With ζ represents the cost function and Nj, Ek, Up, Lm, Sn represent respectively subclasses of the transmission networks, the used equipments, the user group, collaboration and security that are associated along this paper to the solution i.

The comparison between the costs of the solutions is carried out in the following way:

� If the solutions to be compared belong to different classes, the comparison is limited to the class level, and takes in account the costs of the principal parameters of the classification.

� If the solutions belong to the same class, the comparison of the costs is carried out on the subclass level. A solution is considered costly compared to another if and only if the cost of the combination of subclasses related to the first exceeds the second. This deduction is not always possible. This is why the comparison of the solutions can be made only in a relative way.

Thus, two cases have to be treated, according to whether the solutions belong to the same class or different classes.

1-4244-0406-1/06/$20.00 ©2006 IEEE.

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1. Cost comparison at class level

Between two e-learning applications belonging to two different classes, the comparison remains obvious if we manage to establish an order between the costs of the classification parameters. This task proves to becomplicated due the variability of the costs in time and according to the localization (i.e. country).

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16

Transport network technology fixed

Resources energy of the equipment

limited non limited

Membership dynamic static dynamic static dynamicPresence of

collaboration yes no yes no yes no yes no

Presence of security yes no yes no yes no yes no yes no yes no yes no yes no

C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32

Transport network technology mobile

Resources energy of theequipment limited non limited

Membership dynamic static dynamic static dynamicPresence of

collaborationyes no yes no yes no yes no

Presence of security yes no yes no yes no yes no yes no yes no yes no yes no

Table 1 : E-learning classification, class-level

In table 1, the order of appearance of the parameters is considered arbitrary and does not influence, in any case,the established classification. In order to work out a comparison of the classes according to the costs of the parameters, the order of the latter is of primary importance. In other words, being given two parameters I and J, the cost of I is higher than that of J if and only if parameter I appears before J in the established order. This assumption intervenes because we one cannot quantify the costs of the parameters, but we can compare them according to their order of importance.

Based on this principle, the comparison of the costs of the classes depends on the importance of the classification parameters. Therefore, it will be necessary to define this order before proceeding to the comparison of the costs of the classes, thing that we cannot decide easily. Consequently, we must foresee all the possible scenarios.

Our classification is based on five parameters, each parameter can have two values, thus 120 combinations are possible (C1

5 * C 1

4 *C1

3 * C1

2 * C1

1 = 120). Each combination is a possible scenario that can give a different comparison. In the continuation of this paper, we will use the following scenario which appears to us the most realistic one:

ζ(user group) = ζ(equip ment) = ζ(collaboration) = ζ(security) (2)

For the parameter “Transport network technology”, we will consider the two technologies, fixed and mobile, without deciding which one is costly.

The costs of classes with limited energy resources equipment, a static group of users, a collaboration and a security present, is definitely higher than those with unlimited energy resources equipment, a dynamic group of users, a collaboration and a security absent. Consequently, we can easily note that the C16 class is the least expensive when C1 is the most expensive among the sixteen classes defined for the fixed network technology. In the same way, C17 and C32 are respectively the most expensive class and the less expensive class in the case of a mobile network.

In the following sections, we will compare the costs of the solutions taking into account each main parameter.

1.1. Transport network technologyCurrently mobile and fixed technologies are competitive on the market of the telecommunications networks [3].Consequently, the comparison of the costs of the solutions of a given class depends on the chosen technology, in other words:

ζ(Ci) < ζ(Cj) if mobile technology is costly, ζ(Cj) < ζ(Ci) if fixed technology is costlyWith i ∈ [1..16] et j ∈ [17..32]

(3)

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1.2. Resources energy of the equipmentAs defined in [2], equipment having a limited autonomy, remains expensive compared to equipment normally supplied with electricity when functioning. According to the energy resources of the equipment, the comparison of the costs on the class level is as follows:

ζ(Ci+8j) < ζ(Ck+8p)With i ∈ [1..8] ; k∈ [1..8] ; j = 1 ; p = 0 in the case of fixed network

i ∈ [1..8] ; k∈ [1..8] ; j = 3 ; p = 2 in the case of mobile network(4)

1.3. Membership dynamicThe cost of a solution allowing a dynamic group of users remains lower than the cost of any other solution. Indeed, the solutions, which allow a static group of users, ensure a good quality of training. Taking into account of this parameter, the comparison of the costs is as follows:

ζ(Ci+4j) < ζ(Ck+8p)With i ∈ [1..4] ; k∈ [1..4] ; j ∈ [1..3] ; p ∈ [0..1] in the case of fixed network

i ∈ [1..4] ; k∈ [1..4] ; j ∈ [5..7] ; p ∈ [2..3] in the case of mobile network(5)

1.4. CollaborationIt is clear that an e-learning solution, allowing collaboration, is more expensive than another solution where this aspect misses, i.e.:

ζ(Cwith collaboration) < ζ(Cwithout collaboration) (6)

Thus, the comparison of the costs of the classes according to the collaboration parameter is as follows:

ζ(Ci+4j) < ζ(Ck+4p)With i ∈ [3..4] ; k∈ [1..2] ; j ∈ [0..3] ; p ∈ [0..3] in the case of fixed network

i ∈ [3..4] ; k∈ [1..2] ; j ∈ [4..7] ; p ∈ [4..7] in the case of mobile network(7)

1.5. SecurityAs for the collaboration parameter, the presence of the security generates an additional cost. In other words:

ζ(C2i) < ζ(C2j+1)With i ∈ [1..8] ; j ∈ [0..8] in the case of fixed network

i ∈ [9..16] ; j ∈ [8..16] in the case of mobile network(8)

By combining (4), (5), (7), (8) and by taking in account the order of the parameters decided in the previous paragraph, we could deduct what follows:

� If the network technology is fixed :

ζ(Ci) < ζ(Ci-4)ζ(Cj) < ζ(Cj+6)

With i ∈ [4..16] ; j ∈ {3, 4, 7, 8}(9)

� If the network technology is mobile :

ζ(Ci) < ζ(Ci-4)ζ(Cj) < ζ(Cj+6)

With i ∈ [17..32] ; j ∈ {19, 20, 23, 24}(10)

2. Cost comparison at subclass level

Generally, the comparisons will be made at the subclass level because after the specification of needs, thesolutions will probably belong to the same class, with a variety of subclasses. Thus, it will be necessary to proceed to a comparison of the costs at the subclass level concerning each aspect of the classification.

2.1. NetworkParameters associated to network’s requirements are used to define eleven sub-classes, denoted N1..N11: seven for a fixed network and four for a mobile network (table 2). According to our previous decision to do not compare the costs of the solutions according to the adopted transport technology, we proceed in two steps, the first one for the fixed technology and the second for the mobile technology.

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Table 2 : The subclasses of transport network

A solution, which requires a high bandwidth, is expensive with regard to the one, which need only lowbandwidth. Thus, by considering the bandwidth parameter, we can conclude that:

� If the network technology is fixed :

ζ(Ni) < ζ(Nj)With i ∈ [1..2] ; j ∈ [3..7] for bandwidth in entering flow

i ∈ [1..4] ; j ∈ [5..7] for bandwidth in outgoing flow(11)

� If the network technology is mobile :

ζ(Ni) < ζ(Nj)With i ∈ [10..11] ; j ∈ [8..9] (12)

In an e-learning solution, the isochronicity and the media synchronization generate an additional cost, because the solution uses audio and/or video media, two important features used nowadays, by the e-learningapplications. Thus:

� If the network technology is fixed :

ζ(Ni) < ζ(N7)With i ∈ [1..7] (13)

� If the network technology is mobile :

ζ(Ni) < ζ(N8)With i ∈ [9..11] (14)

A reliable network is more expensive than a not reliable one, consequently:

� If the network technology is fixed :

ζ(Ni) < ζ(Nj)With i ∈ {2, 3, 6, 7}; j ∈ {1, 4, 5}

(15)

� If the network technology is mobile :

ζ(Ni) < ζ(Nj)With i ∈ {8, 11}; j ∈ {9, 10}

(16)

2.1.1. Fixed network technologyAccording to (11), (13) and (15) we can conclude that:

ζ(N2) < ζ(N1) < ζ(N4) < ζ(N5)ζ(N2) < ζ(N3) < ζ(N4) < ζ(N5)ζ(N2) < ζ(N3) < ζ(N6) < ζ(N5)

(17)

� If the cost of bandwidth is greater then the cost of reliability, then :

ζ(N1) < ζ(N3) and ζ(N4) < ζ(N6) (18)

� If the cost of isochronicity is greater then the cost of reliability, then

ζ(N5) < ζ(N7) (19)

According to (18) and (19):

� If the costs of isochronicity and bandwidth are greater then the cost of reliability, then:

ζ(Ni) < ζ(Ni-1) < ζ(Ni+1)ζ(Nj-1) < ζ(Nj) < ζ(Nj+2)

With i ∈ {2, 6} ; j = 4 (20)

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11Transport network technology

fixed mobile

Bandwidth in entering flow low high lowBandwidth in outgoing flow low high lowIsochronicity non required required non requiredMedia synchronization non required required non requiredTransfer reliability reliable non reliable reliable non reliable reliable non reliable

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Sometimes, we cannot decide about some situations, for example :

� For the bandwidths in entering and outgoing flow, we have ζ(N1) < ζ(N6), but for reliability, we have ζ(N6)< ζ(N1),

� For bandwidth in entering flow, for the isochronicity and for the media synchronization we have ζ(N4) < ζ(N7), but for reliability we have the contrary, ζ(N7) < ζ(N4).

2.1.2. Mobile network technologyAccording to (12), (14) and (16) we can conclude that:

ζ(N11) < ζ(N10) < ζ(N9) (21)

� If the cost of isochronicity is superior of the cost of reliability then :

ζ(N9) < ζ(N8) and therefore ζ(N11) < ζ(N10) < ζ(N9) < ζ(N8) (22)

On the other hand, we have:

� ζ(N10) < ζ(N8) while considering only the bandwidths in entering and outgoing flow.

� ζ(N8) < ζ(N10) for the transfer reliability parameter.

We cannot decide about this situation, therefore:

ζ(N11) < ζ(N10), ζ(N8) < ζ(N9) (23)

2.2. EquipmentEquipment is characterized by four parameters of two values each one, which gives sixteen possiblecombinations (24). Table 3 illustrates the eight remaining subclasses (E1..E8) after the elimination of the non realistic combinations.

E1 E2 E3 E4 E5 E6 E7 E8Resources energy of the equipment limited non limited

Processing power High low highFunctionalities Multimedia simple multimediaAdaptability automatic manual automatic

Table 3 : The sub classes of used equipment

According to the table 3, E4 and E1 represent respectively the least and the most expensive subclass in the case of an equipment with limited resources of energy, otherwise, they are E5 and E8 respectively the least and the most expensive subclasses. Furthermore, a high processing power, multimedia functionalities and automaticadaptation generate additional costs. Now, let us take the equipment parameters one by one:

� Energy resources of the equipment: Equipment with an autonomous battery is more expensive than the one that must be energized in functioning. Thus:

ζ(Ei) < ζ(Ej)With i ∈ [5..8] ; j ∈ [1..4]

(24)

� Processing power: an equipment with a high processing power is expensive than the other with a lowprocessing power. Consequently:

ζ(Ei) < ζ(Ej)With i ∈ [4..5] ; j ∈ {1, 2, 3, 6, 7, 8} (25)

� Multimedia features: it is clear that the multimedia aspect enriches the features of equipment even if it generates a supplementary cost. Thus, the cost comparison considering only this parameter, will be as follows:

ζ(Ei) < ζ(Ej)With i ∈ [3..6] ; j ∈ {1, 2, 7, 8}

(26)

� Adaptation: the adaptable equipments, called sometimes intelligent, are those who change parameters automatically according to their localization. This characteristic is an added value with regard to those who need a manual adaptation of their parameters. Consequently, the cost of an automatically adaptableequipment is superior, in other words:

ζ(Ei) < ζ(Ej)With i ∈ [2..7] ; j ∈ {1, 8}

(27)

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Thus, by considering (24), (25), (26) and (27) we can conclude that subclass E1 and E5 are respectively the most and the least expensive. For the others:

ζ(Ei) < ζ(Ei-1)ζ(Ej) < ζ(Ej+1) < ζ(E1)

With i ∈ [2..4] ; j ∈ [5..7](28)

2.3. Users GroupWith only three parameters, the group of the users is characterized by six sub classes illustrated in the table 4.

U1 U2 U3 U4 U5 U6Membership dynamics Static DynamicUser profile Known UnknownUser mobility total Limited total Limited

Table 4 : The sub classes of users group

Managing a static group is more expensive than managing a dynamically one because in the first case, learnersmust be enrolled in advance and require a quality of service. By considering the parameter “Membershipdynamics”, we can conclude:

ζ(Ui) < ζ(Uj)With i ∈ [3..6] ; j ∈ [1..2] (29)

On the other hand, an application with known user profiles is expensive than the one with no identified learners, thus:

ζ(Ui) < ζ(Uj)With i ∈ [5..6] ; j ∈ [1..4] (30)

The mobility of learners is considered as an added value to the e-learning applications, and thus they are costly.Consequently:

ζ(Ui) < ζ(Uj)With i ∈ {2, 3, 6} ; j ∈ {1, 4, 5}

(31)

The parameter “Membership dynamics” is considered mo re important than the mobility. Therefore , ζ(U4) < ζ(U2) and ζ(U5) < ζ(U2). As the same, the parameter “user profile” is considered more important than the user mobility, so: ζ(U5) < ζ(U3).

Following theses considerations, and the comparisons (29), (30) and (31) we can deduce:

ζ(U6) < ζ(U5) < ζ(U3) < ζ(U4) < ζ(U2) < ζ(U1) (32)

2.4. CollaborationThe collaboration is very important for the E-learning applications. It expresses an important aspect of the face-to-face learning. Thus, once this aspect is present in an E-learning solution, it generates a supplementary cost.

L1 L2 L3 L4 L5 L6 L7 L8 L9 L10Architecture of collaboration centralized decentralizedMode of communication real time differed real time differedCompetition in transmission controlled not controlled controlled not controlledDuration of collaboration limited not limited limited not limited limited

Table 5 : The sub classes of collaboration

A solution implemented on decentralized architecture costs more than the other, implemented on a centralized architecture. Thus, considering this parameter, we can establish the following comparison:

ζ(Li) < ζ(Lj+5)With i ∈ [1..5] ; j ∈ [1..5] (33)

The real-time communication between learners is more expensive than the differed one, in particular for the solutions, which are based on the audio and/or video conference. Consequently:

ζ(Li+5j) < ζ(Lk+5p)With i ∈ [4..5] ; j ∈ [0..1] ; k∈ [1..3] ; p ∈ [0..1] (34)

A solution, which demands a controlled competition in transmission and a limited duration of collaboration, is considered more expensive than the others, which demand a no controlled competition in transmission and a no limited duration of collaboration respectively. Thereafter, we determine the followed comparisons:

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� For the competition in transmission :

ζ(Li+5j) < ζ(Lk+5p)With i ∈ [2..5] ; j ∈ [0..1] ; k= 1 ; p ∈ [0..1] (35)

� For the duration of collaboration :

ζ(Li+5j) < ζ(Lk+5p)With i ∈ [3..4] ; j ∈ [0..1] ; k ∈ {1, 2, 5}; p ∈ [0..1] (36)

According (33), (34), (35), (36) and considering that the communication mode and the collaboration architecture are, respectively, more expensive than the duration of collaboration and the communication mode, in other words: ζ(L5) < ζ(L3) and ζ(L2) < ζ(L10) < ζ(L8), we find the following result:

ζ(Li) < ζ(Li-1) < ζ(L6)ζ(Lj) < ζ(Lj+1) < ζ(Lj-1) < ζ(L6)

With i ∈ {2, 3, 4, 8, 9} ; j ∈ {4, 9}(37)

2.5. SecurityThe security is considered an important aspect for the majority of service providers, in particular those who are specialized in E-learning services. On the other hand, mobile networks are characterized by an important vulnerability to intrusions, and therefore, the implementation of security solutions of E-learning will be considered as a priority, so it can generate further costs for training operators. The security aspect is definedthrough six subclasses as follow:

S1 S2 S3 S4 S5 S6Access control yesAuthentication no yesData integrity no yesConfidentiality no yes no yes

Non repudiability no yes

Table 6 : The sub classes of security

According to the table 6, it is clear that the subclass S6 is the most expensive, because all security parameters are taken in account, while the subclass S1 is considered the cheaper because only the parameter “access controls” is taken in account. The costs of others subclasses can be compared easily as follow:

� For the authentication :

ζ(S1) < ζ(S2) , ζ(S3) , ζ(S4) , ζ (S5) , ζ(S6) (38)

� For the data integrity :

ζ(S1) , ζ(S2) < ζ(S3) , ζ(S4) , ζ(S5) , ζ(S6) (39)

� For the confidentiality :

ζ(S1), ζ(S2), ζ(S3), ζ(S5) < ζ (S4), ζ(S6) (40)

� For the non repudiability :

ζ(S1) , ζ(S2) , ζ(S3) , ζ(S4) < ζ (S5) , ζ(S6) (41)

According to (38), (39), and (40) and (41), we can deduct:

ζ(S1) < ζ(S2) < ζ(S3) < ζ(S4), ζ (S5) < ζ(S6) (42)

The subclass S4 adopts the confidentiality and ignores the non-reputability, what is adopted inversely by the subclass S5. However, the confidentiality parameter is considered more important that the non-repudiabilitytaking into account its importance in a security process. Then:

ζ(S5) < ζ(S4) (43)

According to the inequalities (42) and (43), we can conclude that:

ζ(Si) < ζ(Si+1) < ζ(Sj+1) < ζ(Sj) < (Sj+2)With i ∈ {1, 2} ; j = 4

(44)

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3. Examples of costs comparisons

According to [1], the videoconference solution on mobile networks belongs to the class C25 and one of following combinations of subclasses: (N8, E8, U1, L1, S2), (N8, E8, U2, L1, S2), (N8, E8, U1, L6, S2) and (N8, E8, U2, L6, S2)denoted respectively as SC1, SC2, SC3, SC4.

According to the comparisons established in the previous paragraph, we can easily decide what solution or what combination of subclasses is more or less expensive than the other subclasses . In fact, after the comparisons (32)and (37), we can conclude that:

ζ(U2) < ζ(U1)ζ(L1) < ζ(L6) (45)

Therefore,

ζ(CS2) < ζ(CS1) < ζ(CS3) < ζ(CS4) (46)

So, a solution belonging to the combination of subclasses SC2 (N8, E8, U2, L1, S2) is considered the least expensive solution while SC3 (N8, E8, U2, L6, S2) is the most expensive one.

Conclusion

This paper covers a very important aspect of E-learning solutions: the costs comparison. Indeed, decision makers are generally faced by a panoply of solutions that answer more or less to their needs, but expresses some difficulty in the choice of this one or there. With the establishment of a costs comparison taking in account allsolutions, decision makers will be able now to combine their objectives and their budgets to proceed to the better choice.

The quantitative aspect of the cost is not treated in this paper because it depends on several components that are not all tied directly: network operators in different country, solution providers, users, etc. Our objective takes basis on the principle: for well-defined features, what is the appropriate solution among those suggested by the E-learning market?

References

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2. R. Mrabet, C. Leghris, “Classification of E-Learning applications in a context of mobility”, FirstInternational Conference on E-Business and E-Learning EBEL 2005, Amman, Jordan, May 23-24, 2005.

3. Jill Attewell, Mikael Gustafsson, “Mobile Communications Technologies for Young Adult Learning and Skills Development (m-Learning)”, IEEE International Workshop on Wireless and Mobile Technologies in Education WMTE'02.

4. Paul J.M. Havinga “Mobile Multimedia Systems”, PhD Thesis, Faculty of Computer Science, University of Twente, Netherlands, february 2000.

5. Muhammad Ali Kazmi, “Radio Resources Control in Radio Access Networks with Distributed Coverage”, PhD thesis at Ecole Nationale Supérieure de Télécommunication de Paris, January 2001.