Ahmed Amine Loukili

Damien Saucez

Thierry Turletti

Mathieu Bouet

Seamless content distribution with OpenFlow

With the advent of virtualization and network function softwarization, the networking world shifts to Software Defined Networking (SDN) and OpenFlow is one of the most suitable candidates to implement the southbound API. In the meanwhile, the generalization of broadband Internet has led to massive content consumption. However, while content is usually retrieved via layer 7 protocols, OpenFlow operations are performed at lower layers (layer 4 or lower) making the protocol ineffective to deal with contents. To address this issue, we define an abstraction to unify network level and content level operations and present a straw-man logically centralized architecture proposal to support it. Our implementation demonstrates the feasibility of the solution and its advantage over fully centralized approach.

INTRODUCTION

Over the last decade we have seen the emergence of Software Defined Networking (SDN) making networks programmable thus enabling network operators to automate their network management. In parallel to the advent of SDN, network communications have diverted to massive content distribution via the HTTP protocol that operates at the layer 7 of the networking stack (e.g., YouTube). However, OpenFlow ( [START_REF] Mckeown | Openflow: Enabling innovation in campus networks[END_REF]) that is the most prominent solution to implement SDN concepts relies on match-action rules on layers up to 4 such that it cannot be directly used to manage content distribution.

Several approach are taken to reconcile content distribution and SDN ( [START_REF] Chanda | Contentflow: Mapping content to flows in software defined networks[END_REF][START_REF] Fayazbakhsh | Less pain, most of the gain: Incrementally deployable icn[END_REF][START_REF] Sakurauchi | Open web: Seamless proxy interconnection at the switching layer[END_REF]) and our approach is to define an abstraction that unifies the network and content related tasks. Our abstraction uses network and content operations as primitives and leaves the details of which layers the operations must be performed on to the implementation of the abstraction itself. To implement it, we propose an architecture offering a centralized control with a distributed state by the means of control plane caches. To validate our straw-man proposal, we implemented a proof-of-concept leveraging, OpenFlow controllers, HTTP proxy, and a REST API. This implementation shows that by introducing the notion of control plane caches, a centralized approach can be used to manage content distribution with OpenFlow.

In the remaining of the paper, Sec. 2 defines our OpenFlow content distribution abstraction, Sec. 3 presents a straw-man logically centralized architecture proposal to implement this abstraction, and Sec. 4 provides a first evaluation of the architecture based on a prototype implementation. Finally, Sec. 5 concludes this work.

NETWORK ABSTRACTION

To leverage the SDN principle and distribute contents using OpenFlow, it is necessary to provide a new layer of abstraction that hides the notion of network layers to focus on network operations and on contents. To that aim, we propose to model the content distribution network as an abstract directed graph where each node represents an entity or an operation of the network and where edges indicate the relationship between them.

Our model defines the following three atomic types of node: (i) compute, (ii) network, and (iii) storage. Compute nodes are used to represent entities and functions related to processing (e.g., CPU, process) while network nodes are used to represent entities and functions related to networking (e.g., NIC, routes). Finally, storage nodes are used to represent entities and operations related to contents (e.g., hard-drive, file). As elements of a content distribution network are often constituted of compute, network, and processing parts our model defines the meta-node type called slice that allows to compose complex entities. Each node is allocated a unique identifier such that, in conjunctions with types and attributes, the validity of the model can be verified with static analysis before deploying it in the network.

Fig. 1 shows a simple two-network-ports Linux router with two routes abstract graph representation. The router is composed of two network ports (port1 and port2) modeled as network nodes, the Linux instance is modeled as a compute node, and the FIB modeled as a storage node. Each route (route1 and route2) is represented by a network node with attributes corresponding to the destination and the port to use. All these independent nodes are linked to a slice representing the whole router.

ARCHITECTURE

Our abstraction puts at the same level content and network features but content distribution usually relies on HTTP while OpenFlow matching is limited to the lowest level of the network stack. HTTP is transported over TCP and by virtue of separation principle, no content information is visible at the TCP layer that is the upper layer at which OpenFlow works. In addition, to offer reliability, TCP relies on sessions which state is built before the HTTP flow itself. To implement the abstraction, it is thus necessary to use HTTP proxies that will terminate the TCP connection until they learn the content actually requested in order to reconstruct the TCP sessions to the endpoints fulfilling the policies defined in the model. As proxies operations are computationally expensive, they are only performed at the edge where HTTP flows enter the network. Each such proxy is also an OpenFlow switch and flows are colored by the proxy with tags that can be processed directly by OpenFlow. To ensure core stability, it is possible to predefine the tags, at most one per potential path, such that the arrival of a new flow does not cause flow table modifications in the core network.

We leverage the centralized nature of OpenFlow to simplify the abstraction implementation via the Open-Flow controller. However, networks being inherently distributed, concentrating all information and decisions would impair performances by causing high signaling load. To alleviate the signaling cost but keep the centralized decision making, we introduce the concept of control plane cache. The principle of control plane caches is the same as the flow tables in OpenFlow but extended to our abstraction needs such that packet tagging and statistics are always performed locally by using the control plane cache. Before taking specific decisions, the controller gets statistics from the control plane caches and updates them with the new tagging rules. To ensure the scalability of the overall system, the abstraction is implemented by the intermediate of a REST API.

EVALUATION

We prototyped our proposition with open source software. We use Open vSwitch [START_REF]Open vSwitch[END_REF] and Floodlight [START_REF]Floodlight OpenFlow Controller -Project Floodlight[END_REF] for OpenFlow parts, and CherryProxy for the HTTP parts [START_REF]CherryProxy -a filtering HTTP proxy extensible in Python | Decalage[END_REF]. The REST API and the control plane cache are implemented with Flask [START_REF] Flask | A Python Microframework[END_REF] and PostgreSQL [START_REF]PostgreSQL: The world's most advanced open source database[END_REF].

The implementation demonstrates the feasibility of the model and the architecture and illustrates the benefits of the control-plane caches. The first scenario is the case where all information and decisions are treated centrally by the controller, i.e., without cache. The second scenario corresponds to the case where both tagging and statistics are ensured by the control plane caches.

Fig. 2 shows the evolution of the data plane and control plane rates with the content demand rate. Each network function runs in a separate virtual machine deployed on the same host. The network is fed with HTTP requests sent according to a Poisson process which average is given on the x-axis. As expected, the controlplane caches approach guarantees a control plane load independent of the data plane rate. On the contrary, the centralized scenario shows a direct correlation between control and data plane rates. Interestingly, when control plane caches are used, the proxy requires more CPU cycles to process flows, which reduces data plane rates. This performance drop can be explained by our suboptimal implementation of the control plane with SQLAlchemy that adds overhead.

CONCLUSION

This work proposes an abstraction and a straw-man architecture with logically centralized decision making to implement content distribution with OpenFlow. Our first prototype demonstrates the feasibility of the approach and its potential performance gains.

Figure 1 :

 1 Figure 1: Model of a two ports router with two routes.

Figure 2 :

 2 Figure 2: Evolution of the control and data plane rates with content demand.

Acknowledgments

This work is funded by the French ANR under the "ANR-13-INFR-013" DISCO project on SDN.


Yvonne Treis

"They are only two, like the teats of a donkey": Kambaata Denumerals Revisited

données et modèles (CNRS, FR 2559).

Introduction

Kambaata is a Highland East Cushitic language spoken around the Hambarrichcho massif in Southern Ethiopia, about 350km from the Ethiopian capital Addis Ababa. It is spoken by more than 600,000 speakers (Central Statistical Agency 2007: 74), the large majority of whom live in the Kambaata-Xambaaro Zone of the Southern Nations, Nationalities and Peoples' Regional State. Kambaata is used as a medium of instruction in primary schools and taught as a subject up to grade 8. The official Kambaata orthography is based on the Latin script (Treis 2008: 73-80), which is also adopted in this contribution with minor adaptations, the most important being that stress is consistently marked.2 Despite having been taught in schools since 1997, Kambaata has remained an overwhelmingly oral language. The national language Amharic is the written language in private and official contexts. The linguistic landscape of Kambaata towns, e.g. on signs and billboards, is entirely in Amharic, sometimes with English additions. Written Kambaata documents are hardly accessible to the population, but the Kambaata radio programme FM 105.8 can be received for several hours a day. This article departs from earlier analyses of Kambaata numerals [START_REF] Treis | Cardinal numerals in Kambaata[END_REF], Treis 2008: 202-21), significantly expanding and partly revising them with new fieldwork data collected in February 2016 3 as well as data from a corpus of educational material, a Kambaata-Amharic dictionary and the Kambaata translation of the Gospel of John. 4 The title of this contribution is inspired by a comment a Kambaata speaker made about me when he learned that I had only one sister:

(1) harr-é hanx-í=g-a lám-ee-t donkeys-fGEN teat-mGEN=SIM-mOBL two-fPRED.VV-COP3 '(They) are (only) two, like the teats of a donkey.'

As the formation of cardinal numerals in Kambaata has already been described in detail, I will focus in this article especially on denumerals, i.e. derivational and compounding processes that have cardinal numerals as inputs. The description of Kambaata was inspired by [START_REF] Fradin | [END_REF] typological overview of the formation of denumerals. In section 2, I give a brief introduction to Kambaata word classes with a focus on the properties shared and not shared between true adjectives and numerals. In section 3, I summarise the formation of cardinal numerals. In section 4 I elaborate on ordinal derivation. Section 5 is dedicated to adjectival and nominal compounds based on numerals. Sections 6 and 7 deal with the derivation of distributive and multiplicative numerals. Section 8 looks at how fractions are expressed. Section 9 provides information on approximation and, finally, section 10 illustrates the use of numerals in calculation. Whenever possible, denumeral formation in Kambaata is compared to that of the closely related Highland East Cushitic (HEC) languages K'abeena, Alaaba, Hadiyya and Sidaama. No information is available on denumerals in the remaining HEC languages, Libido, Gedeo and Burji.

Word classes in Kambaata

Kambaata has five open word classes: nouns, verbs, adjectives, ideophones and interjections, as well as a closed word class of pronouns. Adverbs and conjunctions are two negligible word classes with only a few members. Kambaata distinguishes between fully finite main clause verbs and various types of dependent clause verbs: relative verbs, converbs, purposive verbs and verbal nouns. Verbs are marked inflectionally for subject agreement, aspect, mood and subordination. Nouns are marked for nine cases and two genders. Adjectives are defined in Kambaata as a class of lexemes that display case and gender-agreement with a head if used as modifiers in a noun phrase. This feature clearly distinguishes them from nouns and verbs: modifying nouns are marked by the genitive case, modifying verbs are relativised.

The class of adjectives subdivides into true adjectives, demonstrative determiners and cardinal numerals, all of which distinguish two genders (masculine, feminine) and three cases (accusative, nominative, oblique) if used as modifiers in a noun phrase. When I speak of "adjectives" in the remainder of this paper, I refer to true adjectives. Although true adjectives and numerals could be considered two subclasses of a (macro-)class of adjectives, there are also features that clearly help to distinguish numerals from adjectives on formal grounds, for example (for details see Treis 2008: 88-96).

(i)

In the case/gender paradigm, a vowel change can be observed between the feminine and masculine forms of numerals but not of true underived adjectives; compare mat-ú (m) / mat-í-ta (f) 'one' (cardinal numeral) with qeraa'rr-ú (m) / qeraa'rr-ú-ta (f) 'long' (adjective).

(ii) All underived adjectives have a corresponding zero-derived inchoativestative verb with the same stem, e.g. qeraa'rr-ú(-ta) 'long' and qeraa'rr-'be(come) long'. Cardinal numerals have no such corresponding verbs.

(iii) Adjectives and numerals are subject to different derivational processes; see, for instance, that quality nouns in -im-áta can be derived in a productive way from adjectives but not from numerals: kall-ú(-ta) 'naked' > kall-im-áta 'nakedness'.

(iv) Predicative adjectives select copula 2: -ha (m) /-ta (f) (2). In contrast, cardinal numerals select copula 3, -VV-t (1), if they function as the head of the predicate, and trigger a zero copula if they are modifiers to a predicate noun (3).

(2) ti mán-ch-ut bíiz-a-ta DDEM1.fNOM people-SG-fNOM kind-fPRED-fCOP2 'This woman is kind.'

(3) harr-é hanx-í=g-a lám-e óos-o donkeys-fGEN teat-mGEN=SIM-mOBL two-fOBL children-fPRED '(They) are (only) two children, like the teats of a donkey.' Not all number words are members of the numeral word class: The numbers xibb-í-ta (f) '100', kum-í-ta (f) ~ (AMH) shiih-á (m) '1000' and miloon-á (m) 'million' are members of the noun word class. Furthermore, not all members of the numeral word class are numbers. If morphological and (morpho-)syntactic features are taken into account, the lexemes mexx-ú (m) / -í-ta (f) 'single' and me'-ú (m) / -í-ta (f) 'how many, how much?' need to be categorised as numerals: they show the characteristic vowel change between masculine and feminine forms, they lack zeroderived inchoative-stative verbs, they select copula 3 as predicates and they trigger a zero copula as predicate modifiers. Finally, in the same way as other numerals, they serve, for instance, as input for multiplicative derivation (section 7).

The quantifier hoolam-á (m) / -í-ta (f) or -á-ta (f) 'many' is difficult to classify. On the one hand it displays the characteristic vowel change of numerals (at least for some speakers) and is the input for multiplicative derivation (section 7). On the other hand, it selects the same copula as adjectives and has a zero-derived inchoativestative verb hoolam-'be(come) many'. Other quantifiers do not share the typical features of numerals.

Cardinal numerals

The cardinal numerals agree in case and gender with their head noun, if they are used as modifiers. For this purpose, numerals have a masculine and a feminine form. Accusative numerals precede accusative nouns, and nominative numerals precede nominative nouns (4); the oblique form of the numerals is used to show gender agreement with a non-nominative, non-accusative noun, e.g. a locative noun (5). In Table 1, note that the feminine forms do not only differ from the masculine ones in the additional gender morpheme -ta / -t in the accusative and nominative cases but also in the quality of the case vowel, which precedes the gender morpheme. Numerals do not require nominalization when used as heads of noun phrases. 7In this function, they are simply inflected like nouns. As such, they can be marked for nine different case forms, as illustrated with shool-ú 'four' (Table 2). Table 2. Case paradigm of numerals as NP head (example shool-ú 'four')

In (5) above, the masculine numeral shóol-u is used as the head of a nominative NP; the counted referent (qaf-á (m) 'branch(es)') is understood from the context. In (6), the numeral is marked for ablative case and masculine gender; the case form is determined by its function in the sentence (standard in a comparative construction), and the gender by its implicit referent, i.e. su'mm-á (m) 'name(s)'. In (7), the immediate context mentions what is counted by the numeral, namely tam-íta (f) 'use(s)', and thus determines its gender. The accusative case of the numeral is due to its function as a direct object of 'write'. In counting, the masculine oblique case is used, e.g. mát-o, lám-o, sás-o '1, 2, 3'. (6) tordum-íichch kot-ún-ka ten-mABL be_small_in_number-3mJUS-NEG 'It should not be less than (lit. from) 10 (names).' The numbers consisting of tens and units are not just combinations of the synchronic terms for tens and units, rather, they are based on the old tens, i.e. they lack the new '-ty'-morpheme -dum. The tens are linked to the unit by -na CRD (Table 4). 9 tóo-na + NUM1...9 e.g. '19' tóo-na hons-ú lam-ée-na + NUM1...9 e.g. '28' lam-ée-na hezzeett-ú sajj-áa-na + NUM1...9 e.g. '37' sajj-áa-na lamal-á shool-áa-na + NUM1...9 e.g. '46' shool-áa-na leh-ú ont-áa-na + NUM1...9 e.g. '55' ont-áa-na ont-ú leh-áa-na + NUM1...9 e.g. '64' leh-áa-na shool-ú lamal-áa-na + NUM1...9 e.g. '73' lamal-áa-na sas-ú hezzeett-áa-na + NUM1...9 e.g. '82' hezzeett-áa-na lam-ú hons-áa-na + NUM1...9 e.g. '91' hons-áa-na mat-ú Table 4. Formation of tens plus units

The number words xibb-íta '100' and kum-íta '1000' are feminine nouns. In everyday language, the number word kum-íta '1000' of Cushitic origin is usually replaced by the Amharic loan shiih-á '1000', a masculine noun. The numeral milooná 'million', a masculine noun, is an English loan via Amharic. As modifiers, these noun-like number words are marked for the genitive case (as any other modifying noun), i.e. they are unable to show case or gender-agreement with a head noun.

(8) kum-é mann-á kum-é lokk-áta thousand-fGEN people-mACC thousand-fGEN foot-fACC '(one) thousand people' '(one) thousand feet'

For the formation of hundreds and thousands, the numerals xibb-íta (f) '100' and kum-íta (f) 'thousand' are modified by simple numerals which agree in case and gender with their (numeral) head noun, e.g. ont-íta xibb-íta (five-fACC hundred-fACC) '500', lam-ú shiih-á (two-mACC thousand-mACC) '2000'. For more details on complex cardinal numerals see [START_REF] Treis | Cardinal numerals in Kambaata[END_REF]2008: 202-21).

Ordinal numerals

Starting with the number 'two', ordinals are derived from cardinal numerals by the suffixation of one of the ordinal allomorphs {-kí, -qí, -iqqí, -qqí} (Table 5).

CARDINAL NUMERAL ORDINAL NUMERAL

mat-ú woná '1 st ' lam-ú lan-kí '2 nd ' sas-ú sak-kí '3 rd ' shool-ú shool-kí '4 th ' ont-ú ont-iqqí '5 th ' leh-ú leh-iqqí '6 th ' lamal-á lamal-qí '7 th ' hezzeett-ú hezzeett-iqqí '8 th ' hons-ú hons-iqqí '9 th ' tordum-á tordun-qí '10 th ' tóona mat-ú tóona mat-iqqí (*tóona woná) '11 th ' tóona lamal-á tóona lamal-qí '17 th ' lamoodum-á lamoodun-qí '20 th ' xibb-í-ta (n) xibb-e-qqí '100 th ' shiih-á (n) ~ kum-íta (n) shiih-i-qqí ~ kum-e-qqí
'1000 th ' me'-ú me'-iqqí 'of which rank?' The first ordinal is suppletive: mat-ú 'one' > woná 'first'. The suppletive 'first' is, however not used for the ordinal forms of tens plus one, e.g. '21 st ', which is literally "twenty-oneth" (9). ( 9) hanqaf-fóo lam-ée-na mat-iqqí bar-éen fushsh-itáa'u hatch-3f.PVO.REL two-TY-CRD one-ORD day-mLOC take_out-3fIPV 'They make (them) come out (of their eggs) on the 21st day (after they have started) hatching.'

[K89: 2.101]
The distribution of the ordinal allomorphs {-kí, -qí, -iqqí, -qqí} is partly lexically, partly phonologically, and partly morphologically conditioned: 'second', 'third' and 'fourth' are marked by -kí. Starting with 'fifth', all true numerals attach -qí and -iqqí to the numeral stem. The short -qí is found after stem-final sonorants (see lamal-qí 'seventh' and tordun-qí 'tenth'), the long -iqqí is found elsewhere. Place assimilation between stem-final nasals and the following ORDmorpheme is observed in the case of 'second' and 'tenth'. In the ordinal 'third' the stem-final /s/ assimilates totally to the ordinal morpheme. Ordinals of noun-like cardinal numerals ('100 th ', '1000 th ') are formed by the suffixation of the ordinal morpheme to the genitive form (and not the stem) of the numeral noun. The ordinal morpheme itself could be still further segmented into a consonantal part {-k, -q, -iqq, -qq} and a genitive morpheme -í.

The interrogative ordinal numeral me'-iqqí 'of which rank (lit. how manieth)?' ( 10) is based on the interrogative numeral me'-ú / -íta 'how much?'.

(10) antabée'-u me'-iqqí bar-éen fushsh-itáa-'i? chicken-mNOM how_many-ORD day-mLOC take_out-3fIPV-Q 'On which day (lit. on the how manieth day?) do chicken make (their chicks) come out (of their eggs)?' If ordinal numerals are used as the head of an NP, they need to be nominalised. In (12), we find three nominalised ordinal numerals. If the ordinal is to be marked for the accusative or nominative case, it receives the nominaliser =bii(-ta/-ha); for all other cases it receives the nominaliser =hann/=tann. 10 (12) woná semisteer-áan lan-kí=bii(ha) fúll-eemm first semester-mLOC two-ORD=NMZ1mACC go_out-1sPVE lan-kí=hann-éen woná=bii(ha) ful-íi tass-áa two-ORD=NMZ2-mLOC first=NMZ1mACC go_out-mDAT hope-mACC ass-áyyoomm do-1sPROG 'In the first semester I came second. In the second (semester) I hope to come first.' A limited degree of morphological variation is attested for the ordinals woná 'first' and lankí 'second'. Unlike all other ordinals, they can be used adverbially and, for this purpose, special adverbial forms are created. The ordinal 'first' allows for four adverbial forms: wóna ~ wónan 'earlier, before, in the beginning' (13), wonáa 'firstly, first of all' [START_REF] Treis | ' lam-oo-dum-á Compare: '2' lam-ú '30' sajj-aa-dum-á '3' sas-ú '40' shool-aa-dum-á '4' shool-ú '50' ont-aa-dum-á '5' ont-ú '60' leh-aa-dum-á '6' leh-ú '70' lamal-aa-dum-á '7' lamal-á '80' hezzeett-aa-dum-á '8' hezzeett-ú '90' hons-aa-dum-á '9' hons-ú góon-u hikkánne afuu'll-ée' men-mNOM IDEM2.mOBL sit-3mPVE 'About 5[END_REF] and wonáachch 'than, compared to before' (15). ( 13 For the ordinal 'second' two adverbial forms are attested, lankíi ~ lankée 'a second time, again', which a consultant considered to be regional variants. ( 16) lan-k-ée dikk-úta mar-eenán abbis-éen two-ORD-DAT market-fACC go-3honICO exceed-3honICO qoraphph-eennó=g-a yóo'u take_care.MID-3honIPV.REL=SIM-mOBL COP1.3 'One needs to be careful when one goes to the market again.' [DW2014-12-24_market] Fractions are based on ordinal numerals (see section 8). K'abeena, Alaaba and Sidaama make use of an ordinal suffix that is cognate with that of Kambaata. Like Kambaata, Alaaba and Sidaama have a suppletive ordinal 'first', which is not used for the ordinals '11 th ', '21 st ' etc. Instead, these ordinals are derived regularly and translated literally as 'ten-and oneth', 'twenty-and oneth' etc. [START_REF] Schneider-Blum | A Grammar of Alaaba. A Highland East Cushitic Language of Ethiopia[END_REF]: 132, Kawachi 2007: 137). K'abeena has no suppletive 'first' at all but only a regularly derived mat-ikk'i lit. "oneth" (Crass 2005: 217f). Compared to these languages, the ordinal formation of Hadiyya is fairly different. Ordinals of simple numerals are derived from cardinals by the replacement of the final vowel and, for some numbers, by the glottalisation of stem-final consonants. Ordinals of numerals higher than 'ten' are formed periphrastically with the noun 'place '. 11 In Hadiyya, too, 'first' is suppletive; the suppletive form is, however, not used for '11 th ', which is lit. "ten oneth place" (Tadesse 2015: 150).

Numeral-based compounds

Compounding is only a semi-productive morphological process in Kambaata. Consequently, not many compounds are attested in my database. Below I list all known adjectival and nominal compounds containing a numeral stem. The numeral is the first part in all the examples; compounds whose second stem is a numeral are not (yet) attested. The adjectival compounds in ( 17)-( 23) all have a nominal stem as the second part. The adjectival inflectional morphology is attached to this second lexical stem. If the second stem starts with /h/, there is a tendency to drop this phoneme; see ( 17) and ( 22). The meaning of the compounds is not always the sum of its parts, e.g. in ( 21), and they would thus have to be included in a dictionary. ( 17) mat-'one' + hagar-'type' (ACC: hagar-á)  matagar-á(-ta) or (K89: 5.29) mathagar-á(-ta) 'of one type' (18) sas-'three' + hagar-'type' (ACC: hagar-á)  sasagar-á(-ta) (mostly negative:) 'of more than one colour, not coloured regularly, not washed properly (e.g. of clothes) (lit. of three types)' ( 19) mat-'one' + ill-'eye' (ACC: ill-íta)  matill-á(-ta) 'one-eyed' (GH: 96) (20) mat-'one' + ang-'hand' (ACC: ang-áta)  matang-á(-ta) 'one-handed (of a person), simple (of a rope with only two threads)' (21) lam-'two' + fool-'soul' (ACC: fool-í)  lamfool-á(-ta) 'highly pregnant (lit.

two-souled)' ( 22) Udders of different domestic animals: lam-'two' + hanx-'teat' (ACC: hanx-á)  lamanx-á(-ta) 'with two teats' sas-'three' + hanx-'teat' (ACC: hanx-á)  sasanx-á(-ta) 'with three teats' shool-'four' + hanx-'teat' (ACC: hanx-á)  shoolanx-á(-ta) 'with four teats' (23) shool-'four' + kof-'upper arm' (ACC: kof-ú)  shoolkof-á(-ta) 'with four branches (of a stick)' (K89: 6.113)

In ( 24)-( 27), the numeral and the nominal stem of the compounds are further extended by a derivational morpheme, the proprietive derivation ('having N'), which is described in more detail in Treis (2008: 274-77).

(24) lam-'two' + macc-'ear' (ACC: macc-áta) + -aam-ú / -íta PROP  lammaccaam-ú / -íta 'with two handles (lit. two-eared)' (25) sas-'three' + macc-'ear' (ACC: macc-áta) + -aam-ú / -íta PROP  sasmaccaam-ú / -íta 'with three handles (lit. three-eared)' ( 26) lam-'two' + lokk-'foot, leg' (ACC: lokk-áta) + -aam-ú / -íta PROP  lamlokkaam-ú / -íta 'two-legged, two-footed' (27) lam-'two' + gooc-'door' (ACC: gooc-á) + -aam-ú / -íta PROP  lamgoocaam-ú / -íta 'with two doors' (GH: 148)

By the same mechanism the compound in (28) has been created. Note, however, that the numeral stem is a loan from the neighbouring language Hadiyya.

(28) soor-'four' (Hadiyya) + macc-'ear' (ACC: macc-áta) + -aam-ú / -íta PROP  soormaccaam-íta 'four-eared' (of a type of spear)

One compound adjective ( 29) is attested in which the second stem is a verb. As in the other examples, the adjectival inflectional morphology is attached wordfinally. Furthermore, examples ( 29) and ( 18) show that 'three' is often interpreted as 'several, many' (see also section 11).

(29) sas-'three' + hoog-'not have, not do'  sasoog-á(-ta) 'with various bad traits, with various deficiencies, useless (when insulting someone; lit. not having three)'

The compound adjectives can assume the same functions as any simple adjective. In (30) we see the compound as a modifier of the direct object dist-íta 'pot'.

(30) aayíchch lammaccaam-íta dist-íta dikk-óochch hir-éemma mum.fNOM two_handled-fACC pot-fACC market-fABL buy-3honPVE 'Mum has bought a two-handled pot at (lit. from) the market.' [Elic.] A small group of complex adjectives whose first part is a numeral (31)-( 34) have an element (h)aqq-as a second part. Most of these adjectives characterise blankets and shawls with different numbers of layers. It is unclear whether (h)aqq-goes back to a nominal stem or whether its origin is the middle morpheme -aqq. (Only in the first case would the examples merit treatment in this section.) One informant proposed the noun haqq-á as the source of the second part. However, according to other native speakers, the noun haqq-á is only used with the meaning 'tree, wood' but never 'layer'; therefore I tend to interpret the second element as the middle morpheme.

(31) mat-'one' + (h)aqq-'[?]' → mataqq-á(-ta) 'one-ply, of one layer'; (neo.)

'singular' (K89: 6.131; KXS: 22) (32) mexx-'single' + (h)aqq-'[?]' → mexxaqq-á(-ta) 'one-ply, of one layer' (33) lam-'two' + (h)aqq-'[?]' → lamaqq-á(-ta) 'two-ply, of two layers (e.g. of woven blankets and shawls such as the gaab-íta)'; (neo.) 'compounded, composite', e.g. lamaqq-áta laagaakk-áta 'compound words' (K89: 4.15), 'reduplicated words' (K89: 8.26), 'consisting of two letters, digraph' (KXS: 4) (34) hool(-am)-'many' + (h)aqq-'[?]' → (neo.) hoolaqq-á(-ta) 'plural' (K89: 6.131; KXS: 22) Some of the complex adjectives above have been used in local linguistic publications to denote grammatical concepts such as singular (31), plural (34), composite or reduplicated words (33), and digraphs (33).

The compounds in ( 35)-( 37) consist of an ordinal numeral and one or two nouns. The compound itself also belongs to the noun word class. Interestingly, it is not only the stem (lank-) but the complete ordinal with its genitive case vowel (lankí) which serves as the input. The case vowel (-í) assimilates to the initial vowel of the second V-initial constituent, creating a long vowel at the boundary. Example (38) demonstrates the use of the compound noun in (36): it serves as a modifier to the predicate noun 'children' and thus carries the copula for the predicate noun. The initial syllable of the compound is reduplicated to mark reciprocity. Reduplication is not only a means to express reciprocity; it is also a means to create distributive numerals, as we will see in the next section.

Distributive numerals

Distributive numerals ('1 each', '2 each' etc.) are marked by partial prereduplication. The addition of the distributive morpheme to numeral stems is the only prefixing operation in an otherwise entirely suffixing language.

The initial CV of the stem is copied and prefixed. Even if the initial syllable of the numeral contains a long vowel (e.g. shool-ú 'four'), the vowel of the prefix is short (e.g. shó-shshool-ú 'four each'). In this example, the first C of the numeral stem is realised geminate after the prefix because the second stem consonant is single. In contrast, the stem-final Cs of hé-hezzeett-ú 'eight each' and hó-hons-ú 'nine each' are not geminate, because the second stem consonants are bi-phonemic, namely zz and ns, respectively. 13 Only one example violates this gemination rule, the morpheme tóona 'NUM-teen', of which the distributive form is tó-tóona (*tóttóona) 'NUM-teen each'; see Table 6, Table 8 and(39).

For reasons of space, the distributive numerals from 1 to 10 are presented only in their masculine accusative form in Tables 6, 7 and 8. As modifiers, the distributive numerals do, however, inflect like ordinary cardinal numerals (see Table 1). They can also be used as heads of an NP, and then they inflect like nouns; see Table 2 13 To the best of my knowledge, this phonotactic restriction is not applied elsewhere in the language. It is, for instance, possible that underived lexemes contain more than one geminate consonant or cluster; see e.g. xilliill-íta 'hawk'.

The formation of distributive numerals for the tens and hundreds follows the same mechanism as that of units. The only exception is '1000', which is fully reduplicated in its distributive form. Recall that the number words '100' and '1000' are nouns. shiih-á shiih-á ( ? shi-shiih-á) '1000 (each)' 14Table 7. Distributive numerals (tens and hundreds)

While the formation of distributive forms of non-complex numerals is fairly straightforward, there are two, and possibly even three mechanisms to generate the distributive forms of numerals consisting of tens plus units. As Table 8 illustrates, either (i) only the unit is pre-reduplicated or (ii) both the tens and the units are prereduplicated. In a schoolbook text, even a third possibility is attested. The distributive of the numeral '15' in (39) has a pre-reduplicated ten but no pre-reduplicated unit. (41) isso'óont mé-méxx-i-s lá-llám-o-'indo 3pNOM<N> RED-single-fNOM-DEF RED-two-mOBL-DISJ sá-ssás-o boos-í qax-á RED-three-mOBL type_of_pot-mGEN amount-mACC af-fáa-haa=rr-a íkke hold-3fIPV.REL-mCOP2=NMZp-mPRED INACT 'They (= six zaale-pots), each one of them, each held the contents of two or three boosu-pots.' [John 2,6] The distributive form of the numeral one, mámmat-ú, means not only 'one each' but also 'some' (Treis 2008: 312).

CARDINAL NUMERAL DISTRIBUTIVE

The formation of distributives is not restricted to cardinal numerals but can also depart from ordinal numerals, e.g. lá-lankí 'every second', sá-sakkí 'every third', shó-shoolkí 'every fourth', lá-llamalqí 'every seventh' (42).

(42)

Shaaméeb-i-i

Abbís-u-u la-lan-kí kod-áta [Name]-mNOM-ADD [Name]-mNOM-ADD RED-two-ORD time-fACC áag-g it-tóo'u enter-3fPCO eat-3fPVO 'Shaameebo and Abbiso each entered and ate a second time.' [Elic.] The distributive ordinals support the gemination rule proposed for cardinal distributives above, namely that the second stem consonant triggers (or blocks) steminitial gemination. While, for instance, sá-ssas-ú '3 each' has a geminate stem-initial C triggered by the monophonemic /s/ as C2, the corresponding ordinal distributive, sá-sakkí 'every third' lacks the gemination because C2 /kk/ is bi-phonemic.

Fractions (see section 8) can also be the input of the distributive formation: matú sakkichch-ú 'one third' > má-mmat-ú sakkichch-ú 'one third each' or sakkí af-óo 'one third (lit. the third share)' > sá-sakkí af-óo 'one third each'.

While distributivity is often encoded by partial reduplication (43a), conversational data shows that full reduplication is also an option in similar contexts (43b). In K'abeena, distributive numerals are always formed by full reduplication (Crass 2005: 218f).

Multiplicative numerals

A fully productive derivational process generates multiplicative numerals 'NUM times' by the addition of the morpheme -é to the cardinal numeral stem. The derivational process can be applied to lower, adjective-like numerals as well as higher, noun-like numerals; see lam-ú 'two' + -é MULT > lam-é 'twice' and xibbíta '100' + é MULT > xibb-é '100 times'. Multiplicative numerals are only used in adverbial function. K'abeena and Alaaba have a multiplicative derivation, which does not seem to be cognate with that of Kambaata. In both languages a morpheme -V-ra is suffixed to the cardinal numeral stem; see Crass (2005: 219f) on K'abeena and the Alaaba ex. 25-27 and 51 in text 3 of Schneider-Blum (2007: 416f, 421). 16 In (44), the multiplicative sas-é 'three times' is an adverbial to the verbal noun xúur-u 'milking (mNOM)'. In (45), the multiplicative numeral is focussed and made the predicate of a cleft sentence. The period of time spanning a repeated action is encoded by a locative noun; see bar-éen 'in a day, per day' (44) and hezzeett-óon 'in a week, per week' ( 46). ( 44) bar-éen sas-é xúur-u qal-amm-ó day-mLOC three-MULT milk-mNOM give_birth-PASS-3mPVO.REL wo'-ichch-ú qoh-áno calves-SG-mACC harm-3mIPV 'Milking (the cow) three times a day harms the (new-)born calf.' [K89: 2.40] (45) sá'-u qall-ó=g-anka bar-éen cow-mNOM calve-3mPVO.REL=SIM-mACC<N> day-mLOC sas-é-nee-t has-is-anóo-hu three-MULT-L.VV-COP3 want-CAUS-3mIPV.REL.NMZ.VV-mNOM 'When a cow has calved, one needs to milk her THREE TIMES a day.' [Elic.] Multiplicative numerals can also be derived from the three special members of the numeral word class; see hoolam-á / -íta 'many' > hoolam-é 'many times', mexxú / -íta 'single' > mexx-é 'a single time' and me'-ú / -íta 'how many?' > me'-é 'how many times?' (46). ( 46) hezzeett-óon me'-é abbaas-seenán? week-mLOC how_many-MULT sweep-2pICO 'How many times a week do you sweep?' [K89: 2.13] 16 As pointed out by the editors, the K'abeena and Alaaba morpheme -V-ra is possibly cognate with the Kambaata noun irá 'time(s)' used in the periphrastic multiplicative in (52).

Apart from expressing 'a single time', the multiplicative mexx-é can also mean 'at once, instantly' (47). ( 47) tah-íchch-u dángo hitt-íta afuu'll-ít zug-gáni-yan fly-SG-mNOM suddenly like_this-fACC sit-3fPCO ambush-3fICO-DS waall-ó=da arrab-í-se mexx-é come-3mPVO.REL=COND tongue-fACC-3fPOSS single-MULT buqqís-s tokkós-s fushsh-ít ke'éechch pull_out-3fPCO shoot-3fPCO go_out.CAUS-3fPCO then xámm át-t aphph-ít aag-ís-s qúrc at-táa' stick do-3fPCO take.MID-3fPCO enter-CAUS-3fPCO swallow do-3fIPV

'When a fly comes suddenly while she (= the chameleon) is sitting in ambush in this way, she shoots out her tongue at once, makes (the fly) stick (to it), puts (it) in (her mouth) and swallows (it).'

[TD2016-02-11_001]
Finally, the distributive numeral má-mmat-ú / -íta 'one each; some' can host the multiplicative morpheme: má-mmat-é 'sometimes' (48). ( 48) múumm-u má-mmat-é bobir-á has-áno hair-mNOM RED-one-MULT wind-mACC want-3mIPV 'The hair needs (fresh) air sometimes.' [K89: 2.35] Despite having a fully productive multiplicative derivation at hand, Kambaata also makes frequent use of multiplicative periphrases. Two periphrases that are attested in my data: NUM + kod-áta 'NUM times, turns' and NUM + j-áata 'NUM times' are in free variation with the multiplicative derivation. In the following examples, from three different schoolbooks, the derived multiplicative mat-é (49), the periphrasis with kod-áta (50) and the periphrasis with j-áata (51) are used in almost identical contexts. (51) muumm-í-nne hezzeett-í aaz-éen lam-íta j-áata hair-mACC-1pPOSS week-mLOC inside-mLOC two-fACC time-fACC saamun-íin áa'll-u has-is-áno-nne soap-mICP wash-mNOM want-CAUS-3mIPV-1pO 'We have to wash our hair twice a week with soap.' [K89: 2.33] Furthermore, the multiplicative hoolam-é 'many times' is in free variation with the periphrasis hoolam-á ir-á 'many times' (52). However, ir-á cannot be combined with true numerals (*sas-ú ir-á intended meaning: 'three times'). The counted entity is expressed in an ablative phrase, see uull-áachch (58). ( 58)

ann-i-nné uull-áachch lam-ú father-mGEN-1pPOSS land-fABL two-mACC sak-k-ichch-únka-s bahír-u three-ORD-SG-mACC<N>-DEF older-mNOM hiz-óo-nne aaqq-í kámm-ee'u brother-mNOM-1pPOSS take-3mPCO do_completely-3mPVE 'Our eldest brother took two thirds of (lit. from) our father's land.' [Elic.] As for percentages, a schoolbook example (59) shows the use of xibb-éechch NUM ang-áta lit. 'NUM hands from hundred'. In a text for religious instruction (Brook/Yonathan 2013), 21 examples expressing percentages are found, all of which are expressed as xibb-éechch NUM af-óo lit. 'NUM mouths from hundred' (60). Note that both af-óo 'mouth' and ang-áta 'hand' also have the meaning 'part'.

Approximation

Kambaata does not have an approximate number derivation; instead approximation is expressed by means of three periphrastic strategies. Both in the written (61) and oral text corpora (62), the use of the cardinal numeral mat-ú /-íta 'one' is attested as a marker of approximation. antabée'-u-s hoolám-a-ta, chicken-mACC-DEF many-fPRED-fCOP2 mat-íta ont-é leh-é qax-áta ik-káa' one-fACC five-fGEN six-fGEN number-fACC be-3fIPV 'The chicken were many, they were about five (or) six in number (lit. in one number of five, six).' [TD2016-02-11_001] If the exact number is not known or not meant to be expressed, the speaker can also resort to a second strategy, the use of the nomino-adjective qax-á(-ta) '(having the) number, amount (of)'. 19 It precedes and agrees in gender and case with the noun whose number is estimated, e.g. mann-á 'people' and mínn-at 'houses' (63). Qaxá(-ta) itself is modified by a genitive marked numeral or by a relative clause containing the numeral (64). The phrase 'people having the number of hundred' is interpreted as an approximation, 'about one hundred people'. (63) xibb-é qax-á mann-á hundred-fGEN having_number-mACC people-mACC 'about one hundred people' [Elic.] lamoodum-é qáx-at mín-n-at twenty-fGEN having_number-fNOM house-PL-fNOM 'about twenty houses' [Elic.] (64) ont-íta kum-íta ih-anó qáx-u five-fACC thousand-fACC be-3mIPV.REL having_number-mNOM (68) Subtraction in schoolbooks ont-ú kot-is-ú mat-ú ih-áno shool-ú five-mACC decrease-CAUS-mACC one-mACC be-3mIPV four-mACC 'Five minus one is four (lit. Five decreasing one it-is four).' [DW2014-07-16] (69) Subtraction in natural Kambaata ont-íichch mat-ú kot-is-eemmá=da five-mABL one-mACC decrease-CAUS-3honPVE.REL=COND shool-ú ih-áno four-mACC be-3mIPV 'Five minus one is four (lit. If one decreases one from five it is four).' [DW2014-07-16] (70) Multiplication in schoolbooks lam-ú bat-is-ú sas-ú ih-áno leh-ú two-mACC increase-CAUS-mACC three-mACC be-3mIPV six-mACC 'Two times three is six (lit. Two increasing three it-is six).' The marking patterns of the natural Kambaata examples correspond to the patterns observed in the expression of calculation in K'abeena (Crass 2005: 215ff).

Postscript

Although the morphology and morphosyntax of Kambaata numerals and denumerals can become fairly complex, the translation of simple cardinal numerals seemed for a long time to be a fairly straightforward task. It is when collecting more conversational data during my last fieldtrip that I also came across contexts where certain numerals could clearly not be interpreted as indicating number (numerosity). In section 9 we saw, for instance, that mat-ú / -íta 'one' is used as a marker of approximation. Furthermore, the numerals lam-ú / -íta 'two' and sas-ú / -íta 'three' turned out to have common idiomatic uses that cannot be translated literally and that can even be considered synonyms. So while the morphology and morphosyntax of Kambaata numerals and denumerals has been disentangled in this contribution, further challenges, such as the study of idiomatic expressions containing numerals, still lie ahead.

Abbreviations

  shool-í shool-íi shool-óon shool-íin shool-íichch shóol-o shóol-o F shool-í-ta shóol-i-t shool-é shool-ée shool-éen shool-éen shool-éechch shóol-e shóol-e

  use-fABL two-fACC-DEF write-2sPCO 'Write down two uses of enset fibres […] (lit. From the uses of enset fibres, write down two […]).'

[

  K89: 2.101] In contrast to cardinal numerals, ordinal numerals are (almost) morphologically invariant. As modifiers in a noun phrase, ordinals do not show gender or case agreement with the head noun; they thus behave like modifying genitive nouns.(11) sak-kí-na shool-kí maar-aakk-á sawwitt-á xáaf three-ORD-CRD four-ORD line-PL-fGEN idea-mACC write.2sIMP 'Write (explain) the idea/message of the third and fourth line.'[K89: 4.130]

[

  K89: 4.125]

( 35 )

 35 lankí 'second' + am-áta 'mother'  lankaam-áta 'maternal aunt' (36) lankí 'second' + ann-á 'father'  lankaann-á 'paternal uncle' (37) lankí 'second' + ann-á 'father' + oos-úta 'children'  lankaannoos-úta (DIC: 174) 'cousins (via the paternal uncle)' 12

  -fNOM-ADD [Name]-fNOM-ADD lá-lankáann-i-ta óos-u RED-paternal_uncle-mGEN-fCOP2 children-fPRED 'Zaraare and Maassaame are cousins via the paternal uncle.' [K89: 4.138]

  NUMERAL tóona mat-ú (i) tóona má-mmat-ú (ii) tó-tóona má-mmat-ú '11 (each)' laméena mat-ú (i) laméena má-mmat-ú (ii) lá-llaméena má-mmat-ú '21 (each)' xibb-íta mát-o (ii) xí-xibb-íta má-mmat-ú '101 (each)' 15

  newspaper-PL-fNOM day-mLOC day-mLOC RED-eight-mLOC tó-tóo-na ont-óon te agan-áan agan-áan attaman-táa'u RED-ten-CRD five-mLOC or month-mLOC month-mLOC be_published-3fIPV 'Newspapers are published daily, every eight (days) (i.e. weekly), every fifteen (days) (i.e. fortnightly) or monthly.' [K89: 4.92] While (39) shows the use of distributive numerals as heads of NPs, distributive numerals are, of course, also used as modifiers in an NP. The following examples illustrate the distributive numeral modifier of an accusative noun (40) and of a genitive noun (41). (40) kifil-í aaz-éen tó-tordum-á rosaan-n-ú class-mGEN interior-mLOC RED-ten-mACC student-PL-mACC gur-á-na makk-é wud-íin uurr-ís-s […] left_side-fGEN-CRD right_side-fGEN side-mICP stand-CAUS-2sPCO 'Let ten students each stand on the left and on the right sides of the class room […].' [K89: 8.106]

  foot-fGEN-3fPOSS top-mLOC shó-shshóol-it zuru'mm-ichch-áakk-at yoo-se-táa […] RED-four-fNOM toe-SG-PL-fNOM COP1.3.REL-3fO-fCOP2-ADD '[…] she is (an animal) which has, on her four feet, four small toes each and […].' (43b) SPEAKER DW mat-éen-ta-s mat-éen-ta-s one-fLOC-L-DEF one-fLOC-L-DEF 'On each one of them (= the feet)?' [TD2016-02-11_001]

  -1pPOSS week-mLOC one-MULT water-mICP-ADD saamun-iiní-i áa'll-u has-is-áno-nne soap-mICP-ADD wash-mNOM want-CAUS-3mIPV-1pO 'We have to wash our body […] once a week with water and soap.' [K89: 5.59] (50) mannoom-a-nné-e muumm-i-nné-e […] hezzeett-óon body-fACC-1pPOSS-ADD hair-mACC-1pPOSS-ADD week-mLOC mat-íta kod-áta áa'll-u has-is-áno-nne one-fACC turn-fACC wash-mNOM want-CAUS-3mIPV-1pO 'We have to wash our body and our hair […] once a week.'[K89: 4.118]

  time-mACC office-fACC-3mPOSS return_again_and_again-1sPVO 'I returned to his office many times.' [DW2016-02-12_NB] 17Kambaata does not have multiplicative verbs of the type 'double, triple, quadruple'. This is instead expressed periphrastically: one-mACC two-mACC three-mACC add.2sIMP 'Double / triple / quadruple it! (lit. Add one / two / three of this!)'[Elic.] Unlike simple adjectives, which all have a corresponding inchoative-stative property verb, e.g. qeraa'rr-ú(-ta) 'long' -qeraa'rr-'be(come) long' (for details seeTreis 2008: 268-73), numerals do not share their stems with verbs, nor are they the input of any derivation processes leading to denumeral verbs. The only exception is

  how_much-fOBL hand-fPRED 'What percentage of the water is drinkable (lit. serves as a drink)?'[K89: 7.117]

  two-fOBL hundred-fGEN birr-mACC find.MID-3mIPV.REL mín-u […] house-mNOM 'A house(hold) which earns about two hundred birr (lit. one birr of two hundred)

  time-fACC three-mNOM six-mACC be-3mIPV 'Two times three is six.' divide-mACC two-mACC be-3mIPV three-mACC 'Six divided by two is three (lit. Six dividing two it-is three).' [DW2014-07-16] two-mDAT divide-3honPVE.REL=COND three-mACC be-3mIPV 'Six divided by two is three (lit. If one divides six for two, it is three).'[DW2014-07-16]

[

  (74) kabár lam-éechch [~ sas-éechch] fúll hoshsh-óomm today two-fABL three-fABL get_out.1sPCO spend_the_day-1sPVO [Speaker coming home in the evening:] 'I have achieved nothing today (lit. I have spent the day today getting out of two/three).' Speaker exhausted:] 'This girl has just wasted my time today (lit. This girl has taken me out of two/three).' [DW2016-02-23_NB]

Table 3 . Formation of tens

 3

Table 5 .

 5 Ordinal numerals

Table 8 .

 8 Distributive numerals (tens plus units)

Affiliation: COMUE Sorbonne Paris Cité, INALCO CNRS UMR 8135 LLACAN Langage, langues et cultures d'Afrique noire

The following graphemes are not in accordance with the IPA conventions: <ph> /p'/, <x> /t'/, <q> /k'/, <j> /dʒ/, <c> /tʃ'/, <ch> /tʃ/, <sh> /ʃ/, <y> /j/ and <'> /Ɂ/. Geminate consonants and long vowels are marked by doubling, e.g. <shsh> /ʃ:/ and <ee> /e:/.

I am indebted to my language assistant Deginet Wotango and to my Kambaata language consultants Teshome Dagne, Tessema Handiso, and many others who readily taught me their language over the past few years. I am grateful to the Culture Department of the Kambaata-Xambaaro Zone for their support during my fieldtrips. An earlier version of this paper was presented at the meeting of the project Les dénuméraux à travers les langues (led by Bernard Fradin) on 30 th June 2014. This research project

Hereafter, the internally complex feminine case/gender-morphemes, i.e. -í-ta (fACC) and -i-t (fNOM), are no longer subdivided but simply given as -íta (fACC) and -it (fNOM).

The masculine form of the independent numeral hezzeett-ú 'eight' cannot be formally distinguished from the noun hezzeett-ú 'week' and is surely etymologically related to it.

7 The same is true of adjectives in Kambaata.

For reasons of space only the masculine accusative form is given in Table3, the tens do however inflect in the same way as e.g. tordum-á / -í-ta 'ten' (Table1).

For reasons of space only the masculine accusative form is given in Table4.

The description in Tadesse (2015) is not very clear and only the ordinals 'first' to '19 th ' are provided.

The hypothetical term *lankaamoosúta 'cousins via the maternal aunt', modelled on (35) and (37), was not accepted by native speakers.

As the Cushitic '1000', kum-íta, is not in use in daily life, I was unable to elicit a distributive form.

A native speaker consultant considered hoolam-á ir-á equivalent to the derived multiplicative hoolam-é.

Note that the Kambaata causative derivation with -(i)s has not only verbal stems but also nominal stems as inputs; see, for instance, koh-á 'guests' > koh-is-CAUS 'invite as a guest' (*koh-'be(come) a guest').

The word class membership of qax-á(-ta) is not entirely clear. Sometimes it can be used as a case and gender-agreeing modifier, in many other contexts it rather behaves like a noun.

is sponsored by the Federation Typologie et universaux linguistiques :

xibb-is-'have a lot of cattle' (DIC: 310), 18 which is the semantically unpredictable causative form of xibb-íta 'hundred'.

Fractions and percentages

Kambaata makes a formal distinction between fractions with the numerator 'one' and with a numerator greater than 'one'. Fractions with the numerator 'one' are expressed periphrastically as 'N th mouth, N th part', e.g. sakkí afóo '1/3', shoolkí afóo '1/4' and ontiqqí afóo '1/5'. When used in an NP, the fraction is the head and the noun referring to the counted entity serves as a genitive (55) or ablative modifier (56). ( 55) uull-á sak-kí af-óo aaqq-ée'u land-fGEN three-ORD mouth-mACC take-3mPVE 'He took one third of the land.' [Elic.] (56) Kambaat-í minaadab-íichch tordun-qi-sí af-óo Kambaata-mGEN people-mABL ten-ORD-DEF mouth-mACC ammanáat-ut yóo-ba'-i-a belief-fNOM COP3.1-NEG.REL-mCOP2 'One tenth of (lit. from) the Kambaata population is not religious.' [Elic.] To express'1/2' Kambaata uses the noun bakkaní 'half'.

Fractions with a numerator greater than 'one' take a cardinal numeral as the numerator and a singulative noun derived from an ordinal numeral as the denominator. The numerator and the denominator agree in gender and case (57).


Radhika Garg

Burkhard Stiller
email: garg|stiller@ifi.uzh.ch

Trade-off-based Adoption Methodology for Cloud-based Infrastructures and Services

Keywords:

Adoption and consequent management of cloud-based infrastructures and services is driven by business requirements and objectives within an organization. The decision of either to move from a legacy system to a cloudbased system or to move from one cloud solution to another is based on various factors. A potential customer, therefore, should evaluate (a) relevant factors affecting the adoption of a cloud and (b) impacts cloud services will have on multi-faceted objectives of an organization. Existing methods for such an adoption process do not evaluate these two aspects for the decision of cloud adoption. Thus, this paper fills this gap by introducing a new Trade-off-based Adoption methodology for Cloud-based Infrastructures and Services (TrAdeCIS), which is based on the impact cloud-based services will have on the organization. This methodology developed will support organizations in decisions concerning (a) the selection of cloud service provider, (b) the type of cloud service to be adopted, and (c) the suitable type of cloud to be adopted. TrAdeCIS is illustrated based on a survey conducted with 10 organizations, who have adopted or plan to adopt cloud-based solution to fulfil their advanced IT requirements.

Introduction

Organizations are increasingly concentrating on adopting new and emerging IT solutions to fulfill their business requirements and objectives. A cloud computing environment foresees advantages for organizations such as lower IT administration and managed service costs and a better business continuity and disaster recovery process [START_REF] Armbrust | A View of Cloud Computing of Cloud[END_REF], [START_REF] Li | Cloudcmp: Comparing Public Cloud Providers[END_REF]. However, there are also disadvantages in terms of loss of control of services and/or data [START_REF] Sultan | Reaching for the "Cloud": How SMEs can Manage[END_REF] as well as lower security, privacy, and reliability [START_REF] Geczy | Cloudsourcing: Managing Cloud Adoption[END_REF], [START_REF] Greenwood | The Cloud Adoption Toolkit: Addressing the Challenges of Cloud Adoption in Enterprise[END_REF]. Therefore, in a decision of either moving from a legacy infrastructure to a cloud-based solution or switching the cloud provider, contradicting and interdependent factors must be evaluated in full. These factors can be based on technical, economical, legal, and business oriented requirements and objectives. The difficulty in the decision of cloud adoption exists because of multiple criteria of selection, and due to the presence of more than one alternative solution. The current decision methodology for the selection of the best available cloud-based solution for IT requirements in organizations is an ad-hoc process, which does not only fail to achieve a trade-off between multiple contradicting factors, but also lacks a quantitative validation of this decision made.

Researchers have suggested a generic framework for such a decision using multiattribute decision algorithms [START_REF] Menzel | The (MC2)2 Criteria, Requirements and a Software Prototype for Cloud Infrastructure Decisions; Software: Practice and Experience[END_REF], [START_REF] Saripalli | MADMAC: Multiple Attribute Decision Methodology for Adoption of Clouds[END_REF]. However, this work did not incorporate that (a) attributes can be mutually dependent, and (b) a trade-off-based decision is required based on multi-faceted business objectives. Hence, the need of a highly integrated yet flexible methodology for the decision of cloud adoption was distinctly identified [START_REF] Zardari | Cloud Adoption: A Goal-Oriented Requirements Engineering Approach[END_REF]. The methodology developed and followed in this paper is called Trade-off-based Adoption methodology for Cloud-based Infrastructures and Services (TrAdeCIS) and is motivated by those gaps still existent in terms of identifying tradeoff strategies for a cloud adoption and the management of cloud-based infrastructures and services. Trade-off strategy means altering the importance allotted to business objectives so that the best possible technical solution, based on traditional IT metrics, such as availability, response time, scalability, or efficiency, can be selected. Therefore, the methodology discussed in this paper focuses on the impact of business processes and business-level objectives on cloud adoption and vice versa. The aim of this approach is to find the best possible technical solution on an acceptable business value. This methodology can be used for a cloud-based decision concerning cloud-service providers, the cloud type, and services that should be migrated to the cloud. The application case of cloud-based solutions, has been selected due to its current importance, the demand from companies to see guided help, and to formalize the methodolgy in a concrete setting.

The methodology developed in this paper consists of following three steps: First, the identification of relevant factors, based on which the available alternative solutions will be evaluated. The list of such factors for this paper is retrieved based on the survey conducted with organizations who plan or have adopted cloud-based solutions for their IT needs. The following two steps of the decision support system are based on two multi-criteria decision analysis methods: (a) The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), and (b) the Analytic Network Process (ANP) [START_REF] Hwang | Multi Attribute Decision Making: Methods and Applications[END_REF], [START_REF] Saaty | Fundamentals of the Analytic Network Process-dependence and Feedback in Decision-making with a Single Network[END_REF]. These two methods are chosen due to their inherent nature of being able to compare components of an adoption scenario and to rank alternatives under consideration. While TOPSIS is used to rank alternative solutions based on technical requirements, ANP is used to establish a trade-off-based decision for multiple contradicting Business Performance Metrics. These algorithms will be used within the envelope of business-level objectives, so that a holistic method is achieved for the decision regarding adoption of cloud.

This paper is structured as follows. Sec. 2 discusses relevant research work and gaps existent in a cloud adoption process. Sec. 3 provides an in-depth view of TrAde-CIS for establishing the trade-off-based decision methodology for adoption of clouds in an organization. Sec. 4 illustrates the new methodology based on results obtained from the survey conducted. Finally, Sec. 5 summarizes and concludes the paper.

Terminology and Related Work

Business-driven IT management deals with fulfilling IT requirements by evaluating impact of IT on business processes and vice versa. However, business objectives are contradicting in nature and, therefore, a trade-off strategy is necessary. Such a strategy can fulfil IT requirements in a best possible way by balancing various requirements and goals. The term business value or return value refers to the impact IT (in the context of this paper, a cloud-based solution) has on organizational performance using process-level, economic, and operational metrics, called Business Performance Metrics (BPM).

In order to compare related work to TrAdeCIS, it is divided into two groups. Category one consists of current efforts in cloud adoption and management of cloud resources and services concentrating on technical aspects, such as resource provisioning [START_REF] Ferrer | OPTIMIS: A Holistic Approach to Cloud Service Provisioning[END_REF] or migration and implementation processes [START_REF] Chang | Towards a Structured Cloud ROI: The University of Southampton Cost-Saving and User Satisfaction Case Studies[END_REF], [START_REF] Khajeh-Hosseini | Cloud Migration: A Case Study of Migrating an Enterprise IT System to IaaS[END_REF]. Category two comprises of methodologies for the decision of cloud adoption for an organization. Research on a cloud adoption decision process suggests various approaches such as Goal-oriented Requirement Engineering (GRE) [START_REF] Zardari | Cloud Adoption: A Goal-Oriented Requirements Engineering Approach[END_REF], [START_REF] Beserra | Cloudstep: A Step-by-Step Decision Process to Support Legacy Application Migration to Cloud[END_REF] and a quantified method of Multi-Attribute Decision Analysis (MADA) [START_REF] Menzel | The (MC2)2 Criteria, Requirements and a Software Prototype for Cloud Infrastructure Decisions; Software: Practice and Experience[END_REF], [START_REF] Saripalli | MADMAC: Multiple Attribute Decision Methodology for Adoption of Clouds[END_REF]. These approaches present a method of decision making based on evaluating various factors that impact such a decision. However, they are not integrated and do not incorporate business-level objectives and requirements. For example, the effect on the net profit after adopting cloud-based services cannot be addressed by such methods.

However, from the cloud providers perspective, the last few years have seen research on business-driven IT management [START_REF] Chhetri | Policy-based Automation of SLA Establishment for Cloud Computing Services[END_REF], [START_REF] Fito | Business-Driven IT Management for Cloud Computing Providers[END_REF], [START_REF] Sedaghat | Unifying Cloud Management: Towards Overall Governance of Business Level Objectives[END_REF]. These approaches concentrate on managing the ever increasing scale of cloud-based resources and services, by providing business level objectives-driven cloud management for the cloud provider. These are holistic approaches as cloud providers have to consider the context where services are used in order to make any service management related decision.

As shown in Tab. 1 the comparison of related work to TrAdeCIS is based on four key features, "Yes" describing the presence and "No" denoting the lack of that feature.

A cloud adoption decision methodology based not only on monitoring technical requirements and factors but also targeting to reach a overall governance process, itself based on business-level policies and objectives, does not exist for a potential cloud customer. The overall adoption decision for a cloud becomes more complex when services and resources are distributed in diverse legacy infrastructure.

Therefore, TrAdeCIS establishes a novel methodology, with which an organization can take a decision based on a trade-off strategy of business objectives. TOPSIS and ANP serve as underlying mathematical models to support this decision of establishing a trade-off strategy. The capability of ANP and TOPSIS to work with interdependent and conflicting factors, effecting the decision, qualifies them to be applicable. Both methods have also been used for solving decision problems with certainty and making forecasts in various fields of science, manufacturing, and finance [START_REF] Deng | Inter-company Comparison Using Modified TOPSIS with Objective Weights[END_REF], [START_REF] Niemira | Saaty: An Analytic Network Process Model for Financial-crisis Forecasting[END_REF], [START_REF] Wang | Application of TOPSIS in Evaluating Initial Training Aircraft under a Fuzzy Environment[END_REF].

Table 1. Feature Comparison of Cloud Implementation and Adoption Methods

Features

Implementation Methods MADA GRE TrAdeCIS

The Development of TrAdeCIS

The overview of the methodology developed in this paper to establish trade-off-based decision for the selection of (a) cloud service provider, (b) cloud service to be adopted, and (c) the suited type of cloud to be adopted, is shown in Fig. 1. As the decision to move from legacy infrastructure to cloud-based solution or to switch the cloud provider is effected by several factors, TrAdeCIS begins with the selection and prioritization of these factors. The selection and prioritization of these factors is based on the technical requirements, and business objectives and policies of organization. Once TrAdeCIS is implemented as a decision support tool, it will include a generalized list of factors, which organizations planning to adopt cloud-based solutions should consider. This list of factors will be based on data collected from (a) survey conducted with organizations who have adopted or plan to adopt cloud-based solution, and (b) academic and industry literature on relevant factors in such a scenario. However, TrAdeCIS would provide flexibility to the organizations to adapt this list of factors based on use-case specific details. This process of identification and prioritizing factors is discussed and presented in Sec. 4. Once an organization identifies its requirements and business objectives TrAdeCIS is an easy, efficient, and a structured approach for making a decision for adoption of cloud-based solutions, which involv multiple attributes and objectives. This is possible because TrAdeCIS is a fully quantitative approach based on mathematical models with clearly identified steps.

Business Layer

The first step for making a decision for the adoption of a cloud-based solution is driven by business level considerations of an organization who plans to a adopt cloudbased solution. Based on the status of current infrastructure (e.g., resources, processes interdependencies), and business goals and policies (e.g., availability level, risk) relevant factors for the evaluation of alternative new cloud-based solutions are selected. To illustrate the process of selection of relevant factors consider an organization dealing with private information of its clients. Such an organization will target to have a control over such data to make sure data is not lost and tampered by anybody. Therefore, privacy of data and data control are two most important factors to be considered. Criteria which serve as benefits are considered positive (e.g., bandwidth, availability) while those which are risk or cost prone are considered to be negative (e.g., latency, cost) [START_REF] Menzel | The (MC2)2 Criteria, Requirements and a Software Prototype for Cloud Infrastructure Decisions; Software: Practice and Experience[END_REF]. Also, depending on the criticality of the business goal,selected on the basis of business policies, relevant factors can be given a relative rank. Criticality of business goals is a metric to define the relevance as it is defined in an organization for each process and service for evaluating IT operations, for example, in terms of, risk in terms of vendor lock-in, technical requirements of availability, latency, security, and business goals and vision of reducing operational cost, increasing available resources.

TOPSIS

Once relevant factors are identified and prioritized a multi-attribute decision making algorithm is required to rank alternative solutions. TOPSIS is such a technique for solving decision problems by determining the relative advantage of available alternatives [START_REF] Hwang | Multi Attribute Decision Making: Methods and Applications[END_REF]. An optimum alternative is mathematically at the shortest geometrical distance from the best solution and at largest geometrical distance from the worst solution. The alternative solution that is at the maximum distance from the worst solution has the least risk attached to it. With this method it is possible to compare a set of alternatives by identifying priorities for each factor and normalizing score for each factor. This gives the advantage of identifying how an alternative scores per attribute in form of the following steps: 1. TOPSIS assumes that there are m alternatives and n attributes/criteria and the score of each option with respect to each criterion is known [START_REF] Wang | An extension TOPSIS for Fuzzy MCDM Based on Vague Set Theory[END_REF]. Let X = (xij) and a matrix represent xij the score of alternative i with respect to criterion j. Let J be the set of benefit attributes (to be maximized) and J' be the set of negative attributes or criteria (to be minimized). 2. The matrix X is normalized to form a normalized decision matrix. This step transforms the attributes having different dimensions into non-dimensional attributes, hence allowing comparisons across criteria. Normalized weights are obtained as

m n × r ij x ij x ij 2 1 i m ≤ ≤ 1 j n ≤ ≤ ∑ ----------------------- = 3.

Evaluation of Alternatives Based on Business Performance Metrics

While the alternative solutions, in the previous step, were ranked based on the relevant factors from the technical and operations perspective, this step evaluates the alternative solutions from the business value perspective. This is important so that returns in terms of business value can be quantified and measured for each of the alternatives. These factors fall in the category of cost, time, profitability, or quality, for example, earned value, planned dollar expenditure per month, workload vs. utilization, and speed of cost reduction. Therefore, based on the business objectives and policies, appropriate BPM are identified and ranked. Each alternative is then evaluated for each of these metrics.

Trade-off-based Decision using ANP

The final step is the most crucial step as it lets decision makers evaluate alternative solutions from the perspective of a return value. ANP evaluates the decision by considering the interdependence of attributes as well as the influence of alternatives in a decision making process [START_REF] Saaty | Fundamentals of the Analytic Network Process-dependence and Feedback in Decision-making with a Single Network[END_REF]. The ranking obtained here can be different than the one obtained from TOPSIS. This happens because factors used to evaluate alternatives in ANP are BPMs as identified by organizations. ANP provides the flexibility of altering weights allotted to factors to establish a trade-off in TrAdeCIS. Establishing a trade-off is necessary so that the best technical solution is selected at an acceptable return value. The possibility of calculating the interdependence of attribute and ability to forecast benefits, costs, and risks qualify ANP for establishing a trade-off strategy for cloud adoption. In this method criteria and alternatives are considered as nodes in a network as shown in Fig. 2. Each node can be compared to all other nodes it has a relation with, thus, a logical overview of those steps is given here only [START_REF] Saaty | Fundamentals of the Analytic Network Process-dependence and Feedback in Decision-making with a Single Network[END_REF]: -------------------= C i * 1. ANP makes a pare wise comparison of all nodes with respect to the objective. An equally spaced scale is also chosen to assign priorities. 2. These priorities are represented in a matrix and the normalized principle Eigen vector is computed. As a result local priorities for all connections are obtained. 3. Steps 1 and 2 are repeated for all connections to obtain the unweighted super matrix. 4. The unweighted super matrix is normalized to calculate the weighted super matrix. 5. The limit matrix is now calculated, which is the weighted super matrix raise to the power of k+1, where k is an arbitrary positive integer. This gives the ranking for alternative solutions with respect to the objective. After applying ANP, a ranking of alternatives is obtained, which is based on the evaluation of available alternative solutions on the basis of BPMs identified by organizations. In this step, if the ranking obtained is different from the one obtained using TOPSIS (as different factors are considered), priorities given to factors can be adjusted in order to achieve the same ranking as with TOPSIS. These priorities represent the trade-off between the return value and technical features of a selected solution.

1 j n ≤ ≤ v ij w ij r ij × = A * v 1 * v n * [ , ] = v j * max v ij ( ) = j J ∈ min v ij ( ) j J' ∈ A' v 1 ' v n ' [ , ] = v j ' min v ij ( ) = j J ∈ max v ij ( ) j J' ∈ S i * v j * v ij - ( ) 2 ∑ = S i ' v j ' v ij - ( ) 2 ∑ = 1 j m ≤ ≤ C i * S' i S i * S i ' + -

Illustration of the Method Based on Survey Results

This section illustrates the new methodology using parameters and their respective weights, based on interviews conducted with 10 organizations, who adopted or plan to adopt a cloud-based solution to fulfil their IT requirements. A qualitative research approach is followed in order to investigate diverse and complex data in depth [START_REF] Blaxter | Tight: How to Research[END_REF].

As shown in Tab. 2, organizations that participated in the survey vary in size, the scope of their expertise, and their geographical scope. Therefore, their IT requirements also vary. In turn, the aim of these interviews was to understand parameters

C10

Financial Services 140000 Worldwide these organizations evaluate before making a decision to make any changes in their existing IT infrastructure. These interviews were semi-structured so that those interviews could be adapted according to individual circumstances, such as focusing on specific areas or discarding questions, which did not apply. This survey helped in collecting a list of factors (e.g., availability, functionality, scalability), which depending on the use-case specific details were considered by organizations before adopting any cloud-based solution. In order to illustrate TrAdeCIS only the data collected from company C2 is used. This helps in evaluating a specific use-case in depth using TrAdeCIS. However, this methodology can be applied to any of the other use-case specific data obtained from other organizations. All the other use-cases are that of similar nature, and discussing them in depth would not provide any new insights to the illustration of TrAdeCIS. The plan of C2 is to scale the existing infrastructure in order to accommodate requirements of the peak season. Therefore, C2 required to evaluate the best available cloud-service provider.

Business Layer

Business requirements for C2 were to increase scalability and availability of the existing infrastructure as the business profitability depends mainly on the web-based platforms and applications that are used by customers and partners of C2. Also, as these applications dealt mainly with private and sensitive data of clients, privacy and security were also important aspects. In addition, as per the legal and regulative requirements, compliance and location of data storage were also critical factors for evaluating the alternative cloud-based solutions. After, finding the list of factors, C2 was asked to give both the weights of attributes and ranking of alternatives by numbers in the range of 1 to 10. As TOPSIS normalizes weights and rankings, the range and the number chosen to rank the alternatives does not matter, as shown in Sec. 4.2., These factors along with their relevant priorities (as identified by C2) are shown in Tab. 3. This table also consists of ranking of each of the available alternative service providers (A1, A2, A3) per factor, which were being considered by C2.

Ranking the Alternative Solutions using TOPSIS

Alternatives are ranked in TOPSIS on the basis of distance from positive ideal and negative ideal solution as explained in Sec. 3.2. Applying formal steps of TOPSIS on the data shown in Tab. 3 positive ideal and negative solutions are calculated as shown in Tab. 4. While the positive ideal solution is the set of the maximum values {2.001, 4.988, 4.460, 2.340, 1.068, 2.356, 0.843} for all these factors amongst all alternatives, the negative ideal solution is the set of minimum values {1.410, 1.995, 2.230, 3.745, 3.208, 0.388, 0.240}.

In these sets element 4 and 5, namely scalabilty and compliance, are considered to be negative factors, i.e., they contribute to risk and cost of the decision. Therefore, in the positive ideal set maximum value is taken and in the negative ideal solution minimum value is considered. The next step of TOPSIS is to find the distance of the alternative solutions from the positive and negative ideal solutions as shown in Tab. 5 and Tab. 6. Depending on the value of relative closeness of the alternative solutions (A1, A2, A3) to the ideal solution( ) the ranking of these alternatives is identified. for three alternatives are {0.2363, 0.071, 0.2361}. As seen from this example, A1 and A3 perform almost similar at these attributes due to similar . In this case establishing a trade-off strategy is most relevant as the final decision can be now based purely on business performance metrics. In other cases, especially when there is a substantial difference in , a trade-off strategy is mandatory, since a customer can judge the level of compromise that is to be made on returns to be expected. Trade-off are necessary as the best possible solution based on technical attributes might not be the most profitable as per business value and vice versa.

Evaluation of Alternatives based on Business Performance Metrics

This step expects organizations using TrAdeCIS to identify and prioritize BPMs for measuring expected return in terms of business value for each alternative. The process of ranking each of the available alternative solutions (here, A1, A2, A3), per factor or BPM, is based on the experience of organization, and the market history of the service or cloud-solution. For example, if the market history of alternative A1 is better than A3, A1 will be ranked higher for the considered factor.

As obtained during the discussion with C2 the BPMs are migration time, cost reduction, and workload versus utilization. These are the only factors by which C2 decided to evaluate the business value of the available alternatives as C2 planned to serve the peak load requirements with minimum cost. Also, as this service is very critical, the business migration time should be the least possible, and critical workloads should be handled by the service provider by prioritizing resources. C2 identified that its cost reduction is twice as relevant as migration time. Remaining relevant priorities as identified by C2 for these factors are shown in Tab. 7.

Trade-off-based Decision using ANP

The ranked alternatives obtained in previous step of TrAdeCIS using TOPSIS, are now evaluated with respect to BPMs identified and ranked by the C2. As shown in Fig. 2 in ANP factors and alternative solutions are represented as nodes and inter-connections between them are marked with their relative importance, which is obtained by pair-wise comparison of each node. In this example, the decision is to be made for alternatives A1 and A3 as they scored same when evaluated using TOPSIS.

Following these steps as explained in Sec. 3.4, the normalized Eigen vector is calculated and priorities are found by TrAdeCIS. Hence the obtained unweighted super

C i * C i * C i * C i *
matrix is shown in Tab. 8. After normalizing the unweighted super matrix, the limit matrix is obtained as shown in Tab. 9. In ANP each alternative is evaluated independently of other alternatives. Now A3 gains higher priority owing to its high ranking in cost reductions, which overrule the high performance of A1 in the other two attributes (performance of alternatives in each of the attribute in Tab. 5). Therefore, A3 gives higher returns than A1 -it is a better solution in terms BPMs (migration time). cost reductions, and workload vs. utilization). However, as proven by TOPSIS A1 is a better alternative with respect to attributes important for the service. Now, if C2 desires to change the priorities of BPMs it can happen that A1 is again chosen. If this happens then the best technical solution will be chosen at a trade-off of return value.

On the other hand, if A3 is chosen then the solution with best return value will be chosen at a trade-off of technical specifications. This paper has determined and discussed the existing gap between adopting cloud services and evaluating the impact cloud-services will have on business processes and organization. To fill this gap the concept of establishing a trade-off strategy is introduced -the new TrAdeCIS methodology -by which an organization can evaluate available alternative cloud-based solution based on the impact selected alternative will have on business. To establish this trade-off strategy two multi-attribute decision analysis methods are applied: TOPSIS and ANP. While TOPSIS is used to rank alternative solutions based on attributes from the technical perspective, ANP identifies a trade-off strategy based on returns expected. Thus, TrAdeCIS quantifies this process of decision making for a cloud adoption by (a) identifying relevant attributes and their relative importance, (b) ranking attributes on the basis of requirements, and (c) establishing the trade-off strategy on the basis of returns expected. This paper also illustrates TrAdeCIS based on survey results collected from organizations who have adopted or plan to adopt cloud-based solutions for their IT requirements.

It can be concluded that the current ad-hoc process of cloud adoption in organizations can be replaced with the quantitative methodology of TrAdeCIS. This approach developed fills the gap of evaluating cloud-based solutions not only from the technical perspective, but also from the view of impact it will have on the organization.

The next step of this work is to implement TrAdeCIS as a working prototype, which will be tested and evaluated with further organizations, who plan to adopt cloud-based solution for their advanced IT needs. This will help to evaluate the impact of TrAdeCIS in full and in such a decision making process of these organizations, all in comparison to existing, though, functionally restricted related work.

Fig. 1 .

 1 Fig. 1. Methodology for Business Driven Trade-off-based Decision for Cloud Adoption

  Construct the weighted normalized decision matrix, where each weight is represented by wj for . Multiply each column of the normalized decision matrix by its associated weight. An element of the new decision matrix is . Using this method TrAdeCIS obtains a ranked list of available alternative cloudbased solutions, which are evaluated on technical parameters based on business objectives and policies as shown in Sec. 4.2.

	4. Determine the ideal positive solution		, where	, if
	or	if	. Determine the ideal negative solution	,
	where	, if	or	if	.
	5. Determine the separation from the ideal solution for every alternative j. Dis-
	tance from the positive solution is		and that from the nega-
	tive solution is		for		.
	6. Calculate the relative closeness to the ideal solution	. Give highest
	rank to the option with	closest to 1.

Table 2 .

 2 Organizations Overview

	Company	Domain of Expertise	Size of Company a	Geographic Scope Served
	C1	ICT Provider	60000	Europe, USA, Singapore
	C2	Health Insurance	450	Switzerland
	C3	Telecommunications	20000	Switzerland
	C4	IT Infrastructure provider	5000	Europe, USA, Australia, China
	C5	Financial Services	2600	Worldwide
	C6	Property and Life	4000	Switzerland
		Insurance
	C7	Professional Services	180000	Worldwide
	C8	Networking Solutions	67000	Worldwide
	C9	ICT Association	-	Switzerland
	a number of employees as per June, 2013

Table 3 .

 3 Ranking of Alternatives per Attribute

	Factors	Weights	A1	A2	A3
	Functionality	3	7	6	5
	Privacy	7	9	4	10
	Availability	6	4	3	2
	Scalability	5	5	8	5
	Compliance	4	1	2	3
	Storage Location	2	3	1	6
	Simplicity	1	4	2	7

Table 4 .

 4 Positive Ideal Solution and Negative Ideal

	Factors	A1	A2	A3
	Functionality	2.001	1.710	1.410
	Privacy	4.489	1.995	4.988

Table 7 .

 7 Relative Priorities of BPMs

Business Performance Metrics Migration Time Cost Reduction Workload vs. Utilization

	Migration Time	1	1 / 2	1 / 3
	Cost Reduction	2	1	1 / 3
	Workload vs. Utiliza-	3	3	1
	tion

Table 8 .

 8 Values Obtained in Unweighted Super Matrix

	-/-	Returns	Migra-tion Time	Cost Reduction	Workload vs. Utilization	A1 A3
	Returns	1	0	0	0	0	0
	Migration Time	16	1	0	0	75	13
	Cost Reduction	25	0	1	0	13	75
	Workload vs. Utiliza-	59	0	0	1	13	13
	tion
	A1	0	5 0	2 0	6 7	1	0
	A3	0	5 0	8 0	3 3	0	1

Table 9 .

 9 Values Obtained in Limit Matrix for Returns

	-/-	Returns	Migra-tion Time	Cost Reduction	Workload vs. Utilization	A1 A3
	Returns	0	0	0	0	0	0
	Migration Time	0	1 8	1 8	1 8	0	0
	Cost Reduction	0	2 6	2 6	2 6	0	0
	Workload vs. Utiliza-	0	6	6	6	0	0
	tion
	A1	36	0	0	0	18	18
	A3	64	0	0	0	32	32

Conclusions, and Future Work

Acknowledgments. This work was partly funded by FLAMINGO, the Network of Excellence Project ICT-318488, supported by the European Commission under its Seventh Framework Programme.

Availability 4.460 3.342 2.230