Preprint: " An Example of Cloud Business Application Development using the Continuous Quantity Identifier of the Cellular Data System", Lecture Notes in Electrical Engineering ISSN: 1876-1100, in print, March 2011, Springer-Verlag, Heidelberg, Germany. An Example of Cloud Business Application Development using the Continuous Quantity Identifier of the Cellular Data System Toshio Kodama 1, Tosiyasu L. Kunii 2, Yoichi Seki 3 1 Maeda Corporation, Advanced Computer Systems, Inc., 3-11-18 Iidabashi, Chiyoda-ku, Tokyo 102-0072 Japan 2 Morpho, Inc., Iidabashi First Tower 31F, 2-6-1 Koraku, Bunkyo-ku, Tokyo 112-0004 Japan 3 Software Consultant, 3-8-2 Hino-shi, Tokyo 191-0001 Japan 1 kodama@lab.acs-jp.com, kodama.ts@jcity.maeda.co.jp 2 kunii@ieee.org, kunii@acm.org, 3 yseki@amber.plala.or.jp Abstract. In the era of cloud computing, cyberworlds as information worlds have grown rapidly and on an extremely large scale to encapsulate real world activities like finance, commerce, education and manufacturing in the form of e-financing, e-commerce, distance education and e-manufacturing despite the lack of a firm mathematical foundation. In software engineering, many software development methodologies, including the waterfall model and object-oriented model have been introduced. But these current methodologies cannot yet solve the combinatorial explosion problem. A new approach, different from conventional engineering approach, is needed. We have developed a data processing system called the Cellular Data System (CDS) as a new methodology, based on the Incrementally Modular Abstraction Hierarchy (IMAH) in the cellular model, which offers powerful mathematical background in data modeling. In this paper, we develop a continuous quantity identifier to deal with objects that can express continuous quantity on the presentation level of IMAH and integrated it into the data search function of CDS. By taking advantage of continuous quantity identifiers with the data search function of CDS, development of business application logic using continuous quantity becomes much simpler and significantly reduces development and maintenance costs of the system. In addition, we show the effectiveness of a continuous quantity identifier by taking up some examples of core logic development of a car sharing reservation system. Keywords: cyberworlds, cellular model, formula expression, continuous quantity identifier, condition formula 1 Introduction The cyberworlds in cloud computing are distributed systems. Data and its dependencies are constantly changing within them. Cyberworlds are more
complicated and fluid than any other previous worlds in human history and are constantly evolving. Millions of people use Twitter or Facebook every minute through Web services on mobile phones which are one of main elements of cyberworlds. At the same time, user requirements for cyberworlds also change and become more complicated as cyberworlds change. If you analyze data using existing technology, you have to modify the schema design and application programs whenever schemas or user requirements for output change. That leads to combinatorial explosion, because user requirements, and their combinations and schemas must be specified clearly at the design stage. That is a fundamental problem, so we have to reconsider development from the data model level. Is there a data model that can reflect the changes in schemas and user requirements in cyberworlds? We consider that Incrementally Modular Abstraction Hierarchy (IMAH) of the cellular model built by one of the authors (T. L. Kunii) to be the most suitable model. The IMAH can model the architecture and the changes of cyberworlds and real worlds from the homotopy level which is most general to the view level which is the most concrete preserving invariants while preventing combinatorial explosion [1][13]. From the viewpoint of IMAH, existing data models are positioned as special cases. For example, UML can model objects at levels below the presentation level, and in the relational data model, a relation is an object at the presentation level which extends a cellular space because it has necessary attributes in which a type is defined, while the processing between relations is based on the set theoretical level. In the object-oriented model, an object is also the object at the presentation level, which extends a cellular space, while the relation between Classes is the tree structure, which is a special case of a topological space. An Object in XML is considered a special case of a cellular space that extends a topological space, because an attribute and its value are expressed in the same tag format. In our research, one of the authors (Y. Seki) proposed an algebraic system called Formula Expression as a development tool to realize the cellular model. Another (T. Kodama) has actually implemented CDS using Formula Expression [12]. In this paper, we have introduced the concept of a continuous quantity identifier into CDS. A continuous quantity formula is effective when a continuous quantity is dealt with in business application development. In addition, we have placed emphasis on practical use by taking up some examples. Firstly, we explain CDS and its main data search function briefly in Section 2, 3. Secondly, we design the properties of a continuous quantity by Formula Expression, and integrate them into the condition formula search function in Section 4. Next, we implement them in Section 5. We demonstrate the effectiveness of the continuous quantity identifier by developing a business application system, thereby abbreviating the process of designing and implementing most application programs in Section 6. The business application system is the core logic of a car sharing reservation system, where cars are reserved in accordance with customers required times and car reservation schedules. Related works are mentioned in Section 7. Lastly, we conclude in Section 8.
2 The Cellular Data System (CDS) 2.1 Incrementally Modular Abstraction Hierarchy The following list constitutes the Incrementally Modular Abstraction Hierarchy to be used for defining the architecture of cyberworlds and their modeling: 1. the homotopy (including fiber bundles) level 2. the set theoretical level 3. the topological space level 4. the adjunction space level 5. the cellular space level 6. the presentation (including geometry) level 7. the view (also called projection) level In modeling cyberworlds in cyberspaces, we define general properties of cyberworlds at the higher level and add more specific properties step by step while climbing down the Incrementally Modular Abstraction Hierarchy. The properties defined at the homotopy level are invariants of continuous changes of functions. The properties that do not change by continuous modifications in time and space are expressed at this level. At the set theoretical level, the elements of a cyberspace are defined, and a collection of elements constitutes a set with logical operations. When we define a function in a cyberspace, we need domains that guarantee continuity, such that neighbors are mapped to a nearby place. Therefore, a topology is introduced into a cyberspace through the concept of neighborhood. Cyberworlds are dynamic. Sometimes cyberspaces are attached to each other, an exclusive union of two cyberspaces where attached areas of two cyberspaces are equivalent. It may happen that an attached space is obtained. These attached spaces can be regarded as a set of equivalent spaces called a quotient space, which is another invariant. At the cellular structured space level, an inductive dimension is introduced into each cyberspace. At the presentation level, each space is represented in a form which may be imagined before designing the cyberworlds. At the view level, the cyberworlds are projected onto view screens. 2.2 The definition of Formula Expression Formula Expression in the alphabet is the result of finite times application of the following steps. 1. a (a Σ) is Formula Expression 2. unit element ε is Formula Expression 3. zero element φ is Formula Expression 4. when r and s are Formula Expression, addition of r+s is also Formula Expression 5. when r and s are Formula Expression, multiplication of r s is also Formula Expression 6. when r is Formula Expression, (r) is also Formula Expression
7. when r is Formula Expression, {r} is also Formula Expression 3 The Condition Formula Search of CDS If users can specify search conditions, data searching will become more functional. Here, we introduce the function for specifying conditions defining a condition formula by Formula Expression into CDS. Let propositions P, Q be sets which include characters p, q respectively. The conjunction, disjunction and negation of them in logical operation are defined by Formula Expression as follows: 1) Conjunction 2) Disjunction 3) Negation P Q = p q. (1) P Q = p+q. (2) P =!p. (3) A formula created from these is called a condition formula. Here "!" is a special factor which means negation. Recursivity by () in Formula Expression is supported so that the recursive search condition of a user is expressed by a condition formula. Condition formula processing is processing that results in a disjoint union of terms that satisfy a condition formula from a formula. When condition formula processing is considered, the concept of a remainder of spaces is inevitable. The processing consists of two maps: a quotient acquisition map f that derives a term that includes a specified identifier and a remainder acquisition map g that derives a term that does not include a specified identifier. If you assume x to be a formula and p,!p, p+q, p q,!(p+q),!(p q) to be condition formulas, the images of (x, p+q), (x, p q), (x,!(p+q)), (x,!(p q)) by f, g are the following: x = f(x, p)+g(x,!p) where f(x, p) g(x,!p) = φ. (4) f(x, p+q) = f(x, p)+f(g(x, p), q) (5) f(x, p q) = f(f(x, p), q) (6) f(x,!(p+q)) = g(g(x, p), q) (7) f(x,!(p q)) = g(f(f(x, p), q) (8) It is obvious that any complicated condition formula can be processed by the combinations of the above four correspondences.
4 A Continuous Quantity Identifier and Its Application to the Condition Formula Search of CDS 4.1 Definition The continuous quantity identifier is defined as one case of identifiers in Formula Expression, and therefore it follows the general operation of Formula Expression. If it is assumed that r and s (r<s) are arbitrary numerical identifiers, a continuous quantity identifier to express continuous quantity from r to s is defined [r+s]. If you assume t, u (t<u) and v, w (v<w) are also arbitrary numerical identifiers and a is an arbitrary letter factor, the continuous quantity identifier has the following properties: [s+r] = φ (if r<s). (1) [r+r] = ε. (2) a [r+s] = [r+s] a. (3) [r+s]+[t+u] = [r+u] (if r t<s u) = [t+s] (if t r<u s) = [r+s] (if r t<u s) = [t+u] (if t r<s u) = [r+s]+[t+u] (if t u r<s or r<s t u). [r+s] [t+u] = [t+s] (if r t<s u) = [r+u] (if t r<u s) = [t+u] (if r t<u s) = [r+s] (if t r<s u) = φ (if t u r<s or r<s t u). (4) (5) Next, the quotient acquisition map f of condition formula processing is applied to the continuous quantity identifier according to the above definitions as follows: f([r+s],[t+u]) = [t+s] (if r t<s u) = [r+u] (if t r<u s) = [t+u] (if r t<u s) = [r+s] (if t r<s u) = φ (if t u r<s or r<s t u) f([r+s],![t+u]) = [r+t] (if r t<s u) = [u+s] (if t r<u s) = [r+t]+[u+s] (if r t<u s) = φ (if t r<s u) = [r+s] (if t u r<s or r<s t u). (6) (7)
4.2 Applied Map g The applied map g, which replaces a formula including continuous quantity identifier(s) with the remainder of a specified continuous quantity identifier using the above f, is designed as follows; If you assume the entire set of formulas to be A, g: A, and arbitrary terms r, s, t, u follow these rules: g([r+s],u+v) = g([r+s],u)+g([r+s],v). (8) g([r+s],(u)) = (g([r+s],u)). (9) g([r+s],a [p+q] b) = a f([r+s],![p+q]) b. (10) A simple example of the map g is shown here. g([1+24], Kodama([12+14]+[16+18])) = Kodama([1+12]+[14+16]+[18+24]) 5 Implementation This system is a Web application developed using JSP and Tomcat 5.2 as an application server. The client and the server are the same machine. (OS: Windows XP; CPU: Intel Core2 Duo, 3.00GHz; RAM: 3.23GB; HD: 240GB) The quotient acquisition map f is the main function of condition formula processing. In this algorithm, the absolute position of the specified factor by the function of the language and the term including the factor are acquired first. Next, the nearest brackets of the term are acquired, and because the term becomes a factor, a recursive operation is performed. Details are abbreviated due to the restriction on the number of pages. 6 Case Study: A Car Sharing Reservation System 6.1 Outline Car sharing is a model of car rental where people rent cars for short periods of time, often by the hour. We take up the example of development of core logic of a car sharing reservation system as a business application using CDS. In this case study, we assume that there are five customers; customer (A, B, C, D, E) and three shared cars; car (1, 2, 3), and that each reservation is to be arranged by adjusting customers required times and car reservation schedules within a given period from 0 to 20. Firstly, formulas for customer s requirement times and car reservation times are designed using a continuous quantity identifier and an operation for getting the
formula for each s available time from them (6.2). Secondly, sample data of customers and cars are inputted and the operation is carried out according to the design. Thirdly, required data is outputted by the condition formula processing map (6.3). 6.2 Space design We design a formula for the space and the operation as follows: 1. The formula for a customer and their required times as a topological space Customer(Σcustomer id i Σ[r i +s i ]). (1) customer id i : a factor which identifies a customer [r i +s i ]: a continuous quantity identifier from r i to s i 2. The formula for shared cars and their reserved times as a topological space Shared Car(Σcar id i Σ[p i +q i ]). (2) car id i : a factor which identifies a car [p i +q i ]: a continuous quantity identifier from p i to q i 3. The operation for getting the formula for available times of shared cars g([0+20], Shared Car(Σcar id i Σ[p i +q i ])). (3) [0+20]: a continuous quantity identifier of the entire period (from 0 to 20) 6.3 Data input/output If customer A requires a shared car from time 7 to 8 and from time 13 to 15, a term for customer A is created according to the space design (1) as below: Customer(customer A ([7+8]+[13+15])) And if customer B requires a shared car from time 4 to 5 and from time 15 to 17, a term for a customer B is created and added to the previous term as below: +Customer(customer B ([4+5]+[15+17]))
Terms for customer C, customer D and customer E are also created as below and added to the previous formula: Customer(customer A ([7+8]+[13+15])+customer B ([4+5]+[15+17])+cust omer C ([8+20])+customer D ([6+10])+customer E ([7+8]+[13+15])). (4) In the same way, a term for car reservations is created and added to the previous formula according to the space design (2) as below: Shared Car(car1([0+4]+[10+14])+car2([4+7]+[14+17])+car2([7+10]+[12+1 4]+[17+20])). (5) The following operation is performed to get the formula for times when cars are available from formula (5) according to the operation design (3), which is then added to the formula (4). formula (4)+g([0+20],formula (5)) =Customer(customer A ([1+3]+[16+18])+customer B ([0+2]+[5+8])+cust omer C ([4+7]+[11+13])+customer D ([10+14]+[17+19])+customer E ([2+6]+[12+15]+[17+20]))+Shared Car(car1([4+10]+[14+20])+car2([0+4]+ [7+14]+[17+20])+car3([0+7]+[10+12]+[14+17])). (6) The resulting figure is shown in Fig 6.3. Fig 6.3 Times that customers require a car and when cars are available If you want to answer the question When and which cars can customer A use between times 10 and 20?, first you make the condition formula Customer(customer A)[10+20] from the question and get the image of formula (6) and the condition formula by the map f as below:
f(formula (6), Customer(customer A)[10+20] ) =Customer(customer A)[13+15]. (7) And then you get the image of formula (6) and the condition formula Shar ed Car[13+15] by the map f: f(formula (6), Shared Car[13+15] ) = Shared Car(car2 [13+14]+(car1+car3)[14+15]). (8) From the results, you can know that customer A can use car2 between times 13 and 14 and can also use car1 or car3 between times 14 and 15. Next, if you want to answer the question Which customer wants to use car1 from time 8 to 10?, you get the image of formula (6) and the condition formula (Customer+car1)[8+10] by the map f : f(formula (6), (Customer+car1)[8+10] ) = (Customer(customer C+customer D)+Shared Car(car1))[8+10]. (9) From the results, you can know that customer C, D want to use car1 from time 8 to 10. Next, if you want to answer the question Which customer can use which car between times 8 and 10?, you get the image of formula (6) and the condition formula (Customer+Shared Car)[8+10] by the map f: f(formula (6), (Customer+Shared car1)[8+10] ) =(Customer(customer C+customer D)+Shared Car(car1+car2))[8+10]. (10) From the results, you can know that customer C and D can use car1 or car2 from time 8 to 10. 6.4 Considerations Condition formula processing has become more effective by integrating a continuous quantity identifier when a continuous quantity such as time, distance, temperature, etc. is dealt with. If the existing method of business application development is used in this case study instead of the continuous quantity identifier function of CDS, complicated input/output programs would have to be developed according to needs, and the maintenance costs required to meet various and unexpected user requirements would be considerable.
7 Related Works The distinctive features of our research are the application of the concept of topological process, which deals with a subset as an element, and that the cellular space extends the topological space, as seen in Section 2. Relational OWL as a method of data and schema representation is useful when representing the schema and data of a database [2][5], but it is limited to representation of an object that has attributes. Our method can represent both objects: one that has attributes as a cellular space and one that does not have them as a set or a topological space. Many works applying other models to XML schema have been done. The motives of most of them are similar to ours. The approach in [8] aims at minimizing document revalidation in an XML schema evolution, based in part on the graph theory. The X- Entity model [9] is an extension of the Entity Relationship (ER) model and converts XML schema to a schema of the ER model. In the approach of [6], the conceptual and logical levels are represented using a standard UML class and the XML represents the physical level. XUML [10] is a conceptual model for XML schema, based on the UML2 standard. This application research concerning XML schema is needed because there are differences in the expression capability of the data model between XML and other models. On the other hand, objects and their relations in XML schema and the above models can be expressed consistently by CDS, which is based on the cellular model. That is because the tree structure, on which the XML model is based, and the graph structure [3][4][7], on which the UML and ER models are based, are special cases of a topological structure mathematically. Entity in the models can be expressed as the formula for a cellular space in CDS. Moreover, the relation between subsets cannot in general be expressed by XML. Although CDS and the existing deductive database apparently look alike, the two are completely different. The deductive database [11] raises the expression capability of the relational database (RDB) by defining some rules. On the other hand, CDS is a new tool for data management, and has nothing to do with the RDB. 8 Conclusions In this paper, we have designed and implemented a continuous quantity identifier and applied it to condition formula processing, which is the main data search function of CDS. A continuous quantity such as time, distance, etc. can be expressed as a factor in Formula Expression and integrated into business logic modeling in business application development. As a result, the cost of cloud application program development can be significantly reduced. References [1] T. L. Kunii and H. S. Kunii, A Cellular Model for Information Systems on the Web - Integrating Local and Global Information, In Proc. of DANTE'99, IEEE Computer Society Press, pp.19-24, 1999.
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