Defining and Surveying Wireless Link Virtualization and Wireless Network Virtualization

Transcription

1 1 Defining and Surveying Wireless Link Virtualization and Wireless Network Virtualization Jonathan van de Belt, Haed Ahadi, and Linda E. Doyle The Centre for Future Networks and Counications - CONNECT, Trinity College Dublin Eail: vandebej@tcd.ie School of Electrical and Electronic Engineering, University College Dublin, Ireland arxiv: v2 [cs.ni] 4 Jul 2018 Abstract Virtualization is a topic of great interest in the area of obile and wireless counication systes. However the ter virtualization is used in an inexact anner which akes it difficult to copare and contrast work that has been carried out to date. The purpose of this paper is twofold. In the first place, the paper develops a foral theory for defining virtualization. In the second instance, this theory is used as a way of surveying a body of work in the field of wireless link virtualization, a subspace of wireless network virtualization. The foral theory provides a eans for distinguishing work that should be classed as resource allocation as distinct fro virtualization. It also facilitates a further classification of the representation level at which the virtualization occurs, which akes coparison of work ore eaningful. The paper provides a coprehensive survey and highlights gaps in the research that ake for fruitful future work. I. INTODUCTION Network Virtualization (NV) allows network services to view network resources, such as servers, routers, links, and data, in a anner that is independent fro the underlying physical infrastructure, and to use these resources according to service requireents, rather than based on physical granularities [1]. New network functionality can be achieved using virtualization, such as providing heterogeneous networks with custoizable specifications on-deand, the flexible and dynaic anageent of resources, new types of services, and better security and protection against equipent failure. In addition, network virtualization has the potential to enable new networking technologies and protocols to be developed uch faster than they are currently, since these technologies can be tested through isolated virtual networks on existing infrastructure, while ensuring that existing services are unaffected. Lastly, network virtualization can provide cost savings and new business opportunities, through increased efficiencies and through new services and functionality. Wireless Network Virtualization (WNV) has been proposed as an extension of (wired) network virtualization to the wireless doain, with the ain difference being the wireless links. Thus ost work to date has focussed on Wireless Link Virtualization (WLV). Initially, the purpose of this paper is to perfor a survey of WNV, and to identify open research probles. However, the ter wireless network virtualization carries ultiple connotations. It has becoe an ubrella ter for several differing concepts, applied at different layers of the network stack, and also to different types of network resources. In the existing literature, works such as [2] [7] provide a variety of definitions for WNV, but a lack of consistency Abstract Abstract Doain Doain (0, 1) (0, 1) Physical Physical Doain Doain (a) 1 Abstract Abstract Doain Doain Physical Physical Doain Doain p Figure 1. Objects in the physical doain can be represented using objects in the abstract doain, such as (a) a switch with two settings represented as a bit through 1, or (b) ore generally as an object p represented as p through. persists. A coon thee of these definitions is that they regard virtualization as the abstraction and sharing/slicing of resources. As this work will ephasise, virtualization and abstraction are very different concepts, and virtualization is not necessarily liited to the sharing of resources. It is interesting to note that several authors ([8] and [4]) have pointed out a siilar vagueness and lack of clarity in the field of network virtualization. Although several surveys on wireless network virtualization exist such as [5], [6], [9] [11], this paper brings additional and alternative perspectives (for a ore detailed description see Section VI-G). We develop a foral ethod for describing virtualization as a response to the any definitions that currently exist. We then use this foral ethod as a eans of classifying and analysing the papers we survey which allows for a ore systeatic approach to the survey process. More specifically we ake the following contributions: 1) We clarify the concepts of abstraction and representation, which are key to understanding virtualization, by drawing on a theory known as abstraction/representation theory and extending it. 2) We propose a foral ethod for describing virtualization, which we call virtualization theory. 3) We develop a test for virtualization to distinguish virtualization techniques fro resource allocation techniques. 4) We survey the existing work on wireless network virtualization, and classify this work in a coherent and eaningful anner, using virtualization theory. 5) We identify several research gaps in wireless network virtualization which have not yet been addressed and propose next steps forward. (b) p p p

2 2 The paper is structured around these contributions. Section II introduces key concepts such as abstraction, representation and instantiation, which are prerequisite to virtualization and iportant for the rest of the paper. Section III introduces the theory on which the paper is grounded. In Section IV we exaine the constituent coponents of networks, and how these coponents can be virtualized. We give an overview of network and wireless network virtualization in Section V, to introduce the survey. Since the ain focus of this paper is on wireless link virtualization, in Section VI we perfor a survey of existing literature on wireless link virtualization. This survey allows us to identify open research directions in Section VII, before concluding in Section VIII. II. PEEQUISITES TO VITUALIZATION There are a nuber of concepts, which are key to developing a foral theory of virtualization and in the opening section of the paper we carefully define these concepts. The first two of these are the concepts of abstraction and representation. Table I shows an explanation of these and other ters used in this paper. In this paper, the ter abstraction eans the act of ignoring or hiding details to consider general characteristics, rather than concrete realities. Thus abstraction anages the way in which systes interact, and the coplexity of the interaction, by hiding details that are not relevant to the interaction. Increased abstraction allows systes to be used ore easily for specific applications, but this coes at the cost of decreased flexibility and custoization. Although abstraction is an iportant concept in coputing, as it governs the interaction between huans and coputers, it is not necessarily of iportance to virtualization. However, it is iportant to note the difference between abstraction and the adjective abstract. The ter abstract refers to ideas and concepts that do not have physical existence. The ter representation eans to describe or sybolize soething in a particular way. The ter instantiation eans the ipleentation or realization of a concept or idea. epresentation and instantiation are very iportant to coputing as they describe the relationship between abstract entities and the physical world. As this paper will show later, representation and instantiation are of great iportance to virtualization, since virtualization can only be done in the abstract doain, while network resources exist in the physical doain. We now turn to the recently developed Abstraction/epresentation (A) theory, to provide us with a foral fraework of abstraction and representation [12], [13]. Because this theory is very new, we explain the ost iportant aspects here, borrowed fro [12], before we go on to extend the ideas for the purposes of this paper. A. Abstraction/epresentation Theory 1 Abstraction/epresentation theory 2 is concerned with the physical doain and the abstract doain (also known as the 1 Based on [12] 2 A Theory ight be better naed as epresentation Theory, since it deals ostly with representation, but that nae has already been taken. Ter Abstraction Abstract epresentation Instantiation Table I EXPLANATION OF TEMS USED IN THIS PAPE Explanation The act of ignoring details to consider general characteristics Existing as a thought, idea, or concept, but without physical existence The act of sybolising or portraying soething in a particular way Creating a concrete realization of a concept or idea logical doain), and the relationship between these doains. The physical doain, P, is defined as consisting of all physical objects, p P. The abstract doain, M, consists of all abstract objects, M. For instance, a coputer is an object in the physical doain, which can be in different physical states, while a coputation is a set of objects and relations in the abstract doain. Bold font is used to indicate an object in the physical doain; italic font for an object in the abstract doain. 1) epresentation: A physical object can be represented in the abstract doain, through a representational relationship,. For exaple, a physical on-off switch can be represented in the abstract doain by a binary digit, shown in Figure 1. The general representation relation between a physical object, p, and an abstract object, p, is through a directed ap : p p. The abstract object, p is said to be an abstract representation of the physical object p. It it very iportant to keep in ind that the representation relation is not a atheatical function or a logical relation, but rather a odelling relation that bridges the divide between the physical and the abstract spaces. 2) Physical and Abstract Evolution: In the abstract doain, there can be an evolution or process, C : p p, that changes an abstract object p to another abstract object p. Siilarly in the physical doain, a corresponding evolution H : p p, changes the physical state p to physical state p. This physical state, p can then be represented as p, through the representation relation,. These concepts are shown in Figure 2 (a). The two abstract objects, p and p, lead us to a key concept in A theory. If p p ɛ, for soe error ɛ and nor, then we can say that the abstract evolution, C, and the corresponding physical evolution, H, coute. Under the above condition, the two representation relationships, : p p and : p p, and the pair of abstract and physical evolutions C : p p and H : p p, can be said to for a couting diagra. When a set of abstract and physical objects for a couting diagra using the representation,, then p is a faithful abstract representation of physical syste p for the evolutions C( p ) and. This eans we can be confident that the evolution C in the abstract doain corresponds to the evolution H in the physical doain. The iplication of couting diagras is that the abstract representation of the final state of a physical object (i.e. p/ p ) can be found either by following the physical evolution and then representing the output abstractly, or by

3 3 p p C(01,10) C(p) Abstract Abstract Abstract Abstract p 11p 01,10 p pdoain 11 Doain Doain Doain logic gates 01,10 01,10 01,10 01,10 C(01,10) C(01,10) C(01,10) C(01,10) logic logic logicgates gates gates logic gates 01,10 01,10 01,10 p C(01,10) C(01,10) C(01,10) p 11 p pppp logic logic logicgates gates gates C(p) p 11 pp11 p11 ppp p ~ ~ ~ ~ ~ ~ ~ ~ Physical p Doain p p voltage changes (a) Physical Physical pphysical p Doain Doain Doain C( C( C( p ~ ppp pppp pppp pppp pppp voltage voltage voltagechanges changes changes voltage changes voltage voltage voltagechanges changes changes (b) (c) pppp pppp (d) Figure 2. (a) A physical syste p and its representation p can undergo abstract evolution, C(p ), or physical evolution,. (b) A couting diagra for a binary addition, showing that an abstract evolution through logic gates, C, is coutative with a physical evolution in voltage states, H. (c) A coputer can evaluate an abstract apping by instantiating the abstract object in the physical doain, perforing the physical apping, and representing it as an abstract object. (d) The ost interesting use of a coputer is when the abstract apping is unknown. theoretically evolving the representation of the physical state. As an exaple, consider a couting diagra in which physical voltages are represented by binary nubers, shown in Figure 2 (b). Assue that we want to perfor an abstract evolution (binary addition). Then this evolution can be perfored either in the abstract doain using logic gates, or through physical anipulation of voltages in the physical doain and representing the result abstractly. 3) Instantiation: The instantiation relationship,, can be thought of as the inverse to the representation relation. Just as a physical object can be represented in the abstract doain by the representation relation, the instantiation relation, : p p, instantiates an abstract object in the physical doain. However, unlike representation, the instantiation relation can only exist under specific conditions, as there are any abstract objects that have no physical instantiation. It is necessary for a couting diagra to exist for a given representation relation, before any attepts can be ade to find the inverse instantiation relation (see [12]). Finding an instantiation relation is not straightforward and can be thought of as finding a physical syste, that when represented abstractly gives the abstract object that we desire. This often requires trial and error, if such an instantiation is even possible. Figure 2 (c) shows the binary addition exaple, but this tie the voltages instantiate binary nubers. The instantiation relation,, can be used to change the physical state to p, so that it instantiates the nubers we wish to add. In the abstract doain, the abstract apping (i.e. atheatical and logical operations) C, perfors the addition to arrive at the result. Meanwhile, the physical apping, H, anipulates the voltages to produce the physical result. Using the representation relation,, the abstract representation of p0 is found. If we have confidence that the representation is a faithful abstract representation and also that the instantiation relation is correct, then the outcoe of the abstract and the physical evolutions should be the sae. 4) Copute Cycle: The previous exaple describes a coputer perforing a parallel operation in the abstract and physical doains. However, the ost interesting use of a coputer is when the abstract apping C is unknown and we can use the coputer to solve an abstract proble, shown in Figure 2 (d). Provided that we are confident in the capabilities of the coputer, we can use the coputer to find the solution. The full copute cycle is as follows: Levels of epresentation epresentation level n n 3-n epresentation level 3 Abstract Doain n epresentation level epresentation n epresentation level Physical Doain Figure 3. The abstract doain can be divided into any levels of representation, since abstract objects can represent other abstract objects. In this case there are n representation levels, ordered arbitrarily, but there can be an infinite nuber of levels. Each representation level can represent the physical doain directly, through unidirectional representations 1, 2, etc., or can represent another representation level, through the bidirectional representations 1-2, 2-3, etc. These representations are bidirectional to show that any representation level can represent another level. This iage shows the theoretical representation relations, which does not ean that these relations will all exist in practice. H p p p0 [p0 0p ] Thus representation and instantiation enable physical coputing resources to ipleent abstract objects and operations, which can be called abstract resources. B. Levels of epresentation We extend A theory presented in [12] by focusing on the abstract doain and exaining abstract objects in ore detail. Most iportantly, we observe that objects in the abstract doain, which represent physical objects, can in turn be represented by different abstract objects. The sae is true for instantiation; objects in the abstract doain, which are instantiated in the physical doain, can instantiate different abstract objects. For the purpose of brevity, fro here on we only discuss representation and iply that the sae is true for instantiation. In essence there are any different representations that can be used. We use the ter levels of representation to capture ppp

4 4 epresentation Level 2: epresentation Level 1: epresentation character k Level 2: Abstract Doain ~ ASCII ASCII epresentation binary Level 1: character Abstract Doain ~ ASCII (Writing) epresentation k k character character k Level 2: ASCII Abstract Doain Abstract Doain (Writing) ~ ASCII Logical k Level Level 2: character 2: character k ASCII ~ ASCII ~ ASCII binary ~ epresentation EADING EADING ~ EADING binary EADING Logical Level Level 1: 1: ~ binary EADING EADING Level 1: (Writing) k k ASCII ASCII decial ~ DEC ~ DEC DEC DEC binary pixel pixel ~ JPEG ~ JPEG JPEG JPEG binary ~ BIN BIN ~ BIN BIN ~ BIN BIN ~ BIN ~ BIN BIN BIN ~ BIN ~ BIN BIN BIN ~ BIN ~ BIN BIN BIN Physical Doain Physical p(bin) Doain p(bin) p(reading) Physical Doain (a) p(reading) p(bin) Physical Doain Figure 4. The nuber of representation levels is a design choice. For exaple, the character k can (a) directly represent the physical doain, which we coonly know as reading, or (b) represent a binary nuber, which represents the physical doain. We can speak of one representation level in the first case, the character level, and two representation levels in the second case, the character level and the binary level. this idea and this is depicted in Figure 3. In this figure there are n different levels of representation in the abstract doain. We nuber these representation levels fro 1 to n, but the nubering is arbitrary and is only an identifier. It is iportant to note that the representation used is an arbitrary design choice, and that it is possible to represent the physical doain at any representation level. The unidirectional arrows, 1, 2, etc., show the one-way representation relation fro the physical to the abstract doain as seen previously. Siilarly, any representation level can represent another level, shown in the figure through the two-way representation relations 1-2, 2-3, etc. An iportant point to observe is that there can be an infinite nuber of representation levels, as any abstract object can represent another abstract object. However, in practise not every representation level will have a physical representation relation. A practical exaple is shown in Figure 4 (a). In this exaple, a physical object can be represented by the abstract letter k directly, and one representation level exists. However, Figure 4 (b) has two representation levels. In this case the letter k represents a binary nuber, which in turn represents the physical doain. C. Choosing a Hierarchy of epresentation Levels In theory, there can be an infinite nuber of representation levels in the abstract doain, with an arbitrary ordering of representation levels. However, in practise it is ore useful to coputing (and other abstract doain applications) if an ordered hierarchy of representation levels exists. Then it is possible to think of lower representation levels that are ore concrete, and higher representation levels that are ore abstract. When levels of representation are used in this anner, then we can nuber the representation levels in order of increasing abstraction. One advantage of having an ordered hierarchy of representation levels is that existing physical instantiations for abstract objects can be reused, since it is not an easy task to design a physical instantiation of an abstract syste [12]. ather than finding a physical instantiation for an abstract syste, (b) p(reading) p(bin) (a) p(bin) (b) p(bin) Figure 5. Multiple levels of representation enable a single physical instantiation to be reused for several different abstract objects. In this exaple, depending on the representation/instantiation, a binary nuber could instantiate (a) a character, (b) a decial nuber, or (c) a pixel in an iage. an instantiation can be found in ters of an abstract syste which already has a physical instantiation 3. Figure 5 shows the advantage of ultiple representation levels. In this case, the existing physical instantiation of binary nubers can be used to instantiate additional abstract objects. Many types of data such as integers, characters, volue levels, iage brightness, and instructions, can be instantiated in coputing using bits [14]. Thus, using ultiple levels of representation provides flexibility and easier instantiation. In this exaple, the binary representation level can be considered ore concrete, and the character/decial/pixel representation level can be considered ore abstract. D. Hardware and Software through epresentation The concept of levels of representation fits in very well with the idea of hardware and software. We define hardware as a copute cycle in which the representation/instantiation occurs between the physical and the abstract doain. Software, in contrast, is defined as a copute cycle in which the representation/instantiation is copletely in the abstract doain. We observe that the concept of representing the physical doain at any representation level (for exaple in Figure 4.) is consistent with the principle of equivalence of hardware and software, which states: Hardware and software are logically equivalent. Any operation perfored by software can also be built directly into the hardware and any instruction executed by the hardware can also be siulated in software. [15] The need for this distinction between hardware and software will be useful later in this paper (for exaple in section IV-A). E. How epresentation applies to Virtualization We have exained abstraction and representation, firstly to clarify the distinction between these concepts, and secondly because representation plays a role in virtualization in the following ways: 1) Virtualization ust always be done in the abstract doain. The reason for this is that physical resources cannot 3 Which is not an easy task either, but easier than physical instantiation (c)

5 5 be shared or cobined without odifying their physical properties in soe way. For exaple, it is not possible to split one processor physically to create ultiple virtual processors, however it is possible to split a representation of a processor in the abstract doain. Virtualization allows abstract resources to be reorganised in a anner that is is not liited by the underlying physical resources. 2) Since there can be any different representation levels in the abstract doain, virtualization can be perfored at any of these representation levels and virtualization happens within a representation level. However, virtualization does not happen across a representation level - that is the act of virtualization does not change abstract resources fro one representation level to another representation level. As we will see later, it is iportant to know the representation level when virtualizing abstract resources. III. VITUALIZATION THEOY Having gained a better understanding of abstraction and representation, in this section we identify universal concepts of virtualization, and propose a theory of virtualization. Although soe of the concepts have been entioned before in the literature, to the best of our knowledge this is the first tie that these concepts are brought together into a unified theory. A. Virtualization as esource Mapping As we saw earlier, resources in the abstract doain are representations of the physical doain. To be consistent with the language that is typically used in virtualization, we refer to these resources as real resources (). Although the ter real is used, these resources are in the abstract doain, and are not physical resources. Also note that the act of representation is not virtualization, rather representation is a prerequisite for virtualization. eal resources in the abstract doain can subsequently be virtualized. Virtualization is always perfored in the abstract doain and at a specific representation level. Virtualization is a resource apping which can alter the quantity of resources in soe diension(s). The resources after the virtualization process has occurred are referred to as virtual resources (V), as shown in Figure 6. Virtual resources appear to be the sae type of resources as real resources, but can be altered in quantity in soe way. This altering allows abstract resources to be used in a flexible anner, not liited by the underlying representation of the physical doain. However, when virtual resources are apped to real resources, the real resources cannot be used for any other purpose. Virtual resources are used as if they were real resources, and it should not be possible to perceive any difference between virtual resources and real resources. In this paper we consider that virtual resources are offered to one or ultiple users. The ter users in this case refers to independent agents, that ake decisions on resource use independently. Virtual resources can be offered to different users, and each user has the illusion of full ownership of the resources, eaning that virtual resources can be used for differing purposes. epresentation Level 2 epresentation Level 1 ~ HEX V 1 3 E HEX Abstract Doain 0011 Mapping Mechanis V Virtual esources Physical Doain ~ eal esource ~ BIN Figure 6. epresentation allows physical resources to ipleent abstract resources, while virtualization allows abstract resources to be owned and used at tailor-ade quantities. In this exaple the 8-bit abstract resource 1 is not an efficient resource to instantiate a hexadecial nuber, as hexadecial nubers only require 4-bits. Mapping two 4-bit virtual resources, V 1, and V 2, to 1 using a apping echanis is a ore efficient use of this resource. The virtual resources V 1, and V 2 can then be used to instantiate hexadecial nubers using the instantiation relation HEX. The real resource cannot be used to instantiate any higher representation level, shown by the cross in the figure. In Figure 6, the real resource, 1, is an 8-bit nuber. This 8-bit nuber could be used to instantiate a hexadecial nuber, or any other instantiation that uses 8 or less bits. However, a hexadecial nuber only requires 4 bits to be instantiated, and using 1 would not be an efficient use of resources. Mapping two 4-bit virtual objects, V 1, and V 2 to 1, would be ore efficient, and allows two hexadecial (or any other 4-bit instantiation) to be instantiated, using the sae resource, 1. Virtualization is always achieved through the use of a apping echanis (MM) that aps virtual resources to real resources. The apping echanis is responsible for presenting the virtual resources as if they were real resources, and for aintaining the isolation between different virtual resources. We call this the isolation proble. The apping echanis also decides how resources are allocated; in other words deciding how to divide up or cobine real resources to create virtual resources. This proble is known as the ebedding proble. The ebedding proble depends greatly on the isolation proble, since the ethod of isolation deterines how the resources can be used. These two probles will be discussed in further detail later. According to the authors of [16], and [17], the apping echanis is siply a function f that aps the set of virtual resources V, to the set of real resources. The virtual resources can be thought of as the doain of f and the real resources as the codoain of f. The apping function f aps each eleent in V to an eleent in. f : V {t} BIN

6 Many-to-any One-to-one 6 such that if y ε V and z ε then { z if z is the real resource for virtual resource y f(y) = t if y does not have a corresponding real resource The value f(y) = t causes a trap or fault handling procedure to occur by the apping echanis. In all figures and exaples until now, only one physical resource has been considered, represented as one real resource in the abstract doain. However, virtualization can apply to ultiple real resources, that are representations of ultiple physical resources. Siilarly, there are several ways in which the apping of virtual to real resources can be done - we identify four types of virtualization. In Figure 7 we show the general types of virtualization, where there can be ultiple physical resources, ultiple real and virtual resources, and ultiple types of apping. The four types of apping virtual resources, V n, to real resources, are: 1) One-to-one: Mapping a single virtual resource to a single real resource, to allow for easier anageent of resources; 2) Many-to-one: Mapping ultiple virtual resources to a single real resource such as partitioning a single resource into a nuber of saller and ore easily accessible resources of sae type; 3) One-to-any: Mapping one aggregated virtual resource to several real resources. Used to aggregate any individual coponents into larger resource pool; and lastly 4) Many-to-any: Mapping ultiple virtual resources to ultiple real resources. The cobination of aggregating and partitioning resources to create copletely custoizable resources that can be tailored exactly to requireents. Many-to-any can be considered the ideal case, since it enables resources to be used in the ost flexible anner. epresentation Level n t V f 2 V 2.1 f 2 2 V 2.2 f 3 3 V 3.1 f 3 4 f V f 4 V 4.2 f 4 6 Virtual esources eal esources One-to-any Many-to-one B. ecursion When virtual resources are presented in such a way that they are indistinguishable fro real resources, recursion is possible [18]. Users could choose to virtualize their virtual resources, since they perceive the as real resources. The apping of resources is now done twice, the first apping aps the virtual resources received by the user to the real resources, and the second apping aps virtual resources to virtual resources. The ters real and virtual can be confusing when recursion is taken into account. For this reason we always refer to the codoain of the apping function, i.e. the resources that are being virtualized, as real resources, even though these resources ight already have been virtualized by a previous virtualization instance. The resource apping function, f, described above can be extended directly for recursion by applying the apping function, f, ultiple ties and interpreting V and as different instances of virtualization. Mapping function aps virtual resources V 1 to real resources. Now, in a second virtualization instance, f 2 aps virtual resources V 2 to real resources V 1. Figure 7. In this exaple, six physical resources are represented as real resources, 1 6, at soe representation level n. Multiple virtual resources are apped to the ultiple real resources in different ways, showing the four types of virtualization. Many-to-any apping is the ideal case as it enables abstract resources to be used in the ost flexible anner. : V 1 {t 1 } f 2 : V 2 V 1 {t 2 } The real resources for are, and for f 2 the real resources are V 1. Figure 8 illustrates several virtualization instances that recursively ap virtual resources to real resources. We can say that recursion is a requireent for virtualization, since non-recursive virtualization is siply ultiplexing [19]. In the case of perfect virtualization, i.e. that virtual resources can be used exactly as real resources and no overhead exists, infinite recursion is possible [19].

7 tie Many-to-one 7 epresentation Level n t 1 eal esource, 1 V V V 1.n 3 D 3 (a) In the first instance of virtualization, any-to-any apping aps virtual resources V n to real resources 1 3. V 1 V 2 V 4 V 2.1 V 2.2 epresentation Level n f2 t 2 V 1.1 f 2 t 1 1 V 3 D 2 D 1 V Figure 9. The real resource, 1, can be isolated along three diensions, D 1, D 2, and D 3. The users of virtual resources, V 1, V 2, V 3, and V 4, are only aware of and can only access each of their individual resources, which appear to the as real resources. V 1.n (b) Many-to-one apping function f 2 is an exaple of recursive virtualization, since it aps virtual resources V 2.1 and V 2.2 to real resource V 1.1. V 2.1 V 2.2 f2 f 2 epresentation Level n V 1.1 V 1.2 t 2 t C. The Isolation Proble The isolation proble is the proble of choosing how to create virtual resources, and how to aintain independence between the. It should be ipossible for Vs to interact with other Vs in any anner. By isolating along one or ultiple diensions of the real resources, each virtual resource user is only aware of its own virtual resources and can only use those resources, and thus it cannot interfere with other virtual resource users [20] [2]. This is illustrated in Figure 9. The ter diension refers to a easurable feature of a resource. Thus we add the isolation diension(s) to the apping function: : V 1 T {t 1 } V 1.n 3 for exaple using the tie diension. An exaple of how this applies is shown in Figure 10. V 3.1 f 3 f 3 4 V 1.1 epresentation Level n t (c) The one-to-any function f 3 shows that it could be possible to ap virtual resources to a cobination of real resources, whether these have been previously virtualized or not. In this case V 3.1 is apped to 4 and V 1.n. Figure 8. Exaple of recursive virtualization. is the first instance of virtualization, f 2 is the second instance, and f 3 is the third. f 2 and f 3 are recursive virtualization, since they depend on the first instance of virtualization,. t 3 V 1.2 Figure 10. A any-to-one apping using one diension (tie) for isolation. However, the ability to isolate using a particular diension depends on the technical capability of the apping echanis. The granularity used by the isolation process is very 1

8 8 iportant as the user of the virtual resources ust not be able to perceive any difference between the virtual resource and the real resource. For exaple, in processing virtualization, processing resources can be isolated in the tie diension. However, the tiescale used by the isolation process is so sall (saller than huan reaction tie of approxiately 0.2 seconds) that the user can use the virtual resources as if they were real resources. If the tiescale used by the isolation process was too large, say one hour, then the users of the virtual resources would realise that the resources they are using are not real resources. Although the isolation proble is a prerequisite to the ebedding proble, and influences the ebedding proble greatly, in the literature the isolation proble has received significantly less attention copared to the ebedding proble. D. The Ebedding Proble The proble of deciding how to ap virtual resources to real resources is also known as the ebedding proble. Essentially this is a resource allocation proble, which is the distribution of scarce resources to copeting users. There are several probles that can be considered: 1) The first case is that there ight not be enough resources to satisfy all of the users requests; 2) The second case is that the users can request different quantities of resources; and 3) The third case is that each of the resources can be of unequal value. These three probles are not utually exclusive and often occur siultaneously. Depending on the objective(s) that the resource owner wants to achieve, different etrics can be used to deterine the optial resource allocation. Even when there are enough resources to satisfy all of the users requests and a potential solution exists, resource allocation can be a coplex proble to solve. In the context of virtualization, users can ake requests for virtual resources and an ebedding algorith deterines which requests are successful. Figure 11 shows the resource allocation probles that can occur when users ake requests for two-diensional sets of resources. E. Definition of Virtualization Now that we have a better understanding of virtualization, we propose the following definition for virtualization: Virtualization is a resource apping that occurs in the abstract doain. Virtualization takes places within any one representation level in the abstract doain. The representation level used is a design choice. Abstract resources before virtualization, known as real resources, are liited by the granularity of the underlying physical resources. Abstract resources after virtualization, known as virtual resources, are not, and can be larger or saller than real resources. Virtual resources are independent and can be allocated siultaneously to ultiple users, A A C C B B DD E E E DDE Ebedding? A (a) A B The first B type of proble occurs when there are ore user requests than C resources. At least one user A AC D Ebedding? B DB Ebedding? will not receive resources. C C A A C C B B DD Ebedding? Ebedding? (c) A siilar proble can occur if the resources are of different sizes. A C B D D D Ebedding? (b) Another B type of proble can happen A B A when users have different request sizes. Ebedding? CC C A C E B D E Ebedding? Ebedding? Ebedding? (d) The last exaple shows that these three probles can occur siultaneously. Figure 11. This figure shows resource allocation probles that can happen when users A, B, C, D, and E request two-diensional resources fro a resource owner. There are three different types of probles that can occur, shown in a), b) and c). The three can occur siultaneously as shown in d). esources can be allocated request by request in sequence, or by considering ultiple requests together, which could provide ore efficient ebedding. each with the illusion of full ownership of their resources. Virtualization can always be done recursively, since users perceive no difference between the virtual resources and the real resources. This definition is satisfactory since it addresses the concepts o) abstract resources as representations of physical resources. 2) the splitting and cobining of resources, 3) ownership and isolation, 4) allocation, and 5) recursion. F. Validity of the Theory Although we have attepted to validate virtualization theory as uch as possible by referring to previous works, soe aspects are new and need verification. One ethod of verifying the theory is to exaine virtualization technologies and to see if the theory holds. As an exaple we exaine virtual eory, one of the first virtualization techniques developed. Virtual eory, or one-level storage as it is also known, was developed in 1961 by the Atlas group to overcoe the storage allocation proble of distributing inforation between ain eory and auxiliary eory levels in coputers [21]. In a one-level storage syste, a distinction is ade between the address space, which is the set of identifiers used to refer to inforation, and the eory space, which is the set of physical eory locations used to store inforation [22]. Instead of offering coputer progras direct access to the eory space, progras can only access the address space, and a supervisor aps the address space to the eory space. By decoupling the address space in this way fro the physical eory, it is possible to cobine both ain eory and

9 -2-1 x x z z+1 Input epresentation epresentation epresentation p Level 1: Level Level1:1: ~ Disk Meory y y+1 epresentation epresentation epresentation Level 2: Level Level2:2: Abstract Doain Abstract Doain 0 1 Abstract Doain 0 1 Main Meory 9 Physical Doain Physical PhysicalDoain Doain p Input Input pp Output p p p p pp ~ ~ Process Process Process Storage Storage Storage pp Output Output p pp (a) Hardware a-1 Address Space d-1 Mapping Mechanis Meory Space Figure 12. The separation of address and eory spaces allows the address apping echanis to cobine ain eory and disk eory into a onelevel storage space. The address apping echanis can also give users the perception of having a unique address space for ultitasking Input Input Input p pp p p p p pp ~ 2 Output Output ~ ~ 2 2 Process Process Process2 2 2 C(p) C(C( p)p) p pp ~ 1 p Output p p p p pp Storage Storage Storage ~ ~ pp p 1 1 pp (b) Software Figure 13. (a) Model of coputer hardware based on A theory. Coputer hardware can be thought of as having four functions, corresponding to the appings of A theory and storage of the physical states. (b) Software ust be used to enable all four functions to be virtualized, i.e. perforing the copute cycle in the abstract doain, as virtualization can only be done in the abstract doain. IV. N ETWOK ESOUCE V ITUALIZATION auxiliary eory into a single address space, thus offering the illusion of one-level storage, shown in Figure 12. Let us now exaine how virtualization theory applies to virtual eory, suarized in Table II. Firstly, it is iportant to identify the abstract resources that are being virtualized. In this case the abstract resources are inforation storage in the for of bits. Next, it is possible to see that virtual eory is a one-to-any apping, since it aps one virtual resource (the address space) to any real resources (the ain and auxiliary eory spaces) 4. The isolation diension is the address space, which is to say the index of locations to store inforation. In theory recursion is possible in virtual eory, because the resources offered are locations to store inforation, exactly the sae type of resources as nonvirtualized eory. In fact, the authors of [23] develop such a recursive virtual eory syste. As for the ebedding proble, soe exaples of different approaches to ebedding are the different paging and segentation algoriths that have been developed [17]. Table II V ITUALIZATION T HEOY A PPLICATION : V ITUAL M EMOY Concept Abstract resources at a representation level Use in Virtual Meory Mapping Isolation ecursion Ebedding One-to-any / Many-to-any Address space - index of storage locations Possible but not very useful in practise, see [23] Paging algoriths, segentation algoriths Location to store bits The exaple of virtual eory shows how virtualization theory can apply in practise. We see that each aspect of the theory has a practical counterpart in virtual eory. This offers soe validation of the theory. In the next section we exaine several other virtualization technologies in the context of wireless networks, but for each virtualization technology the sae analysis could be perfored. 4 With the developent of ultitasking, in reality virtual eory is now any-to-any, because different progras each have their own address space. Having developed a theory of virtualization, we now consider how virtualization applies to wireless networks. We define a wireless network as a set of nodes that can transfer inforation through links, where soe of the links ay be wireless in nature. Fro this definition, we can deduce that wireless networks consist of two parts: nodes and links. We ust first be able to virtualize nodes and links when creating virtual wireless networks, and thus as a first step in the virtualization process, we exaine what constitutes nodes and links. We also analyse how node and link functionality can be virtualized. A. Nodes In this paper we consider a node or coputer hardware as a physical device that can deterine the outcoe of abstract operations through physical anipulations [12]. Based on the couting diagra of coputer hardware shown in Figure 13 (a), we can identify four specific functions: input (I), i.e. the instantiation of abstract objects in a physical state, storage (S) of that physical state in soe way, processing (P) of the physical state in a way that is coutative to soe for of abstract operations, and output (O) of result of the physical process in the for of an abstract representation. All functions are required within a node, since, for exaple, it would be pointless to have processing available but no input, as there would be no inforation to process. These four functions are consistent with the IPO+S odel of coputing [24]. Each of these resource types can be represented in the abstract doain and virtualized, which allows resources to be used ore efficiently, and also can provide new functionality, such as achine (node) virtualization. However, as entioned previously, virtualization can only be done in the abstract doain. This eans that if all four functions are to be virtualized siultaneously, then it is necessary to introduce an additional level of representation, that is to perfor the virtualization in software. We show the show the general copute cycle in the abstract doain (software) in Figure 13 (b).

10 10 User 2 User 3 User 1 CPU User 4 User 6 User 5 Figure 14. Tie-sharing gives several users the perception of having exclusive use of a processor, by giving each user a short burst of coputing tie. In this exaple, the CPU is processing user five s burst of tie, before it oves on to the next user. We refer to resources according to their function type, for exaple we refer to storage resources rather than resources that instantiate storage functionality. Although technically incorrect, this siplification akes it easier to follow. The types of node resource virtualization are discussed briefly below. 1) Process Virtualization: The idea of process virtualization can be traced back to the concept of copatible tiesharing, first developed at M.I.T. in the early 1960 s [25]. Tie-sharing was developed to overcoe the liited anachine interaction of batch processing, which had led to an increase in prograing errors and debugging tie, as larger and ore coplex progras were being set [26]. Tie-sharing enables several people to ake use of a coputer at the sae tie, shown in Figure 14 [27]. ather than offering users direct access to coputing resources, which can lead to serious crashes and eory probles, a supervisor buffers user input, and sequentially runs user progras for sall bursts of tie. The full sequence of user progras occurs frequently enough (ideally in less than 0.2 seconds) that a coputer appears to be fully responsive to all users. By apping user processing tie to burst of achine processor tie in this way, and by aintaining strict isolation, users have the perception of exclusive use of dedicated processors. Thus the illusion of ultiple virtual processors is created. Thus virtualization both increases resource efficiency, and also offers users new or iproved functionality. The surveys [28] [30] provide further inforation about processing virtualization techniques, and a very interesting and inforative docuentary on the copatible tie-sharing syste can be found at [31]. 2) Storage Virtualization: One ethod of storage virtualization is virtual eory, which we discussed in section III-F. The use of virtual eory not only autoates the storage allocation proble efficiently [32], but also enables achine independence, progra odularity, convenient eory addressing, and the capability of handling structured data [22], [17]. For a ore detailed view on storage virtualization techniques, see the surveys [33], and [34]. 3) Machine (Node) Virtualization: The developent of process and storage virtualization led to new functionality, and coputing becae thought of as a large syste of coponents serving a counity of users, where each of the users could run different progras with different processing, eory, and I/O interaction requireents [35]. In such a syste, software is coonly split into two classes to avoid syste integrity issues: a privileged supervisor (or Operating Syste) which is presued to be correct, and a second non-privileged class which is denied any functionality that can cause interference between processes [36]. However, this arrangeent only allows one privileged supervisor to be run at a tie, and incopatible non-privileged progras cannot be run easily [37]. Machine virtualization overcoes this proble by constructing siulated copies of the achine, known as virtual achines, and each virtual achine can run a different privileged supervisor [38]. A virtual achine onitor (VMM), also known as a hypervisor, isolates process and eory operations for each virtual achine, and aps the to the host achine using tie-sharing and virtual eory techniques [39]. Until recently I/O operations had to be trapped and executed by the VMM. Advances in achine virtualization, especially in server virtualization have reduced the cost of servers hugely and has led to the widespread adoption of oving coputing tasks to the cloud [40]. The recent developent of I/O virtualization (see next part) has allowed full coputer node virtualization, consisting of storage, process and I/O virtualization. There are any contexts in which the use of node virtualization is growing such as desktop, application, and user virtualization. More inforation can be found in the works [39], [41], [42], [43], and [44]. 4) Input and Output Virtualization: One of the probles encountered by early virtual achines was the apping of input and output (I/O) paths fro virtual device addresses to real device addresses, since absolute addressing is required for I/O paths [37]. Early Virtual Machine Monitors (VMMs) trapped I/O instructions used by the virtual achines, copied instructions, and absolutized the by apping the virtual addresses to the correct real I/O addresses. While this solution of eulating I/O devices in software enabled virtual achines to use I/O operations, it was a work-around and not I/O virtualization. The generalized I/O eory anageent unit (IOMMU), developed by Intel, is a hardware device that aps virtual device addresses to real ones across isolated partitions, supervised by syste software [45]. The VMM controls these partitions and thus full virtualization of I/O operations is possible, since virtual I/O operations are apped directly to the devices. One exaple of an I/O peripheral that has been virtualized is the Network Interface Card. A survey of I/O virtualization techniques is given in [46]. B. Links The function of links is to transfer inforation between nodes in a reliable anner. Siilarly to nodes, links can also be thought of as consisting of abstract objects (i.e. inforation) and physical resources which instantiate that inforation and physically send it between nodes. Again, siilar to nodes, links can only be virtualized in the abstract doain. Links can be wired or wireless. However, there are significant differences between wired and wireless links, due to the nature of the physical resources used. Both wired and