#### DMCA

## Distributed Storage in the Plane

### Citations

1552 |
Handbook of mathematical functions with formulas, graphs, and mathematical tables
- Abramowitz, Stegun
- 1964
(Show Context)
Citation Context ...llows readily from Corollary 1 that W p W cmin = ( 1 + a 2 ) k1+a/2B ( k, 1 + a 2 ) , (15) where B(k, 1 + a2 ) denotes the Beta function. Theorem 4. The benefit of coding over partitioning, W p/W cmin, is increasing in k. Moreover lim k→∞ W p W cmin = (a 2 + 1 ) Γ (a 2 + 1 ) . (16) Hence 1 ≤ W p W c ≤ (a 2 + 1 ) Γ (a 2 + 1 ) , (17) with equality on the LHS iff k = 1. Proof: We start with proving that W p/W cmin, is increasing in k. Let b = 1 + a2 . We have ∂ ∂k W p W cmin = bkbB(k, b) [ b k + ψ(k)− ψ(k + b) ] , (18) where ψ(x) = ∫∞ 0 ( e−t t − e−xt 1−e−t ) dt is the digamma function [29]. We need to show that ∞∫ 0 e−kt 1− e−bt 1− e−t dt ≤ b k , (19) but this follows directly from the observation that 1−e −bt 1−e−t ≤ b. The limiting expression follows from an application of Stirlings approximation. Note, that for a = 1, 2, 3, the upper bound in Theorem 4 reduces to 3 √ π 4 ≈ 1.3, 2 and 15 √ π 8 ≈ 3.3 respectively. C. Cache miss probability Next let us consider the cache miss probability. Theorem 5. The cache miss probability of the partitioning and coded strategy are F p = 1− ( 1− e−λπr 2/k )k , (20) F cmin = Γ(k, λπr2) Γ(k) . (21) Proof: For the coded strategy we have F cmin ... |

1336 | Modeling TCP Throughput: A Simple Model and its Empirical Validation
- Padhye, Firoiu, et al.
- 1998
(Show Context)
Citation Context ...Based on R = 1 2 log ( 1 + Pδ−a ) , (4) where a is the path loss exponent of the wireless medium, we see that the transmit power P required to transmit at a guaranteed minimum rate R satisfies P = (exp(2R) − 1)δa. Therefore, the energy required to deliver a symbol from the device is of the form (3), with preconstant proportional to exp(2R) − 1. In this case a denotes the path loss exponent, which in the plane satisfies a ≥ 2. Another example is given by the time required to obtain the data if TCP is used. The throughput of TCP is known to be inversely proportional to the round trip delay, cf. [25] or [26]. The later is given by the sum of the processing/queueing delay (which we assume zero) and the propagation delay, which is proportional to the distance δ. Therefore, W = Cδ, i.e., a = 1, gives the time required to obtain data from a device using TCP. 2) Cache miss probability: We consider the case that clients can only connect to devices within range r. If the complete data cannot be retrieved from the devices within this range, a cache miss occurs. If clients can connect to any cache within range r, but not outside, then E[F (D(I)], with F (δ1, . . . , δk) = { 0, if maxi δi ≤ r, 1, o... |

590 | A Random Linear Network Coding Approach to Multicast
- Ho, Koetter, et al.
- 2006
(Show Context)
Citation Context ... k devices. For notation convenience, denote the minimum expected cost as Gmin = E [G (D(1), . . . , D(k))] . (6) Our next result provides a bound on the deviation of the cost of the coded strategy from Gmin. Theorem 2. The expected cost of the coded strategy is upper bounded as E [G (D(Ic))] ≤ Gmin +G0, (7) where G0 = Gmax(1− (1− 1/q)k). Proof: Let A denote the event that the first k devices provide a full rank system. Then E [G (D(Ic))] = E [G (D(Ic)) |A]P (A) + E [ G (D(Ic)) |A ] P (A) (8) and the result follows from the assumption that G is bounded by Gmax and P (A) ≤ 1− (1− 1/q)k, cf. [27] or [28]. We will illustrate the above result for a specific performance measure below. In particular, we will show that the coded strategy is close to optimal. B. Waiting time Next, we consider specific instances of the cost. First we consider W as defined in Section II-C1. Before giving the results we will provide some definitions and results on the Gamma function. Let Γ(k, x) denote the upper incomplete Gamma function, i.e., Γ(k, x) = ∞∫ x zk−1e−zdz. (9) Furthermore, we define Γ(k) = Γ(k, 0) and γ(k, x) = Γ(k)− Γ(k, x). The use of Γ(k, x) for Poisson processes stems from the fact that for a... |

452 |
Networking named content
- Jacobson, Smetters, et al.
- 2009
(Show Context)
Citation Context ...stributed memory storage and caching in road traffic sensor networks. The second direct application is Information Centric Networking (ICN). ICN is a new paradigm for the network architecture where the data client x2 x1 x1 x1 x2 Fig. 1. Uncoded data allocation client α3x1 + β3x2 α5x1 + β5x2 α1x1 + β1x2 α2x1 + β2x2 α4x1 + β4x2 Fig. 2. Coded data allocation is addressed by its name or content directly rather than by its physical location. There is no predefined location for the data in ICN and the content is naturally cached along the retrieval path. Examples of the ICN architecture are CCN/NDN [9], DONA [10] and TRIAD [11]. Our results can be useful for the design of the wireless networks with the ICN architecture. Next we present our setting in more detail. We consider the very general model where storage devices are located in the plane according to a general point process and the cost of obtaining data from a particular storage device is increasing with the distance between the client and that device. This cost can reflect, for instance, the time required to obtain the data, the transmit power that needs to be used at the storage device to satisfy certain QoS constraints, or the pro... |

381 | Comparison methods for stochastic models and risks, volume 389 - Müller, Stoyan - 2002 |

333 | Network Coding for Distributed Storage Systems
- Dimakis, Godfrey, et al.
- 2007
(Show Context)
Citation Context ...r a broad class of performance measures. In addition, we will be interested in two more specific performance measures. The first is the hit rate, i.e., the probability that the client can retrieve the data from storage devices that are located within a specified range. The second performance measure is the expected total cost of retrieving the data, where total cost is the sum of costs of obtaining individual fragments. The cost of obtaining a fragment is increasing in the distance between client and storage device. Applications of linear network coding for distributed storage were studied in [12], where it has been demonstrated that repair bandwidth can be significantly reduced. In the current work there is no notion of repair. Instead, coding is used to bring the data ‘closer’ to the client. The use of coding was also explored in [13] where it was shown how to efficiently allocate the data at caches with the aim of ensuring that any sufficiently large subset of caches can provide the complete data. The difference with the current work is that we are taking the geometry of the deployment of the storage devices into account. In [14] coding strategies for networks of caches are presente... |

286 | A data-oriented (and beyond) network architecture
- Koponen, Chawla, et al.
- 2007
(Show Context)
Citation Context ...memory storage and caching in road traffic sensor networks. The second direct application is Information Centric Networking (ICN). ICN is a new paradigm for the network architecture where the data client x2 x1 x1 x1 x2 Fig. 1. Uncoded data allocation client α3x1 + β3x2 α5x1 + β5x2 α1x1 + β1x2 α2x1 + β2x2 α4x1 + β4x2 Fig. 2. Coded data allocation is addressed by its name or content directly rather than by its physical location. There is no predefined location for the data in ICN and the content is naturally cached along the retrieval path. Examples of the ICN architecture are CCN/NDN [9], DONA [10] and TRIAD [11]. Our results can be useful for the design of the wireless networks with the ICN architecture. Next we present our setting in more detail. We consider the very general model where storage devices are located in the plane according to a general point process and the cost of obtaining data from a particular storage device is increasing with the distance between the client and that device. This cost can reflect, for instance, the time required to obtain the data, the transmit power that needs to be used at the storage device to satisfy certain QoS constraints, or the probability wi... |

250 | Stochastic Geometry and Wireless Networks, Volume I - Theory
- Baccelli, Blaszczyszyn
- 2009
(Show Context)
Citation Context ... 0 xad ( 1− Γ(i, bx 2) Γ(i) ) = γ ( a 2 + i, bu 2 ) Γ(i)ba/2 . (43) Proof. The result follows directly from the definitions of Γ(i, bx2) and γ(a/2 + i, bu2). Before giving the proofs for the two strategies, recall that b = 1 + a/2 and d = λπδ2max. This leads to δ a max = (d/λ/π)b−1 and P (D(i) > δmax) = Γ(i, d)/Γ(i). A. Uncoded strategy The first thing to note in the uncoded strategy is that for each of the labels t ∈ {1, . . . , k} all caches with label t form a homogeneous spatial Poisson process with intensity λ/k. This follows from the fact that these caches form a thinned Poisson process [32]. Now, for the uncoded strategy we have W p = k∑ i=1 ∞∫ 0 max {(δi)a , δamax} dP (D(X p i ) ≤ δi) =k δmax∫ 0 δad ( 1− Γ(1, λkπδ 2) Γ(1) ) + kδamaxΓ ( 1, d k ) =k ( k λπ )a/2 γ ( 1 + a 2 , d k ) + k ( d λπ )a/2 Γ ( 1, d k ) , where we have used Lemma 4. B. Random linear coding strategy For the coded strategy we start with W cmin = k∑ i=1 δmax∫ 0 δadP (D(i) ≤ δ) + δamax k∑ i=1 Γ (i, d) Γ(i) , (44) where we continue with analyzing each term seperately. First, δamax k∑ i=1 Γ (i, d) Γ(i) = ( d λπ )a/2 Γ(k + 1, d)− dΓ(k, d) Γ(k) , (45) by Lemma 3. Next, δmax∫ 0 δadP (D(i) ≤ δ) = γ ( a 2 + i, d ) Γ(i... |

209 | A Stochastic Model of TCP/IP with Stationary Random Losses
- Altman, Avrachenkov, et al.
- 2000
(Show Context)
Citation Context ... R = 1 2 log ( 1 + Pδ−a ) , (4) where a is the path loss exponent of the wireless medium, we see that the transmit power P required to transmit at a guaranteed minimum rate R satisfies P = (exp(2R) − 1)δa. Therefore, the energy required to deliver a symbol from the device is of the form (3), with preconstant proportional to exp(2R) − 1. In this case a denotes the path loss exponent, which in the plane satisfies a ≥ 2. Another example is given by the time required to obtain the data if TCP is used. The throughput of TCP is known to be inversely proportional to the round trip delay, cf. [25] or [26]. The later is given by the sum of the processing/queueing delay (which we assume zero) and the propagation delay, which is proportional to the distance δ. Therefore, W = Cδ, i.e., a = 1, gives the time required to obtain data from a device using TCP. 2) Cache miss probability: We consider the case that clients can only connect to devices within range r. If the complete data cannot be retrieved from the devices within this range, a cache miss occurs. If clients can connect to any cache within range r, but not outside, then E[F (D(I)], with F (δ1, . . . , δk) = { 0, if maxi δi ≤ r, 1, otherwise... |

177 | Supporting cooperative caching in ad hoc networks.
- Yin, Cao
- 2006
(Show Context)
Citation Context ...the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. Data sharing among multiple caches such that the bandwidth consumption and the data retrieval delay are minimal is considered in [23]. None of [4], [5], [21]–[23] are considering coded caching strategies. We would like to emphasize that none of the above mentioned works considered continuous geometric constraints on storag... |

96 | An architecture for content routing support in the internet
- Gritter, Cheriton
- 2001
(Show Context)
Citation Context ...and caching in road traffic sensor networks. The second direct application is Information Centric Networking (ICN). ICN is a new paradigm for the network architecture where the data client x2 x1 x1 x1 x2 Fig. 1. Uncoded data allocation client α3x1 + β3x2 α5x1 + β5x2 α1x1 + β1x2 α2x1 + β2x2 α4x1 + β4x2 Fig. 2. Coded data allocation is addressed by its name or content directly rather than by its physical location. There is no predefined location for the data in ICN and the content is naturally cached along the retrieval path. Examples of the ICN architecture are CCN/NDN [9], DONA [10] and TRIAD [11]. Our results can be useful for the design of the wireless networks with the ICN architecture. Next we present our setting in more detail. We consider the very general model where storage devices are located in the plane according to a general point process and the cost of obtaining data from a particular storage device is increasing with the distance between the client and that device. This cost can reflect, for instance, the time required to obtain the data, the transmit power that needs to be used at the storage device to satisfy certain QoS constraints, or the probability with which the cl... |

89 | Ubiquitous Access to Distributed Data in Large-Scale Sensor Networks Through Decentralized Erasure Codes
- Dimakis, Prabhakaran, et al.
- 2005
(Show Context)
Citation Context ...within a specified range. The second performance measure is the expected total cost of retrieving the data, where total cost is the sum of costs of obtaining individual fragments. The cost of obtaining a fragment is increasing in the distance between client and storage device. Applications of linear network coding for distributed storage were studied in [12], where it has been demonstrated that repair bandwidth can be significantly reduced. In the current work there is no notion of repair. Instead, coding is used to bring the data ‘closer’ to the client. The use of coding was also explored in [13] where it was shown how to efficiently allocate the data at caches with the aim of ensuring that any sufficiently large subset of caches can provide the complete data. The difference with the current work is that we are taking the geometry of the deployment of the storage devices into account. In [14] coding strategies for networks of caches are presented, where each user has access to a single cache and a direct link to the source. It is demonstrated how coding helps to reduce the load on the link between the caches and the source. Note that we assume that different transmissions from caches ... |

64 | Hierarchical Web caching systems: modeling, design and experimental results.
- Che, Tung, et al.
- 2002
(Show Context)
Citation Context ...from caches to the clients are orthogonal, for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. Data sh... |

37 |
Optimal policy in a dynamic single product, non-stationary inventory model with several demand classes
- Veinott
- 1965
(Show Context)
Citation Context ...ire dExcellence” UCN, by Orange Labs grant on caching systems and by the European Commission within the framework of the CONGAS project FP7-ICT-2011-8-317672. APPENDIX A PROOF OF THEOREM 1 Observe that Theorem 1 provides a stochastic comparison result. To simplify discussion in the remainder we introduce for random vectors Z = (Z1, . . . , Zk) and Z = (Z1, . . . , Zk) the notation Z ≤st Z, to denote that E [F (Z)] ≤ E [ F ( Z )] for all bounded increasing F . We say that Z is less than Z in the usual stochastic ordering. Lemma 1. Ic ≤st Ip. Proof: We will make use of a result by Veinott [30], cf. [31, Theorem 3.3.7] that states that the result holds if Ic1 ≤st I p 1 and for i = 2, 3, . . . , k,[ Ici ∣∣Ic1 = xc1, . . . , Ici−1 = xci−1] ≤st[ Ipi ∣∣Ip1 = xp1, . . . , Ipi−1 = xpi−1] , (25) whenever xcj ≤ x p j for all j = 1, . . . , i− 1. We have Ic1 = 1 and for i = 2, . . . , k[ Ici ∣∣Ic1 = xc1, . . . , Ici−1 = xci−1] = Gi + xci−1, (26) where P (Gi = n) = (1 − gi)gn−1i , gi = qi−1/qk, i.e., Gi is geometrically distributed with parameter gi. The above follows from the fact the coding coefficients are chosen independently for each cache. The probability that the vector of coefficients... |

34 | Energy-efficient caching strategies in ad hoc wireless networks,”
- Nuggehalli, Srinivasan, et al.
- 2003
(Show Context)
Citation Context ...g to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. Data sharing among multiple caches such that the bandwidth consumption and the data retrieval delay are minimal is considered in [23]. None of [4], [5], [21]–[23] are considering coded caching strategies. We would like to emphasize that none of the above mentioned works considered continuous geometric constraints on s... |

31 |
Femtocaching and device-to-device collaboration: A new architecture for wireless video distribution,”
- Golrezaei, Molisch, et al.
- 2013
(Show Context)
Citation Context ...e costs of the allocation strategies for the case that storage devices coincide with currently deployed mobile base stations. I. INTRODUCTION Consider wireless devices located in the plane that serve as storage devices for a big piece of data. Clients are interested in obtaining the complete data. However, the capacity of the storage devices is limited and it is not possible to store the complete data in each device. Therefore, clients will have to gather data from several devices in order to retrieve the complete piece of data. In recent years, there has been a lot of interest— from academia [1]–[5], industry [6] and regulatory bodies [7]— in employing caches at base stations with the aim of bringing data as close as possible to the end user so as to offer a faster and better service. One of the ideas is that several base stations can provide data in a cooperative fashion. Taking this idea further has led to consideration of device-to-device connections in cellular networks where the user devices themselves act as caches [8]. Such means of content delivery provide an immediate application of the setting that was introduced above and that will be explained in more detail below. In add... |

30 | Breadcrumbs: Efficient, best-effort content location in cache networks.
- Rosensweig, Kurose
- 2009
(Show Context)
Citation Context ...d, where each user has access to a single cache and a direct link to the source. It is demonstrated how coding helps to reduce the load on the link between the caches and the source. Note that we assume that different transmissions from caches to the clients are orthogonal, for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between... |

26 | Content and service replication strategies in multi-hop wireless mesh networks.
- Jin, Wang
- 2005
(Show Context)
Citation Context ...are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. Data sharing among multiple caches such that the bandwidth consumption and the data retrieval delay are minimal is considered in [23]. None of [4], [5], [21]–[23] are considering coded caching strategies. We would like to emphasize that none of the above mentioned works considered continuous geometric constraints on storage device placement. Thus, to the best of our knowledge, the current paper is the first work on the analysis of spatial distribu... |

22 |
Network coding fundamentals,” Foundations and Trends R©
- Fragouli, Soljanin
- 2007
(Show Context)
Citation Context ...es. For notation convenience, denote the minimum expected cost as Gmin = E [G (D(1), . . . , D(k))] . (6) Our next result provides a bound on the deviation of the cost of the coded strategy from Gmin. Theorem 2. The expected cost of the coded strategy is upper bounded as E [G (D(Ic))] ≤ Gmin +G0, (7) where G0 = Gmax(1− (1− 1/q)k). Proof: Let A denote the event that the first k devices provide a full rank system. Then E [G (D(Ic))] = E [G (D(Ic)) |A]P (A) + E [ G (D(Ic)) |A ] P (A) (8) and the result follows from the assumption that G is bounded by Gmax and P (A) ≤ 1− (1− 1/q)k, cf. [27] or [28]. We will illustrate the above result for a specific performance measure below. In particular, we will show that the coded strategy is close to optimal. B. Waiting time Next, we consider specific instances of the cost. First we consider W as defined in Section II-C1. Before giving the results we will provide some definitions and results on the Gamma function. Let Γ(k, x) denote the upper incomplete Gamma function, i.e., Γ(k, x) = ∞∫ x zk−1e−zdz. (9) Furthermore, we define Γ(k) = Γ(k, 0) and γ(k, x) = Γ(k)− Γ(k, x). The use of Γ(k, x) for Poisson processes stems from the fact that for a Poisson... |

17 | Analysis of ttl-based cache networks.
- Fofack, Nain, et al.
- 2012
(Show Context)
Citation Context ...ce. Note that we assume that different transmissions from caches to the clients are orthogonal, for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesti... |

13 |
Using proxy cache relocation to accelerate web browsing in wireless/mobile communications,”
- Hadjiefthymiades, Merakos
- 2001
(Show Context)
Citation Context ...sts of the allocation strategies for the case that storage devices coincide with currently deployed mobile base stations. I. INTRODUCTION Consider wireless devices located in the plane that serve as storage devices for a big piece of data. Clients are interested in obtaining the complete data. However, the capacity of the storage devices is limited and it is not possible to store the complete data in each device. Therefore, clients will have to gather data from several devices in order to retrieve the complete piece of data. In recent years, there has been a lot of interest— from academia [1]–[5], industry [6] and regulatory bodies [7]— in employing caches at base stations with the aim of bringing data as close as possible to the end user so as to offer a faster and better service. One of the ideas is that several base stations can provide data in a cooperative fashion. Taking this idea further has led to consideration of device-to-device connections in cellular networks where the user devices themselves act as caches [8]. Such means of content delivery provide an immediate application of the setting that was introduced above and that will be explained in more detail below. In additio... |

13 | On the steady-state of cache networks,”
- Rosensweig, Menasche, et al.
- 2013
(Show Context)
Citation Context ..., for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. Data sharing among multiple caches such that the... |

12 | Optimal throughput-outage trade-off in wireless one-hop caching networks,”
- Ji, Caire, et al.
- 2013
(Show Context)
Citation Context ...s will have to gather data from several devices in order to retrieve the complete piece of data. In recent years, there has been a lot of interest— from academia [1]–[5], industry [6] and regulatory bodies [7]— in employing caches at base stations with the aim of bringing data as close as possible to the end user so as to offer a faster and better service. One of the ideas is that several base stations can provide data in a cooperative fashion. Taking this idea further has led to consideration of device-to-device connections in cellular networks where the user devices themselves act as caches [8]. Such means of content delivery provide an immediate application of the setting that was introduced above and that will be explained in more detail below. In addition to content delivery, there are a number of more specific applications of which we mention two: The first application is in the context of road traffic sensor networks. On one hand, sensors have very limited memory and transmission capabilities; on the other hand, traffic applications like provision of current traffic conditions, suggesting alternative routes or directing to empty parking spots require dealing with a large inform... |

10 |
Fundamental limits of caching,” arXiv preprint arXiv:1209.5807,
- Maddah-Ali, Niesen
- 2012
(Show Context)
Citation Context ...etwork coding for distributed storage were studied in [12], where it has been demonstrated that repair bandwidth can be significantly reduced. In the current work there is no notion of repair. Instead, coding is used to bring the data ‘closer’ to the client. The use of coding was also explored in [13] where it was shown how to efficiently allocate the data at caches with the aim of ensuring that any sufficiently large subset of caches can provide the complete data. The difference with the current work is that we are taking the geometry of the deployment of the storage devices into account. In [14] coding strategies for networks of caches are presented, where each user has access to a single cache and a direct link to the source. It is demonstrated how coding helps to reduce the load on the link between the caches and the source. Note that we assume that different transmissions from caches to the clients are orthogonal, for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according ... |

5 | Content, Connectivity, and Cloud: Ingredients for the Network of the Future,” - Ahlgren, Aranda, et al. - 2011 |

5 | Caching in wireless networks,”
- Niesen, Shah, et al.
- 2012
(Show Context)
Citation Context ...ing that any sufficiently large subset of caches can provide the complete data. The difference with the current work is that we are taking the geometry of the deployment of the storage devices into account. In [14] coding strategies for networks of caches are presented, where each user has access to a single cache and a direct link to the source. It is demonstrated how coding helps to reduce the load on the link between the caches and the source. Note that we assume that different transmissions from caches to the clients are orthogonal, for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using ... |

3 | Cloud storage for small cell networks,” - Bastug, Guenego, et al. - 2012 |

3 |
Content caching and scheduling in wireless broadcast networks with elastic and inelastic traffic,”
- Abedini, Shakkottai
- 2011
(Show Context)
Citation Context ...d according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. Data sharing among multiple caches such that the bandwidth consumption and the data retrieval delay are minimal is considered in [23]. None of [4], [5], [21]–[23] are considering coded caching strategies. We would like to emphasize that none of the above mentioned works considered continuous geometric const... |

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Approximate models for general cache networks,” in INFOCOM,
- Rosensweig, Kurose, et al.
- 2010
(Show Context)
Citation Context ...sions from caches to the clients are orthogonal, for instance by separating them in time or frequency. In [15] the impact of non-orthogonal transmissions is considered and scaling results are derived on the best achievable transmission rates. Systems of distributed storage devices or caches can be classified according to the amount of coordination between the devices. In [16] an approach with implicit coordination is proposed. Networks of caches are notoriously difficult to analyze. Only some very particular topologies and caching strategies (see [17] and references therein) or approximations [18], [19] have been studied. In a recent work [20] ergodicity of cache networks has been investigated. Using continuous geometrical constraints on cache placement instead of combinatorial constraints allows us to obtain exact analytical results. Other work on caching in wireless networks is, for instance, [4], [5], [21]–[23]. In [21] the authors analyze the trade-off between energy consumption and the retrieval delay of data from the caches. In [22], the authors consider the optimal number of replicas of data such that the distance between a requesting node and the nearest replica is minimized. D... |