Toward Fault-Tolerant Deadlock-Free Routing in HyperSurface-Embedded Controller Networks
Taqwa Saeed, Vassos Soteriou, Christos Liaskos, Andreas Pitsillides, Marios Lestas
11 Toward Fault-Tolerant Deadlock-Free Routing inHyperSurface-Embedded Controller Networks
Taqwa Saeed,
Member IEEE , Vassos Soteriou,
Senior Member IEEE , Christos Liaskos,
Member IEEE , AndreasPitsillides,
Senior Member IEEE , Marios Lestas,
Member IEEE
Abstract —HyperSurfaces (HSFs) consist of structurally recon-figurable metasurfaces whose electromagnetic properties can bechanged via a software interface, using an embedded miniatur-ized network of controllers. With the HSF controllers, intercon-nected in an irregular, near-Manhattan geometry, we propose arobust, deterministic Fault-Tolerant (FT), deadlock- and livelock-free routing protocol where faults are contained in a set ofdisjointed rectangular regions called faulty blocks. The proposedFT protocol can support an unbounded number of faulty nodes aslong as nodes outside the faulty blocks are connected. Simulationresults show the efficacy of the proposed FT protocol undervarious faulty node distribution scenarios.
I. I
NTRODUCTION
Large Intelligent Surfaces [1] have recently attracted mo-mentous attention promising to revolutionize wireless com-munications, redefining even their fundamental principles [2].Software-Defined Metasurfaces [3] (SDMs) comprise a vitalcandidate enabler technology for the implementation of LargeIntelligent Surfaces, possessing advanced properties relativeto competing technologies [4]. In recent times, considerableeffort has been spent in complementing the underlying meta-surface hardware with a complete set of protocols and anApplication Programming Interface (API), realizing
HyperSur-face (HSF) units ready to be incorporated in applications, suchas Programmable Wireless Environments (PWEs) [5].HSF operation and structure are defined by a five-tierlayered model [6], depicted in Fig. 1. First, the functionalitylayer comprises the types of electromagnetic (EM) controlfunctions that can be exerted by the HSF over an impingingwave, while the EM layer consists of a periodically repeatedelement, the meta-atom , comprising state-altering material ofa specific geometry [7]. Next comes the Embedded ControlLayer, described later, while the gateway layer connects theHSF to the outer world relaying required external states tothe internal embedded state-altering elements, as well as HSFmonitoring information to the opposite direction. Last, theEM compiler acts as middleware, transforming API callbacksto actual actuation directives that configure the HSF con-trollers and the associated meta-atoms. The HSF embeddedcontrol layer is stationed between the gateway and the EM
Taqwa Saeed and Andreas Pitsillides are with theComputer Science Department, University of Cyprus,Nicosia, Cyprus (e-mail: [email protected] , [email protected]). Vassos Soteriou is with the Department of Electrical Engineering andComputer Engineering and Informatics, Cyprus University of Technology,Limassol, Cyprus (e-mail: [email protected])
Christos Liaskos is with the Foundation of Research and Technology(FORTH), Heraklion, Greece (e-mail: [email protected]).
Marios Lestas is with the Electrical Engineering Department, FrederickUniversity, Nicosia, Cyprus (e-mail: [email protected]). EM CompilerHSF API
HSF Unit
HSF Applications Functionality LayerEM LayerEmbedded Control LayerGatewayLayerSoftware & Applications • Controller Manhattan-likenetwork topology with edge-wraparounds.• Input GW and ACK GW areresponsible for injectingtraffic and receiving ACKs.
Gateway
ACK GW
Input GW
Fig. 1:
Layered HyperSurface (HSF) system. layers [8], constituting the necessary hardware and protocolsestablishment to transfer data between the gateway and thestate-altering elements (DC voltage-controlled, continuouslytunable varactors/varistors). In its simplest form, the controllayer comprises direct wiring of the state-altering elementsto the gateway, sufficient even for some PWE applicationscenarios [5]. However, as the density of meta-atoms increases,a network of embedded data controllers is required to exertcontrol within the HSF for online re-configuration purposes.The design of this control layer is challenged by factors suchas low power consumption, dense deployment, the small sizeof meta-atoms, EM interference avoidance, and robustnessagainst any type of fault, etc. These challenges [9] have led toa Controller Network (CN) topology which is irregular andnear-Manhattan, as shown as part of Fig. 1 in blue color,and in Fig. 2, where the directionality of rows (and columns)alternates from one row (column) to the immediate next,resembling a mesh topology where approximately half of itsunidirectional links are missing. Reconfiguration Directives(RDs) for each interconnected meta-atom are inserted via aGateWay (GW) connected to the lower left periphery of thenetwork, while once a RD datum is received by a meta-atom,then its associated controller sends an ACKnowledgement(ACK) message to the ACK GW connected at the topmostright corner of the CN.In terms of miniaturization and layout, there exist re-semblances between Network-on-Chip-interconnected (NoC)multicore processor architectures and the geometry of HSF-embedded CN. However, the HSF CN suffers from severeresource limitations , and hence exhibits a plethora of distinctoperational characteristics vs. most conventional NoCs, includ- a r X i v : . [ c s . N I] N ov ing a unique unidirectional interconnect geometry and clock-less operation [10], though some NoC routers do functionasynchronously [11], detailed in [9]. As such, the HSF CNmethodologies that we develop here to mitigate targeted chal-lenges faced by the HSF CN, cannot be directly inherited fromNoC designs; instead, customized solutions become necessary.HSFs containing an embedded CN are complex devices withdensely integrated tuning elements, unit cells, controller chips,etc., in non-standard packages. Such HSFs must safeguardagainst faults during fabrication, deployment, or operation,which have been shown to degrade HSF performance andare caused by factors such as connector misalignment, ageing,physical or intentional damage of unit cells, etc. [12]. As such,to establish dependable communication among interconnectedcontrollers in an HSF structure, we propose a link-level Fault-Tolerant (FT) routing algorithm that arms routed packetizeddirectives , that reconfigure EM properties of meta-atoms inthe HSF, in bypassing faulty nodes on their way to theirdestination controllers. Radetzki’s et al. survey [13] providesa broad coverage in the field of FT approaches in NoCs,and the interested reader is directed therein. Essentially, aslong as FT routing provides full connectivity devoid of cyclicchannel dependencies in a sub-connected topology, then the FTfunction crucially guarantees packet delivery in deadlock-free and livelock-free mode [14]. Designing a routing protocol thatis both FT and livelock-/deadlock-free raises major challenges,especially in the case of the HSF network where the controllersare interconnected with said near-Manhattan topology, whichpossesses about fewer links vs. 2-D mesh-connected NoCtopologies, in tandem with minimal HSF CN resources. In thiswork, we focus on devising a deadlock-free routing protocolthat is strongly coupled to said HSF CN topology so as toadhere to the above deadlock-/livelock-free routing designrequirements, tailored to the needs of the specific environment.The adopted design methodology, assumes the formationof disjointed rectangular regions called Faulty Blocks (FBs),initially proposed by Wu [15], and utilizes principles from theTurn Model for adaptive routing by Glass and Ni [16]. Basedon assumptions outlined in Section II, the resultant FT routingprotocol we build for the HSF CN meets the following idealobjectives [15]: 1) it is distributed , with all routing decisionsmade locally at nodes to conserve resources, 2) it is feasible ,ensuring reliable delivery of directives to nodes and ACKmessages to the ACK GW, 3) it is fault-tolerant as it is able tobypass faulty nodes contained in FBs, 4) it is devoid of live-locks and deadlocks , 5) it comprises a reasonable fault modelusing FBs, 6) it ensures that routed directives span short routes when bypassing nodes within FBs, and 7) it is adaptive as itconforms to FB formations. Simulation results demonstrate the We use the terms “software directives,” “directives,” and “data” inter-changeably throughput this paper. We utilize the term “deadlock-freedom” as used in the seminal work byDuato [14] all over this paper; that is, message traversals along the CN networkare devoid of cyclic patterns as no circular channel (i.e., link) dependenciesare allowed. As a result, any messages cannot be involved in a deadlockedsituation, occurring, either (1) between packetized software directives, or (2)between such directives and acknowledgement packets (ACKs), or (3) amongACK packets, all scenarios which may halt the flow of messages indefinitelyand render the CN of the HSF inoperable (refer to Section II). A C K G W D D I npu t G W (0,0) (0,2) (1,2) (4,2)(4,4) o dd e v e n e v e n e v e n o dd (1,1) evenoddevenoddeven Fig. 2: A × HSF-embedded controller network topology withtwo packetized directives routing scenarios shown in solid blue anddotted orange links; the ACK path is shown in solid green. effectiveness of the proposed FT routing protocol under twofault distribution scenarios (see Section III).II. F
AULT -T OLERANT R OUTING IN THE
HSF CNWe progressively build our FT routing protocol suited forthe HSF CN topology by concurrently considering 1) the flowof traffic dictated by link interconnectivity, 2) destination nodepositioning, and 3) the placement of the input and ACK GWs.
A. XY-YX Agnostic Routing for a Fully-Healthy HSF CN
Regular XY-YX routing, built to suit a fully-connected HSFCN topology [9], must be properly adjusted to strongly adhereto the geometrical idiosyncrasy of the HSF CN to reliablydeliver directives in a deadlock-/livelock-free mode. As such,topology awareness is incorporated into base XY-YX routingin a distributed fashion, with the method dubbed agnostic XY-YX routing. To explain its workings, we make use of a demoshown in Fig. 2, where two directives are inserted from theinput GW at coordinates ( x = 0 , y = 0 ), with one destined fornode D residing at ( , ), and the other destined for node D at ( , ). The routing rules for directives are as follows: uponinjection at the input GW, 1) if the destination lies on an evencolumn, route horizontally until the x coordinate offset reacheszero and then turn northwards, otherwise, 2) for an odd columndestination, follow 1) but make a turn up a hop earlier ( x offset= ) and route northwards, 3) once step 1 or 2 is complete,when the y offset becomes zero and the row is even, thenmake a turn to the east and route toward the destination node,otherwise, 4) hop one row further to the north, then make aturn and route eastwards until the x offset is zero and thentraverse one hop south to reach the destination node. In Fig. 2the directive taking the dotted orange route toward D utilizesrules 2 and 3 (route: ( , ) → ( , ) → ( , )), while the blueroute toward D utilizes rules 2 and 4 (route: ( , ) → ( , ) → (1,2) → ( , )). The above topology-agnostic XY-YX algorithmis proven to be deadlock-/livelock-free as no full ° turnsare formed which would produce either cyclic dependencies(deadlocks) or endless cycles in the topology (livelocks). TheACK packet generated by destination (1,2) follows a simpleXY path toward the ACK GW; to avoid deadlocks, the ACKpacket for destination node (1,1) is sent by its neighboringnode at (1,2) (which is aware of the non-faulty status of node(1,1,) through their link interconnectivity) to avoid a forbiddencycle formation, and also follows the green path in Fig. 2. (a) (b) Fig. 3:
Faulty block formations demos with their boundaries markedin bold lines; faulty nodes are marked with an “X” sign, while unsafeand healthy nodes are respectively marked in blue and black.
Fig. 4:
South-last routing with prohibited turns in dotted lines. E O I npu t G W A C K G W o dd e v e n e v e n e v e n o dd o dd e v e n e v e no dd o dd e v e n evenodd evenoddeven evenoddevenodd (2,0)(2,1)(0,1)(0,4) (2,4)(2,6) (3,6) (6,6)(6,8) (10,8) (10,10) Fig. 5:
Routing around faulty blocks: directives (red), ACKs (blue).
B. Faulty Blocks (FBs) Formation Rules for FT Routing
Prior-art in the 2-D mesh interconnection network domainhas struggled to produce ample FT routing schemes that simultaneously satisfy crucial requirements such as messagedelivery guarantee to connected nodes, deadlock- and livelock-freedom in routing, large fault counts handling, and reasonableimplementation [17], [13], [14]. Unfortunately, also here weare faced with the same challenges: the elegant XY-YXagnostic routing algorithm cannot accommodate faulty nodesin the HSF CN, especially when randomly placed. Conductedsimulations with such fault placements showed the XY-YXscheme breaking down as packets reached dead ends, with noturn options to avoid such obstacles in a distributed manner.Fortunately, in our quest of achieving all above FT RoutingAlgorithm (RA) characteristics in the resource-limited HSFCN, we made an important observation: that packetized di-rectives and ACKs which route toward the north-east CNcorner, never use the edge wraparound links (they may beused in future HSF technology node implementations wherecontrollers may also become producers [5]), and rarely travelwestbound along odd rows. All these, along with the fact thatrouting and network topology are strongly coupled [14], [17],prompted us toward the derivation of a FT RA suitable forthe HSF CN where all faulty nodes are “spatially bounded”within simple geometrical shapes. Such setup would effec-tively support routes toward the north-east corner of the HSFCN topology while eliminating south-west turns to ensuredeadlock-freedom (see Section II-C). As such, we decided toutilize the idea of faulty blocks , initially proposed for 2-D mesh interconnects [15], where faults are constrained in disjointedrectangular regions. Such FBs can contain “victimized” non-faulty nodes that are marked as unsafe and are hence unreach-able, so as to maintain FB convexity and facilitate simpler FTrouting; node classifiers also include safe (i.e., healthy), faulty ,and boundary nodes (that are healthy) spanning the peripheryof FBs. We assume that the input GW identifies faulty nodesdynamically, marking the class of each such node. A node isdeclared unsafe according to these two rules: 1) it has twounsafe or faulty 1-hop neighbors, and 2) it has two unsafe orfaulty 1-hop or 2-hop neighbors in two different dimensions.As the two FB examples in Fig. 3 show, a FB comprises fourboundaries, each consisting of two adjacent rows or columns.The reason for having double boundary “lines” is to overcomethe uni-directionality of the network links by including two“lines” of opposite directions for each boundary. The abovetwo rules ensure that no two FBs can intersect without forminga larger FB. This can be proven by the following theorem.
Theorem 1.
The boundary nodes of a faulty block cannotintersect with another faulty block.Proof.
Assume that node v belongs to FB A . According tothe definition of faulty blocks, v must be an unsafe or a faultynode. Thus, it cannot be a boundary node of any other FB.This proves a contrapositive, which infers that the boundarynode of a specific FB cannot belong to any other FB. C. HSF FT Routing: Turns Employed & Prohibited
To achieve the objectives of designing a FT, distributed,deadlock-/livelock-free, feasible, adaptive, short-route routingalgorithm, the following assumptions are used in this paper:1) only node faults are considered, with all four links at acontroller considered faulty and inoperable, 2) only permanentdynamically-occurring faults detected by the input GW areconsidered (though we assume that no new faults occur duringrouting or FB marking), 3) that faulty nodes can neither resideon the periphery of the CN topology, nor on the row andcolumns adjacent to the network northern, western and easternperipheries, while in addition, faults can neither reside on therow adjacent to the southern periphery nor on the row abovethe former, 4) that the destination nodes always reside outsideof faulty blocks, and 5) no limit to the number of faulty nodesexists as long as assumption 3) holds and that all faults arecontained withing FBs according to FB formation rules.As explained in Section II-B, due to the unidirectionalityof the HSF CN links and the positioning of the two GWs,directives (and ACKs) collectively route toward the north-east(NE) direction, and rarely span westbound links. Hence goingsouth comprises the last resort routing direction. As such,and in tandem with the well-defined convex FBs proposedin Section II-B, and using the deadlock-avoidance blueprintdictated by the Turn Model of adaptive routing [16], whereat least a turn in the clockwise and anti-clockwise routingdirections is forbidden so as to eliminate deadlock-inducing ° turns in the absence of virtual channel usage, we prohibitsouth-west (SW) and south-east (SE) turns altogether, to form south-last (SL) routing as shown in Fig. 4. SL is regarded asa subset of the XY-YX RA (see Section II-A) in the widercontext, hence once a fault appears in the CN essentially our topology-agnostic RA becomes tighter. Specifically, we blockSW turns on odd row and column intersections, and SE turnsat odd columns intersecting with even rows; the only timea packet turns south for a last one-hop traversal is when thedestination is on an odd column and an odd row; ACKs remainunaffected as they always also route in the NE direction.The strong coupling of said FBs and the SL RA schemeproduces a deterministic, distributed and more importantlya provably deadlock-/livelock-free FT routing mechanism.Deadlock-freedom can be proven either using theorems suchas the ones formulated by Duato [14], [17] which are basedon set theory, or by using brute-force simulations; both werecarried out and omitted here for brevity. To showcase theworkings of our HSF CN algorithm we make use of theexample demonstrated in Fig. 5. A packetized directive (redroute) is inserted in the CN via the input GW at coordinates( x = 0 , y = 0 ) heading toward destination node (yellow star) at( , ). Due to the distributed nature of our FT routing schemeand based on the rules outlined in Section II-A it makes aneast-north (EN) turn at ( , ) where it encounters the boundaryof the first FB at ( , ); it then misroutes two hops to thewest (left) after a north-west turn and then routes along theperiphery of the FB, eventually making an EN turn at (2,4)toward its destination. Node ( , ) then creates an ACK packetwhich is routed to the ACK GW (blue line), making an ENturn once the boundary of the second FB is met at ( , ). Itthen routes along the periphery of the same FB until it issuccessfully received by the ACK GW. No turn rules wereviolated, hence deadlock-freedom in routing is established.
1) Deadlock Avoidance with Super-Faulty Blocks (SFBs):
In some cases, the specific overlap of FBs can result in adeadlock/livelock-inducing situation. These cases occur whenthe northern boundary of a southern FB overlaps the southernboundary of a northern FB. In such scenario, packets breakSL routing algorithm turn rules by taking a south-eastboundturn. The example of Fig. 6 shows a relevant problematic casewhere the routed directive makes a last south-east turn to reachits destination. In order to overcome this problem, such overlapof two FBs is eliminated by victimizing the overlappingboundary nodes, thus merging the overlapping FBs to form aso-called “super-FB.” This renders the combined FB a convexregion, as shown in Fig. 6-(b) where said super-FB ruleswere applied, making SL routing now feasible. Note thatany overlap between FB boundaries other than northern withsouthern induces no SL routing turn violations. In addition,if the overlapping FBs have the same width and are exactlyon top of each other, i.e., each FB starting on the same leftnetwork column and ending on the same right network column,then such an overlap does not induce any routing deadlocks.III. P
ERFORMANCE E VALUATION
We evaluate the proposed FT routing algorithm by utilizinga custom-coded simulator built using the AnyLogic Toolplatform to model the unique characteristics of the HSFCN system, i.e., its asynchronous operation. We employ a × HSF CN network (Fig. 2 shows a × topology)consistent with the design guidelines of [18]. Beyond that,we consider all design and operational assumptions describedin Section II-C. Two fault distribution models are considered: A C K G W I npu t G W A C K G W I npu t G W (a) (b) Fig. 6:
Routing turns violation: problematic overlap of faulty blocks.
Percentage of faulty nodes A v g . hop c oun t p e r p acke t Random faults (RF)Clustered faults (CF)
Fig. 7:
Average per-packet hop count vs. percentage of faulty nodes. F r a c t i o n o f p a t h s ( % ) Percentage increase in hop count
Fig. 8:
Path length hop count distribution at random faults. Random Faults (RF) and spatially Correlated Faults (CF, orclustered) placements. RFs involve a per-node probability offailure p f , while CFs are modeled using a spatially-dependentfailure model such that nodes closer to a faulty node are morelikely to also fail. To begin fault allocation under CF, a seednode is randomly chosen, while its neighboring nodes areassigned failure probabilities based on the Euclidean distance d e according to the function P cf = d e ∗ p f ; hence a clusterof faulty nodes surrounds the seed node. Due to the mathmodeling differences between the CF and RF distributions, wepicked distinct < p f < values for each distribution at everysimulation iteration, to ensure the same percentage of totalfaulty nodes in each for fair comparisons. Persistent unicasttraffic is generated by the input GW, i.e., data is sequentiallyinjected - once the first receiving node at coordinates ( x =0 , y = 0 ) is freed then another packet is immediately injectedinto the CN. When a packet is received by a node destination,an ACK packet is generated by the preceding node, and isthen routed toward the ACK GW. In every simulation run, apacket is sent to each healthy node; such simulations arerepeated for each p f value and fault distribution, albeit eachcomprising a unique faulty node pattern, and then averaged toproduce a single result point. Delivery reliability is assessed interms of the fraction of network nodes that are healthy, and assuch, guaranteed by our proposed FT RA to receive packetizeddirectives addressed to them, as they neither constitute faultynor unsafe (i.e., victimized) nodes. Our performance metricsfocus on the average routing hop count as a function of faultynode count and FB area size. A. Simulation Results
Fig. 7 depicts the average per-packet hop count of directives delivered to healthy nodes only increasing under the RFand CF scenarios, albeit at a rather slow pace, as a greaterpercentage of network nodes fail. This gradual rate is due to
Number of faulty nodes N u m b e r o f nod es Faulty and victimized nodes - RFFaulty and victimized nodes - CFFaulty block boundary nodes - RFFaulty block boundary nodes - CF
Fig. 9:
Faulty and victimized node counts, FB boundary node countsvs. total network node faults under the RF and CF scenarios. the fact that most route lengths remain unaffected with thepresence of FBs, as they convey packets to destinations thatreside north of FBs under the guidance of the proposed FT RAwith a north-east biased directionality. Also, due to the locationof the two GWs and said nature of routing scheme employed,only the horizontal width, and not the vertical height, of FBscontributes to the elongation of path lengths. With . faultynodes or more, the RF distribution curve wiggles due to theidiosyncrasies exhibited between FB boundary lengths, totalfaulty and unsafe node counts, and FB numbers and their totalarea size, as a result of the factorial growth of the sample spaceat increasing fault counts. Collectively, as Fig. 8 shows, FBformations impact a fraction of paths, where ∼ of pathlengths under the RF distribution with faulty nodes (the CFdistribution behaves similarly) remain unaffected. Notably, theoverall trend depicted in Fig. 8 was also observed at granularscales, each covering a specific percentage of faulty nodesunder both the RF and CF distribution scenarios.The degree of victimization is assessed in Fig. 9 whichdepicts unreachable node sums (i.e., faulty, victimized andFB boundary) as a function of faulty node counts, for theRF and CF scenarios . It is observed that at an average . total faulty nodes, and of all nodes are spanned bythe proposed FT algorithm under the respective RF and CFscenarios; these values constitute acceptable HSF functionalitythat is tolerant to some directives loss [12]. Moreover, Fig. 9depicts the CF case performing worse in terms of the faultyand victimized node counts relative to the RF case, up untila mid-level of faulty node value of ∼ . . This is due tothe formation of a large FB(s) under CF, as opposed to morescattered and smaller FBs produced under the RF scenariowhich causes in-between FB manoeuvring of packets to spanlonger paths. This trend is further exemplified pictorially inFig. 10, where an almost comparable number of faults forboth fault models is considered: for RF and under CF.Despite this, the number of unsafe nodes differs significantly,with nodes victimized under CF, whereas only nodesbecome unsafe in the RFs case. However, due to the scatteredpattern of FBs under RF, a larger number of boundary nodesis often produced; this backs the overall trend of the proposedFT algorithm in performing better under the CF vs. RF cases.IV. C ONCLUSIONS AND F UTURE W ORK
We proposed a deterministic FT deadlock-/livelock-freerouting protocol that delivers configuration directives to con- To maintain deadlock-freedom, the boundary nodes can convey packetsbut cannot serve as destination nodes (see Section II-C).
Fig. 10:
Clustered faults (left) and random faults block formations. nected nodes in an asynchronously-operating irregular near-Manhattan HSF CN. To construct a reasonable protocol givenultra-limited resources, faults are contained in a set of dis-jointed rectangular regions, FBs. Simulation results demon-strate the feasibility of the proposed FT protocol under twofault distribution scenarios. Future work involves the devel-opment of enhanced routing-interconnect geometry rules tofurther minimize the number of victimized nodes.A
CKNOWLEDGEMENT
This work was supported by the European Union’s Horizon2020 research and innovation programme-Future EmergingTopics under grant agreement No 736876 and Cyprus Re-search & Innovation Foundation: HSadapt, COMPLEMEN-TARY/0916/0008, project.R
EFERENCES[1] Q. Nadeem et al. Large intelligent surface assisted mimo communica-tions. arXiv preprint arXiv:1903.08127 , 2019.[2] E. Basar and I. F. Akyildiz. Reconfigurable intelligent surfacesfor doppler effect and multipath fading mitigation. arXiv preprintarXiv:1912.04080 , 2019.[3] C. Liaskos et al. Design and development of software defined metama-terials for nanonetworks.
IEEE CAS Magazine , 15(4):12–25, 2015.[4] X. Tan et al. Enabling indoor mobile millimeter-wave networks basedon smart reflect-arrays. In
IEEE INFOCOM 2018 , pages 270–278.[5] C. Liaskos et al. On the network-layer modeling and configurationof programmable wireless environments.
IEEE/ACM Transactions onNetworking , 27(4):1696–1713, 2019.[6] S. Abadal et al. Computing and communications for the software-definedmetamaterial paradigm: A context analysis.
IEEE Access , 5:2169–3536,2017.[7] A. Pitilakis et al. Software-defined metasurface paradigm: Concept,challenges, prospects. In
METAMATERIALS’18 , pages 483–485, 2018.[8] A. Tasolamprou et al. Intercell wireless communication in software-defined metasurfaces. In
ISCAS’18 - Special Session , 2018.[9] D. Kouzapas et al. Towards fault adaptive routing in metasurfacecontroller networks.
JSA , 106(101703), 2020.[10] Petrou et al. Asynchronous circuits as an enabler of scalable andprogrammable metasurfaces. In proceedings of the ISCAS , pages 1–5.IEEE, 2018.[11] D. Rostislav et al. An asynchronous router for multiple servicelevels networks on chip. In , pages 44–53. IEEE, 2005.[12] H. Taghvaee et al. Error analysis of programmable metasurfaces forbeam steering.
IEEE Journal on Emerging and Selected Topics inCircuits and Systems , 10(1):62–74, 2020.[13] M. Radetzki et al. Methods for fault tolerance in networks-on-chip.
ACM Computing Surveys , 46(1):1–38, 2013.[14] J. Duato. A necessary and sufficient condition for deadlock-free adaptiverouting in wormhole networks.
IEEE Transactions on Parallel andDistributed Systems , 6(10):1055–1067, 1995.[15] J. Wu. A Fault-Tolerant and Deadlock-Free Routing Protocol in 2DMeshes Based on Odd-Even Turn Model.
IEEE Transactions onComputers , 52(9):1154–1169, 2003.[16] C. Glass and L. Ni. The Turn Model for Adaptive Routing.
InternationalSymposium on Computer Architecture (ISCA) , pages 276–287, 1992.[17] J. Duato, S. Yalamanchili, and Ni L.
Interconnection Networks: AnEngineering Approach . Morgan Kaufmann Publishers Inc., 2002.[18] H. Taghvaee et al. Scalability analysis of programmable metasurfacesfor beam steering. arXiv preprint arXiv:2004.06917arXiv preprint arXiv:2004.06917