A Lightweight, Non-intrusive Approach for Orchestrating Autonomously-managed Network Elements
11 A Lightweight, Non-intrusive Approach forOrchestrating Autonomously-managed NetworkElements
Christos Liaskos,
Member, IEEE
Abstract —Software-Defined Networking enables the centralizedorchestration of data traffic within a network. However, proposedsolutions require a high degree of architectural penetration. Thepresent study targets the orchestration of network elements that donot wish to yield much of their internal operations to an externalcontroller. Backpressure routing principles are used for deriving flowrouting rules that optimally stabilize a network, while maximizingits throughput. The elements can then accept in full, partially orreject the proposed routing rule-set. The proposed scheme requiresminimal, relatively infrequent interaction with a controller, limitingits imposed workload, promoting scalability. The proposed schemeexhibits attracting network performance gains, as demonstrated byextensive simulations and proven via mathematical analysis.
Index Terms —software-defined networking, traffic engineering,backpressure routing.
I. I
NTRODUCTION S OFTWARE-Defined Networking can imbue the network man-agement process with an unparalleled level of state monitoringand control. The ability to migrate the routing elements of anetwork from closed, static hardware solutions towards an open,re-programmable paradigm is expected to promote significantlythe adaptivity to demand patterns, eventually yielding a healthyand constant innovation rate. The OpenFlow protocol and assortedhardware [1], which enables an administrative authority to cen-trally monitor a network and deploy fitting routing strategies, hasproduced significant gains in a wide set of application scenarios[2], [3].Nonetheless, SDN-enabled traffic engineering (TE) approachesare presently characterized by a high degree of architectural pen-etration. Each networking element must yield its inner operationto a remote, central controller. While this assumption is validfor networks managed by the same authority (e.g. [2], [4]), itposes an issue for networks comprising self-managed elements.Furthermore, related solutions may come at a high capital cost,requiring multiple powerful controllers to cover a network [5], aswell as a high operational cost, incurred by the need for closeinteraction between the network elements and the controller [6],which naturally translates to traffic overheads. These concerns,combined with point-of-failure and security considerations [7], candiscourage self-managed elements for adopting or even trying anSDN-based, central traffic orchestration.The present study claims that a lightweight TE solution is inneed in order to demonstrate the gains of SDN-enabled collabora-tion and gradually convince self-managed elements to participate
C. Liaskos is with the Aristotle University of Thessaloniki, Department ofComputer Science, GR-54124, AUTH Campus, Greece and with the Foundationfor Research and Technology Hellas (FORTH), Institute of Computer Science,N. Plastira 100, Vassilika Vouton, GR-70013 Heraklion, Crete, Greece. e-mails:[email protected], [email protected]. further. The methodology consists of applying the principles ofBackpressure routing [8] to a backbone network of self-managednodes, deriving stability-optimal flow routing rules. Nodes thatchoose to participate to the proposed scheme initially inform acentral controller of their aggregate, internal congestion states. Inreturn, they receive the aforementioned rule set in the form of aproposal. Apart from its simplicity and ability to respect peeringagreements, the proposed scheme also fills a theoretical gap in therelated work, offering analytically -proven throughput optimalityand network stabilization potential.II. R
ELATED W ORK
Studies on traffic engineering in networks, whether SDN-enabled or not, target the real-time grooming of data flows, inorder to provide the best possible quality of service on a givenphysical infrastructure. To this end, maximizing the network’sthroughput has constituted a prominent goal. MicroTE [9], Hedera[10] and Mahout [11] focus on the detection and special handlingof large "elephant" flows, under the assumption that they constitutethe usual suspects of congestion.When a large flow is detected, it istreated as a special case, and it is assigned a separate path, whichdoes not conflict with the bulk of the remaining traffic. Theseschemes require constant monitoring of the network’s state, whichis achieved by scanning the network for large flows via periodicpolling (at the scale of sec ), raising SDN controller scalabilityand traffic overhead concerns. They differ, however, in where thescanning takes place. Hedera constantly scans the edge switchesof the network, requiring less nodes to visit but more flows pernode to scan. Mahout scans the hosts, scanning on average morenodes than Hedera, but with less flows to be monitored per node.Finally, MicroTE relies on push-based network monitoring, withnodes posting periodically their state to the controller.Companies have also invested in SDN-powered solutions foroptimizing their proprietary networks, within or among data-centers. Emphasis is placed on prioritizing the applications andflows that compete for bandwidth, based on their significanceor operational requirements. B4 [4] incorporates this concern bykeeping tuples of source, destination and QoS traits per networkflow. The network’s resources are constantly monitored and theflows are assigned paths according to their priority, breakingties in a round-robin manner. Microsoft’s SWAN [2] considersclasses of priorities, pertaining to critical-interactive, elastic andbackground traffic. Resources are first assigned per priority class.Within each coarse assignment, a max-min fairness approach isused to distribute resources to specific flows. Bell Labs propose amore direct approach, seeking to solve the formal link utilizationproblem, given explicit flow requests [3]. Other studies focus onscenarios such as partially SDN-controlled networks, or advancingthe efficiency of multipath routing beyond classic approaches [12],exploiting the monitoring capabilities of OpenFlow [13], [14]. a r X i v : . [ c s . N I] N ov Differentiating from the outlined studies, the present workproposes a SDN-enabled traffic engineering approach that isconsiderably more lightweight in terms of overhead, as well asless intrusive in terms of architecture. Its goal is to encourage cen-tralized, SDN-based orchestration among autonomously managednetworked elements. The proposed scheme is throughput-optimal,yields minimal interaction with the controller and minimal numberof required flow rules.III. P
REREQUISITES AND S YSTEM M ODEL
An important term in networking studies is the notion of network stability . It is defined as the ability of a routing policy tokeep all network queues bounded, provided that the input load iswithin the network’s traffic dispatch ability, i.e. within its stabilityregion . With U ( n,c ) ( t ) denoting the aggregate traffic accumulatedwithin a network node n at time t , destined towards node c ,stability is formally defined as [15, p. 24]: lim sup τ → + ∞ τ τ (cid:88) t =1 E (cid:8) U ( n,c ) ( t ) (cid:9) < ∞ , ∀ n, c (1)where τ is the time horizon and E {∗} denotes averaging overany probabilistic factors present in the system.A well-developed framework for deducing network stabilityunder a given network management policy is the Lyapunov Driftapproach. It defines a quadratic function of the form: L ( t ) = (cid:88) ∀ n (cid:88) ∀ c U n,c ) ( t ) (2)The goal is then to deduce the bounds of ∆ L ( t ) = E { L ( t + T ) − L ( t ) } , which describes the evolution of the net-work queue levels over a period T . The Lyapunov stability theorem states that if it holds: ∆ L ( t ) ≤ B − (cid:15) · (cid:88) ∀ n (cid:88) ∀ c U ( n,c ) ( t ) (3)for two positive B, (cid:15) quantities, then the network is stable andaverage queue size of inequality (1) is bounded by B / (cid:15) instead ofdrifting towards infinity.The backpressure algorithm (BPR) defines a joint scheduling-routing algorithm that complies with the stability criteria ofinequality (3) and, most importantly, has been proven to bethroughput optimal [16]. Its goal is to minimize the lower bound of ∆ L ( t ) , ∀ t , effectively suppressing the average queue level withinthe network. The analytical approach, followed by related studies[17], is based on the queue dynamics expressed by the followingrelation: U ( n,c ) ( t + T ) = max (cid:26) , U ( n,c ) ( t ) − O t → t + T ( n,c ) (cid:27) + I t → t + T ( n,c ) + G t → t + T ( n,c ) (4)where O t → t + T ( n,c ) , I t → t + T ( n,c ) and G t → t + T ( n,c ) denotes outgoing, incomingand locally generated data at time interval t → t + T . The usualmethodology then dictates a series of relaxations of the right partof eq. (4), based on the following inequalities: O t → t + T ( n,c ) ≤ (cid:88) l : source ( l )= n (cid:90) t + Tt µ ( c ) l ( t ) · dt (5) I t → t + T ( n,c ) ≤ (cid:88) l : destination ( l )= n (cid:90) t + Tt µ ( c ) l ( t ) · dt (6) C BDA E F CONTROL PLANE
Priority Rules (BPR)Standard Routing Rules (any)Data Routing at "C" {μ ΑΒ , μ ΒΑ } U E,A (t)U
B,A (t) U
F,A (t)
Alarm
Threshold
Priority rule
Figure 1. The employed system setup. A network of autonomously managedelements, A-F, uses Backpressure-derived flow rules on top of its standard routingscheme, in order to mitigate congestion events. A centralized control planeorchestrates the operation of the system. where µ ( c ) l ( t ) is the maximum allowed bitrate over a network link l carrying traffic destined to node c . Squaring both sides of eq.(4) and incorporating relaxations (5), (6), as well as the identity: V ≤ max { , U − µ } + A ⇒ V ≤ U + µ + A − U · ( µ − A ) (7)one derives an inequality of the form of relation (3). Furtherrelaxation by substituting all µ ( c ) l and G t → t + T ( n,c ) with maximumallowed values yields compliance with the Lyapunov stabilitytheorem. Furthermore, it is deduced that the upper bound ofrelation (3) can be minimized when maximizing the quantity: (cid:88) ∀ n,k,c µ ( c ) l : source ( n ) → dest ( k ) ( t ) · (cid:0) U ( n,c ) ( t ) − U ( k,c ) ( t ) (cid:1) (8)The standard backbressure routing process, summarized for refer-ence as the SBPR Algorithm, expresses the optimization pursuitof relation (8). According to SPBR, at timeslot t → t + T , eachnetwork link l must carry data towards node c ∗ l , such that: c ∗ l ← argmax c { U ( c ) source ( l ) ( t ) − U ( c ) dest ( l ) ( t ) } (9)Bidirectional links are considered as two separate unidirectionallinks. Originally meant for use in wireless ad hoc networks,the BPR process and its variants have found extensive use inpacket switching hardware and satellite systems due to theirthroughput optimality trait [17]. SBPR variants have adoptedlatency considerations as well. Most prominently, authors in [18]restrict the node selection step (9) of SBPR only within a subset oflinks that offer a bounded maximum number of hops towards thetarget. Other studies have shown that simply altering the queueingdiscipline from FIFO to LIFO yields considerable latency gains[19]. Finally, it is worth noting that SBPR can be easily madeTCP compatible [20]. A. System Model
The present paper studies the use of BPR-variants in backbonenetworks. The assumed setup, given in Fig. 1, considers a networkcomprising autonomously managed elements. A node can repre-sent a single physical router or a complete subnetwork, providedthat it supports a self-inspecting mechanism for monitoring itsinternal congestion levels, as well as support a flow-based routingscheme. The nodes are connected with links of known, time-invariant bandwidth and can be asymmetric or unidirectional with no restriction. Due to this assumption, the notation µ ( n,c ) ( t ) issimplified to µ ( n,c ) . Data is classified by the originating networkidentifier (e.g. A ), with no further sub-categorization.The formed network may have any traffic-invariant trafficpolicy, such as distance vector or shortest path routing. The BPRapproach operates on top of the underlying routing scheme and isenforced by a centralized controller, which can receive node stateinformation and propose the installation of priority flow rules. Anexample is shown in Fig. 1. At time moment t , the controllerhas assembled a snapshot of the network’s state and notices that U ( F,A ) ( t ) at node F exceeds a predefined alarm threshold. A BPR-variant is executed, which deduces that traffic from F towards A should better be offloaded to neighboring node E for the timebeing. A corresponding routing instruction is given to node F ,which takes precedence over all other routing rules pertaining tolink l F E . Operation is then resumed until the next network statesnapshot is received.OpenFlow-based solutions are most prominent candidates forthe control plane and the interaction with the network nodes [1].In this case, network monitoring can be accomplished by severalpolling techniques [21], [22]. Without loss of generality, we willassume that the controller obtains a consistent network state withperiod T [23].Peering agreements and routing preferences among nodes arealso allowed. For example, returning to the example of Fig. 1,the controller would not propose the illustrated flow rule if itwas disallowed by the peering policy/agreement between F and E . In other words, when the BPR-variant searches for neighbors s ∈ S : { U ( s,A ) ( t ) < U ( F,A ) ( t ) } , the search is assumed to belimited to nodes that comply to any form of policy, preference ofagreement.Finally, targeting minimal controller load, we allow for at mostone priority flow rule per physical network link.IV. A NALYSIS
We begin the analysis by simplifying the RHS of relation(6), based on the fact that the network links have time-invariantbandwidth: I t → t + T ( n,c ) ≤ (cid:88) l : d ( l )= n (cid:90) t + Tt µ ( c ) l dt = T · (cid:88) l : d ( l )= n µ ( c ) l (10)The RHS of relation (5) is simplified even further, given that alltraffic from a node n towards a given destination c is served bya single outgoing link, regardless of the enforcement of any BPRpriority rules: O t → t + T ( n,c ) ≤ (cid:88) l : s ( l )= n (cid:90) t + Tt µ ( c ) l dt = T · µ ( c ) l nb ( n ) (11)where b ( n ) is a neighboring node of n complying with anybilateral agreements. Furthermore, applying identity (7) to eq. (4)produces: U n,c ) ( t + T ) ≤ U n,c ) ( t )+ (cid:104) O t → t + T ( n,c ) (cid:105) + (cid:104) I t → t + T ( n,c ) + G t → t + T ( n,c ) (cid:105) − · U ( n,c ) ( t ) · (cid:104) O t → t + T ( n,c ) − I t → t + T ( n,c ) − G t → t + T ( n,c ) (cid:105) (12) Using the updated relaxations (10) and (11) and setting ∆ U n,c ) ( t ) = U n,c ) ( t + T ) − U n,c ) ( t ) for brevity: ∆ U n,c ) ( t ) ≤ T · (cid:16) µ ( c ) l nb ( n ) (cid:17) + T · (cid:88) l : d ( l )= n µ ( c ) l + G t → t + T ( n,c ) − · U ( n,c ) ( t ) · T · µ ( c ) l nb ( n ) − T · (cid:88) l : d ( l )= n µ ( c ) l − G t → t + T ( n,c ) (13)It is not difficult to show that the RHS of inequality (13) can bereorganized as: ∆ U n,c ) ( t ) ≤ T · (cid:88) l : d ( l )= n µ ( c ) l + U ( n,c ) ( t ) + G t → t + T ( n,c ) + (cid:104) T · µ ( c ) l nb ( n ) − U ( n,c ) ( t ) (cid:105) − · U n,c ) ( t ) (14)Summing both sides ∀ n, c and reminding that ∆ L ( t ) = (cid:80) ∀ n (cid:80) ∀ c ∆ U n,c ) ( t ) : ∆ L ( t ) ≤ (cid:88) ∀ n (cid:88) ∀ c T · (cid:88) l : d ( l )= n µ ( c ) l + U ( n,c ) ( t ) + G t → t + T ( n,c ) B ) + (cid:88) ∀ n (cid:88) ∀ c (cid:104) T · µ ( c ) l nb ( n ) − U ( n,c ) ( t ) (cid:105) A ) − · (cid:88) ∀ n (cid:88) ∀ c U n,c ) ( t ) (15)We proceed by considering the RHS of relation (15) as a func-tion of the BPR-derived routing decisions µ ( c ) l nb ( n ) and attempt astraightforward optimization. The µ ( c ) l nb ( n ) can be initially treatedas continuous variables. Once optimal values have been derived,they can be mapped to the closest of the actually available optionswithin the network topology. The sufficient conditions for thepresence of a minimum are: ∂RHS (14) ∂µ ( c ) l nb ( n ) = 0 ( a ) , H ∂RHS (14) ∂µ ( c ) l nb ( n ) · ∂µ ( c ) l kb ( k ) ∈ R + ( b ) (16)where k denotes a node, H is the Hessian matrix [24] and the < H < ∞ refers to each of its elements. From condition (16-a)we obtain: T · (cid:88) l : d ( l )= b ( n ) µ ( c ) l + µ ( c ) l nb ( n ) − (cid:104) U ( n,c ) ( t ) − (cid:16) U ( b ( n ) ,c ) ( t ) + G t → t + T ( b ( n ) ,c ) (cid:17)(cid:105) = 0 , ∀ n, c (17)For condition (16-b), it is not difficult to show that it is satisfieddue to: ∂RHS (15) ∂µ ( c ) l nb ( n ) · ∂µ ( c ) l kb ( k ) ∝ T > , ∀ n, k (18)Equation (17) represents a generalization over the SBPR Algo-rithm, which operates by equation (9). At first, the eq. (17) definesa linear system with discrete variables µ ( c ) l nb ( n ) and can be solved assuch. However, interesting approximations can be derived, which also exhibit the dependence of the optimal solution from thenetwork topology and traffic statistics.Firstly, the term T · (cid:34) (cid:80) l : d ( l )= b ( n ) µ ( c ) l + µ ( c ) l nb ( n ) (cid:35) represents theaggregate, transit traffic served by node b ( n ) , i.e. the neighborof n that will be the recipient of traffic destined towards c . Anode may assume transit duties in the network, either due to itsbusiness logic, or due to its central placement in the topology. Onthe other hand, the term (cid:104) U ( n,c ) ( t ) − (cid:16) U ( b ( n ) ,c ) ( t ) + G t → t + T ( b ( n ) ,c ) (cid:17)(cid:105) refers to the role of node b ( n ) as generator of new traffic. Thequantity G t → t + T ( b ( n ) ,c ) also introduces dependence from traffic predic-tion. Indeed, at time t the controller must obtain an approximationof the traffic that will be generated at node b ( n ) within theinterval [ t, t + T ] . In other words, equation (17) introduces acomparison between the transit and content provider aspects of thenetwork nodes, requiring equally balanced roles. This conclusionis summarized in the following Lemma. Lemma 1.
Network-wide optimization of throughput requiresrouting decisions that equalize the transit and content providerroles of the nodes.
Assuming a network of nodes where data transit prevails overcontent generation per node, it will hold: (cid:88) l : d ( l )= b ( n ) T (cid:16) µ ( c ) l + µ ( c ) l nb ( n ) (cid:17) > U ( n,c ) ( t ) − (cid:18) U ( b ( n ) ,c ) ( t ) + G t → t + T ( b ( n ) ,c ) (cid:19) (19)for all n, c . In this case, the best approach for approximatelyupholding equation (17) is to maximize the quantity ∆ ( n,c ) ( t ) = (cid:104) U ( n,c ) ( t ) − (cid:16) U ( b ( n ) ,c ) ( t ) + G t → t + T ( b ( n ) ,c ) (cid:17)(cid:105) (20)which depends on the traffic generated locally at node n ( b ) during [ t, t + T ] . In other words, the throughput-optimizing routingdecision at node n , regarding traffic destined to node c are derivedas follows: n ∗ = argmax b ( n ) (cid:8) ∆ ( n,c ) ( t ) (cid:9) (21)where n ∗ is the optimal neighboring node of n to offload datatowards c .We notice that the transit assumption of (19) is also implied bythe SBPR Algorithm. Specifically, SBRP implies that G t → t + T ( b ( n ) ,c ) isuniform for all nodes in the network, reducing equation (21) to (9).This limitation is alleviated by the proposed, Foresight-enabledBackpressure Routing (Algorithm 1) which targets backbonenetworks, where the transit assumption of relation (19) is expectedto hold.Line of the proposed Algorithm reflects the outcome ofequation (21). Inspired by [18], we note that line only considerspossible nodes c towards which the number of hops does notincrease over link l . This approach favors latency and disal-lows routing loops. If an alarm level is defined, the search inline is restricted further within c : U ( c ) n ≥ alarm _ level .The visited [ . ] array is also introduced, to make sure that eachpossible destination is routed via one link at most, at eachnode. The optimization of line pertains to the treatment ofmulti-links that may exist in the network. Assume a triple link M = { l : µ , l : µ , l : µ } and a corresponding set of c ∗ l ( t ) assignments A = (cid:8) c ∗ l ( t ) , c ∗ l ( t ) , c ∗ l ( t ) (cid:9) . Line refers to theoptimal reordering of the assignments out of all possible M × A Algorithm 1
The proposed Foresight-enabled Backpressure Rout-ing algorithm. procedure FBPR( network _ state ( t = mT | m ∈ N ) ) for each node n do (cid:46) Define priority flows. visited [ c ] ← , ∀ c for each link l : source ( l ) = n do c ∗ l ( t ) ← argmax c :! visited [ c ] { U ( c ) n − ( U ( c ) d ( l ) + G t → t + T ( d ( l ) ,c ) ) } visited [ c ∗ l ( t )] ← ∆ Q ∗ l ( t ) ← max { , U ( c ∗ l ( t )) n − U ( c ∗ l ( t )) d ( l ) } end for end for (cid:46) Consider multi-links, if any. µ ∗ ( t ) ← argmax µ (cid:80) ∀ l µ l · ∆ Q ∗ l ( t ) for each link l : ∆ Q ∗ l ( t ) > do Deploy rule { f rom : s ( l ) , to : c ∗ l ( t ) , via : l } . end for return end procedure combinations and for each multi-link of the network, maximizingthe expected throughput. Finally, lines − install the FBPR-derived priority rules to the corresponding nodes. Corollary 2.
FBPR is throughput-optimal.
We notice that the preceding analysis takes place before therelaxation of equation (8) of the classic analytical procedure.Applying this final relaxation to equation (15) leads to compliancewith the Lyapunov stability criterion (relation (3)) to the proof ofthroughput optimality, as detailed in [16].V. S
IMULATIONS
In this Section, the performance of the proposed schemesis evaluated in various settings, in terms of achieved averagethroughput, latency and traffic losses. Specifically, the ensuingsimulations, implemented on the AnyLogic platform [25], focuson: i) The performance and stability gains arising from the com-bination of BPR-based and Shortest Path-based (OPSF) policies,ii) The gains of Foresight-enabled BPR over its predecessors.The simulations assume autonomously managed nodes,arranged in a × grid. Each node n ij , i = 1 . . . , j = 1 . . . isconnected to its four immediate neighbors, n i +1 ,j , n i − ,j , n i,,j +1 , n i,,j − , where applicable. This type of topology is chosen toensure a satisfactory degree of path diversity, i.e. a good choiceof alternative paths to connect any two given nodes. We notethat path diversity is a prerequisite for efficient traffic engineeringin general. Each link connecting two nodes is bidirectional with GBps bandwidth at each direction.Given that packet-level simulation of backbone networks in noteasily tractable in terms of simulation runtimes [10], [11], weassume slotted time ( sec slot duration) and traffic organized in M B -long batches. At each slot, a number G ij of batches isgenerated at each node, expressing concurrent traffic generatedfrom multiple internal users. The destination of each batch ischosen at random (uniform distribution). Then, traffic batches aredispatched according to the routing rules and the channel rates.Each node is assumed to keep track of its internal congestion leveland push it with report/actuation period T to a central controller(e.g. like [9]). G ij and T are set or varied per experiment. A node is assumed to reject/drop incoming or generated traffic whenit has more than batches on hold, using a single queuemodel. Finally, the BPR schemes are enabled on a node wherethe number of batches on hold exceed a certain alarm level ,set per experiment. The alarm _ level can also be perceived as aparameter that defines whether the adoption of the BPR priorityflow rules is partial or global.When enabled, the BPR-derived routing rules handle the en-queued batches in a LIFO manner, as advised in [19]. Thisholds for both SBPR and FBPR in the ensuing comparisons.The Open-Shortest-Path-First (OSPF) approach is used as theunderlying DVR routing scheme in all applicable cases. Finally,while F BP R − OSP F is loop-free due to the described, hop-based filtering at line of Algorithm 1, the routing rules proposedby SBP R − OSP F may create loops. Therefore, a pairwise checkis performed among the nodes for the detection of loops. If oneexists, the specific BPR-derived priority routing rules that causedit are filtered-out and are not forwarded to the nodes.Figure 2 illustrates the performance of pure
OSP F (no over-layed BPR),
SBP R − OSP F and
F BP R − OSP F , for varyingnetwork load. The x-axis corresponds to the number of batchesgenerated at each node per second, G , which is uniform forall nodes ( G ij = G, ∀ i, j ). A load of batches per secondcorresponds to M Bps data generation rate. For a node beingserviced by four outgoing channels of GBps each, this translatesto a channel over-subscription rate with regard to localusers only. At G = 20 batches per second, the ratio rises to . The actuation period, T is set to sec and the alarmlevel is of the buffer size. In terms of batch latency, Fig.2a shows that the proposed F BP R − OSP F approach offers thebest latency times, even over OSPF, until G ≈ batches/sec. Atthat point, OSPF-pure offers better latency, at the expense of anexcessive traffic overflow rate (Fig. 2b). As expected, droppingmuch of the flowing traffic benefits the delivery times of the“surviving” traffic. However, all BPR-based schemes are ableto sustain operation with a limited overflow rate, even undermaximal load. In other words, the stability of the system is clearlyincreased with the use of the BPR class of routing schemes. Thisphenomenon is also evident from the throughput plot of Fig.2c. OSPF-pure offers the worst performance, since it leads toqueue build-up and high overflow rate. On the other hand, theproposed F BP R − OSP F offers significantly improved results.Nonetheless,
SBP R − OSP F offers the maximum throughput inall cases. However, given its performance in term of latency, thesuperiority in raw throughput is clearly not useful and is owed tobatches traveling via excessively long routes within the network[18].We proceed to study the benefits of endowing BPR withforesight. In Fig. 3, the batch generation rate per node is setrandomly at G ij = G ± v · G (uniform ditribution) where v is a percentage ranging from to . Notice that, in theprevious experiment, FBPR and SBPR where equivalent from theaspect of foresight, due to the constant G values over all nodes.The alarm level is kept at of the buffer size and T is variedfrom to sec. Each point in Fig. 3 is derived as the averageover simulation iterations. Since the goal of the comparisonis to deduce the gains derived from foresight, perfect knowledgeof G ij is passed to F BP R − OSP F . Furthermore, for fairnessreasons, the latency-favoring, hop-based node filtering of FBPR (a) Achieved average batch delivery times.(b) Achieved average batch overflow rates.(c) Achieved average throughput.Figure 2. The comparative performance of the Backpressure-based schemes anda standalone OSPF approach. The alarm level is and actuation period T =5 sec . is discarded. (i.e. line of Algorithm 1 considers all neighbors ofnode n ). Thus, F BP R − OSP F drops any latency considerationsthat could have given an advantage over
SP BR − OSP F fromthis aspect. The performance gains in batch latency and overflowrate are apparent in Fig. 3a and 3b respectively. In general, thebonus of foresight is significant as T increases, since the systemcan make more long-lived routing decisions. The gains are alsoaccentuated for medium to high network loads, where BPR ingeneral makes sense. The trade-off between latency and overflowrates is present in 3a and 3b as well. Finally, the throughputoptimality continues to hold (Fig. 3c) with the slight differencebeing owed to the redundant data traveling produced by SBPR.In other words, having no foresight, SBPR takes decisions thatdistribute the network traffic slightly wider, but lead to higher (a) Average batch delivery times.(b) Average batch overflow rates.(c) Average throughput.Figure 3. The Foresight-enabled backpressure routing yields significant perfor-mance gains compared to the standard backpressure algorithm, while retaining thethroughput-optimality trait. latency and overflow rate in the future.VI. C ONCLUSION
The present study brought Backpressure routing (BPR) andits benefits to the SDN-derived traffic engineering ecosystem. Itsinherited benefits include throughput maximization and optimalstability under increased network load. The BPR and SDN com-bination can offer attractive, lightweight and centrally orchestratedrouting solutions. Minimum cost, non-penetrative approachescould be the key for gradually encouraging cooperation betweendistrustful autonomous parties, with significant gains for the end-users. The presented approach can pave the way for a new classof lightweight traffic engineering schemes that require minimalcommitment from the orchestrated network elements. VII. A
CKNOWLEDGEMENT
This work was funded by the EU project Net-Volution(EU338402) and the Research Committee of the Aristotle Uni-versity of Thessaloniki. R
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