Backpressure with Adaptive Redundancy
(Bwar)
^{†}^{†}thanks: This material is supported in part by the following: NSF grant 1049541, the
Network Science Collaborative Technology Alliance sponsored
by the U.S. Army Research Laboratory W911NF0920053, and King Saud University.
Abstract
Backpressure scheduling and routing, in which packets are preferentially transmitted over links with high queue differentials, offers the promise of throughputoptimal operation for a wide range of communication networks. However, when the traffic load is low, due to the corresponding low queue occupancy, backpressure scheduling/routing experiences long delays. This is particularly of concern in intermittent encounterbased mobile networks which are already delaylimited due to the sparse and highly dynamic network connectivity. While state of the art mechanisms for such networks have proposed the use of redundant transmissions to improve delay, they do not work well when the traffic load is high. We propose in this paper a novel hybrid approach that we refer to as backpressure with adaptive redundancy (BWAR), which provides the best of both worlds. This approach is highly robust and distributed and does not require any prior knowledge of network load conditions. We evaluate BWAR through both mathematical analysis and simulations based on cellpartitioned model. We prove theoretically that BWAR does not perform worse than traditional backpressure in terms of the maximum throughput, while yielding a better delay bound. The simulations confirm that BWAR outperforms traditional backpressure at low load, while outperforming a state of the art encounterrouting scheme (Spray and Wait) at high load.
I Introduction
Queuedifferential backpressure scheduling and routing was shown by Tassiulas and Ephremides to be throughput optimal in terms of being able to stabilize the network under any feasible traffic rate vector [1]. Additional research has extended the original result to show that backpressure techniques can be combined with utility optimization, resulting in simple, throughputoptimal, crosslayer network protocols for all kinds of networks [2, 3, 4, 5, 29]. Recently, some of these techniques have been translated to practically implemented routing and ratecontrol protocols for wireless networks [6, 7, 8, 9, 10].
The basic idea of backpressure mechanisms is to prioritize transmissions over links that have the highest queue differentials. Backpressure effectively makes packets flow through the network as though pulled by gravity towards the destination, which has the smallest queue size of 0. Under high traffic conditions, this works very well, and backpressure is able to fully utilize the available network resources in a highly dynamic fashion. Under low traffic conditions, however, because many other nodes may also have a small or 0 queue size, there is inefficiency in terms of an increase in delay, as packets may loop or take a long time to make their way to the destination.
In this paper, we focus primarily on intermittently connected networks, such as encounterbased mobile networks (sometimes also referred to as delay or disruption tolerant networks (DTN)). In such networks, conventional pathdiscoverybased MANET routing techniques like AODV [11] and DSR [12] are not feasible because the network may not form a single connected partition at any time, and thus a full path may never exist between the source and the destination. Instead, it is necessary to use storeandforward type protocols that can handle the underlying mobility. A backpressure based routing scheme can be easily implemented in such a network, with the decision of what information to exchange being made between each pair of nodes based on their queue differentials whenever they encounter each other. However the abovementioned delay inefficiency of the backpressure mechanism at low traffic loads is further exacerbated in such networks, because they are already delaylimited due to sparse network connectivity.
In the literature on intermittently connected networks, there are several proposed schemes for storeandforward based routing, such as [13, 14, 15, 16, 17, 18]. Some of these, such as Spray and Wait, advocate the use of redundant transmissions, to make additional copies of the communicated information in the network. The replication of the content makes it faster for the destination to access a copy. However, as the additional replication always increases the network load, these protocols, which are not throughputoptimal to begin with, suffer additional congestion.
In this paper, we propose a novel hybrid approach, an adaptive redundancy technique for backpressure routing, that yields the benefits of replication to reduce delay under low load conditions, while at the same time preserving the performance and benefits of traditional backpressure routing under high traffic conditions. This technique, which we refer to as backpressure with adaptive redundancy (BWAR), essentially creates copies of packets in a new duplicate buffer upon an encounter, when the transmitter’s queue occupancy is low. These duplicate packets are transmitted only when the original queue is empty. This mechanism can dramatically improve delay of backpressure during low load conditions due to two reasons: (1) due to the existence of multiple copies of the same packets at multiple nodes, the destination is more likely to encounter a massage intended for it. (2) this way, the algorithm builds up gradients towards the destinations faster and reduces packet looping. The additional transmissions incurred by BWAR due to the duplicates utilize available slots which would otherwise go idle, in order to reduce the delay. Particularly for networks that are not energylimited, this offers a more efficient way to utilize the available bandwidth during low load conditions. In order to minimize the storage resource utilization of duplicate packets, ideally, these duplicate packets should be removed from the network whenever a copy is delivered to the destination. Since this may be difficult to implement (except in some kinds of networks with a separate control plane), we also propose and evaluate a practical timeout mechanism for automatic duplicate removal. Under high load conditions, because queues are rarely empty, duplicates are rarely created, and BWAR effectively reverts to traditional backpressure and inherits its throughput optimality property. By design, BWAR is highly robust and distributed and does not require prior knowledge of locations, mobility patterns, and load conditions.
The following are the key contributions of this work:

We propose BWAR, a new adaptive redundancy technique for backpressure scheduling/routing in intermittently connected networks. And we present a timeout mechanism for duplicate removal, which allows BWAR to be easily implemented in practice.

We develop an analytical model of BWAR, and prove theoretically that it yields a smaller upper bound on the average queue size (and hence the average delay) than traditional backpressure, while retaining throughput optimality.

Through simulations using an idealized cellpartition mobility model, we quantify the benefits from using BWAR. Specifically, we show that it outperforms both traditional backpressure and Spray & Wait [15], a state of the art DTN/ICN routing mechanism.
The rest of the paper is organized as follows. In section II, we introduce and describe BWAR. In section IIIA, we review the theory behind traditional backpressure scheduling and routing. We show in section IIIB the queue dynamics for BWAR and how it can improve the delay theoretically. In section IV we present our modelbased simulation results. In section V, we describe related work in this subject to place our contributions in context. We conclude in section VI and discuss future work.
Ii Backpressure with Adaptive Redundancy
In this section, we first describe traditional backpressure scheduling and routing and then our new proposal for backpressure scheduling/routing with adaptive redundancy (BWAR). In both cases, we assume that there are nodes in the network, and time is discretized. We assume a multicommodity flow system in which every node could be a potential destination (corresponding to a particular commodity).
Iia Traditional Backpressure Scheduling and Routing
We assume that each node maintains queues, one for each commodity, with the queue at each node containing packets that are destined for node . Let indicate the number of packets destined to node queued at node at time . Naturally, . Let be the scheduling and routing variable that indicates the number of packets of commodity to be scheduled on link . Traditional backpressure scheduling/routing [1, 2] selects the that solve the following problem (a form of maximum weight independent set selection):
(1) 
Where is the link weight, which denotes the queue differential for commodity on link at slot and the feasibility constraints on pertain to the available network capacity, taking into account the interference between nodes. is the channel state in terms of number of packets that can be transmitted over link during slot . is the link interference set at slot such that if link interferes with link at slot then and hence, those two links can not be both scheduled at slot . The maximization problem in (IIA) can be solved by finding the maximum commodity for each link at slot that maximizes and assign for all and then solve,
(2) 
IiB BWAR Scheduling and Routing
Our proposed enhancement of backpressure with adaptive redundancy works as follows. We have an additional set of duplicate buffers of size at each node. Besides the original queue occupancy which has the same meaning as in traditional backpressure, the duplicate queue occupancy is denoted by , that indicates the number of duplicate packets at node that are destined to node at time . Again, since destinations need not buffer any packets intended for themselves. The duplicate queues are maintained and utilized as follows:

Original packets when transmitted are removed from the main queue; however, if the queue size is lower than a certain threshold , then the transmitted packet is duplicated and kept in the duplicate buffer associated with its destination if it is not full otherwise no duplicate is created. We found that setting both and to the value of the maximum link service rate is enough and gives superior delay results.

Duplicate packets are not removed from the duplicate buffer when transmitted. They are only removed when they are notified to be received by the destination, or a predefined timeout has occurred.

When a certain link is scheduled for transmission, the original packets in the main queue are transmitted first. If no more original packets are left, only then duplicates are transmitted. Thus the duplicate queue has a strictly lower priority.
Similar to original backpressure scheduling/routing, the BWAR scheduling/routing also requires the solution of a similar maximum weight independent set problem:
(3) 
We define an enhanced link weight for BWAR, as follows, to take into account the occupancy of the duplicate buffer.
(4) 
Here the indicator function denotes that node is the final destination for the considered commodity . This gives higher weight to commodities that encounter their destinations. We show later how this effectively results in dramatic delay improvement. Similarly, the maximization problem in (IIB) can be solved first by finding the maximum commodity for each link at slot that maximizes followed by the same approach discussed earlier in IIA. It is important to notice that a solution to (IIB) is indeed a solution to (IIA) assuming that and are integers. The small weight added in (IIB) gives advantage first to links/commodities which encounter the destination and then to higher duplicate buffer deferential to increase the chance of serving duplicates. The small fractions in (IIB) assures this priority when there are ties in (IIA) to boost delay performance.
IiC Backpressure routing in intermittently connected networks
In general backpressure scheduling is NPhard, owing to the MWIS problem that needs to be solved at each time. However, in this paper, we focus on intermittently connected networks, that consist of sparse encounters between pairs of nodes. Therefore, at any given time, the size of any connected component of the network is very small. In this case, the scheduling problem is dramatically simplified.
IiD Practical Duplicate Removal
As can be seen from the above description, BWAR creates duplicate packets whenever the transmitter’s queue occupancy is low. In an ideal setting, for efficiency, the duplicated packets in the network should be deleted instantaneously when any copy is delivered to the intended destination. This could only be implemented practically in intermittently connected networks where a centralized control plane is available that can provide such an instantaneous acknowledgement to all nodes in the network. In other cases, some other mechanism is sought, so we propose the following timeout mechanism. Whenever a packet arrives into the network, it is timestamped. After a timeout period from that arrival time, any duplicate copies of that packet at any node in the network will be deleted. To obtain higher delay performance improvement, when an original packet is duplicated, it is placed in the duplicated buffer giving it lower service priority, however, it is flagged and not deleted when a timeout occurred. It is only removed when it gets acknowledged directly by the destination.
In the next section we undertake an analysis of the performance of BWAR and compare it with the known results for traditional backpressure routing. Specifically, we prove that any feasible rate vector is also stabilized by BWAR, and the bound that we can give on the expected queue occupancy for BWAR is better than that for regular backpressure.
Iii Mathematical Analysis
Iiia Review of the Analysis of Basic Backpressure
We consider a timeslotted network with N nodes that communicate with each other. Packets arrive to each node, and each packet must be delivered to a specific destination, possibly via a multihop path. Each node maintains several queues, one per destination, to store packets. Each queue has the following dynamics:
(5) 
Where is the queue size at time , is the transmission rate out of the queue at time , and is the total packet arrivals to the queue at time .
Each time slot, we observe the queue states and the channel states and make scheduling and routing decisions based on this information. To clear this out, let be the queue backlog (number of packets) in node that are destined for node at slot . Let be the exogenous packet arrivals that come to node and destined to node at time with rate . Exogenous arrivals are the packets that just entered the network. Endogenous arrivals, however, are arrivals from other nodes and were already inside the network. Packets may be forwarded to several nodes before reaching the destination. Let us define the capacity region to be the set of all possible arrival rate vectors that are stabilizing by some scheduling and routing strategy. Let be the channel state from node to node at time in terms of how many packets can be transmitted. Let be the scheduled service rate from node to node at slot . Let be the service rate for commodity routed from node to node at time and must satisfy:
(6) 
The queue dynamics for each time slot and for each queue is the following:
(7) 
Where is the actual transfer rate due to insufficient packets in the queue. For example, on some slots we may able to send 5 packets, but we only send 3, because only 3 were available in the queue. In equation (IIIA), are the exogenous arrivals and are the endogenous arrivals to node .
Define the vector to be the vector of all queues in the network at time . The Lyapunov function can be defined as following:
(8) 
The Lyapunov drift is defined as following:
(9) 
(10) 
Such that:
(11) 
and,
(12) 
Maximizing in (10) which is equivalent to the maximization problem defined in (IIA) yields the backpressure algorithm for scheduling and routing and it has been proven by [2, 1] that it supports the maximum capacity . The average queue occupancy bound for backpressure scheduling and routing is:
(13) 
such that,
(14)  
(15)  
(16) 
Where, is the average of total queue backlog occupancy. is the sum of the second moment of the scheduled transmission rate out of each queue plus the second moment of the sum of the arrivals and scheduled transmission rate into each queue and summed over all queues. is the maximum positive number such that adding to each arrival rate still makes them inside the capacity region .
IiiB Analysis of BWAR
Here is a formal mathematical description of backpressure with adaptive redundancy. As before, let to be queue backlog in node of commodity at time slot . We define to be number of redundant packets in node of commodity at time . Redundant packets are stored separately in redundant buffers. Redundant packets have lower priority in such a way that no redundant packet is served unless the queue of original packets is empty. For all time slots , , , , and are defined exactly as before. Arrival rates are also defined as before. The queue dynamics in equation (IIIA) is updated for adaptive redundancy to be:
(17) 
Where is the number of original packets inside node of commodity at time slot that are known to be delivered by some duplicates to the destination using our BWAR strategy. One ideal model is that we find out which packets are delivered immediately, another is that we find out after some delay. Our analysis allows for any such knowledge of delivered packets. We show later a practical timeoutbased strategy for duplicate removals. Those packets are needed to be removed from the queue since they are already known to be delivered. We assume that the deletion happens during the time slot hence at the beginning of time slot none of those packets are deleted yet but are known to be deleted. The queue dynamics in (IIIB) consider only original packets and does not take into account the duplicate packets. We define the redundant buffer dynamics that are isolated from the original queue dynamics as following:
(18) 
Where denotes the number of duplicates in node of commodity at time that are known to be already delivered to the destination and hence they must be removed. is number of duplicates created at node during slot according to the adaptive redundancy criteria. is the actual duplicate transmissions from node to node of commodity at time . BWAR algorithm chooses and in such away to assure that .
As before, is the vector of all queue backlogs at time . Let to be the undelivered queue backlog in node of commodity at time . Hence,
(19) 
Let be the vector of all queue backlogs of undelivered packets at time . Let be the vector of all removed duplicates at time . Define the Lyapunov function . Assume that , and are defined as before in (14), (15) and (16) respectively.
Let also define,
(20)  
(21)  
(22)  
(23) 
Where, is the average of total queue backlog occupancy for undelivered packets in the main queues. is the second moment of number of removed packets in each original queue because those packets are known that are delivered by duplicates to the destination and summed over all queues. is the joint second moment of number of removed packets and the queue backlog summed over all queues. is the joint second moment of number of removed packets and the queue backlog of undelivered packets summed over all queues.
For simplicity of exposition, we prove the result in the simple case when arrival rates and the channel states are i.i.d. over slots. This can be extended to general ergodic (possibly noni.i.d.) processes using a Tslot drift argument as in [19].
Theorem 1.
If the channel states are i.i.d. and the arrival processes are i.i.d. with rates that are inside the capacity region such that for some , then BWAR stabilizes all queues with the following bound on the average of total queue occupancy of undelivered packets ,
(24) 
Proof:
Squaring both sides of (IIIB),
(25) 
Summing over all and ,
(26) 
Taking the conditional expectation ,
(27) 
Since our BWAR policy maximizes (IIB) and hence (IIA) taking into account the undelivered packets only, it will also maximize:
(28) 
However, because are inside the capacity region , we know from [19] that there exists a stationary and randomized algorithm , which makes decisions independent of , yielding that satisfy:
Because BWAR maximizes (28), it follows that:
(29) 
Using this in (27) yields,
(30) 
Taking iterative expectation,
(31) 
Notice that:
(32) 
Hence by summing over time slots and by telescoping,
(33) 
Dividing by and taking the for implies:
(34) 
∎
Remark: Note that the computation of and is determined by the duplicate removal strategies. Depending on these terms, the queue bound in this above theorem could be much lower than the queue occupancy bound for regular backpressure in (13). Thus we have a formal guarantee that BWAR is no worse in terms of throughput than backpressure, and potentially much better in terms of delay, since by Little’s theorem average delay is proportional to the average number of undelivered packets. We will validate this finding with model in the next section.
Iv Modelbased Simulations
Iva The CellPartitioned Model
The model in this paper simplifies the control variables to be the whole transmission rates for scheduling and the commodity transmission rates for routing.
We simulate BWAR in the context of encounterbased scheduling and routing for a simple model (cellpartitioned network), which yields useful insights on its performance. In this idealized model the network deployment area is separated into disjoint cells and nodes have i.i.d. mobility model [20] as follows. We have nodes and cells. At each slot , node can be inside any cell with equal probabilities of . For collision and interference simplicity, only one transmission (one packet) is allowed in each cell in each time slot. Because of this we set . Another simplifying assumption is that the nodes in the network are organized into pairs, acting as destinations to each other. Each node has Bernoulli exogenous arrivals intended for its pair. Depending on the number of cells in the network we can choose the right number of the nodes in order to maximize throughput as shown in [20]. Our simulation results show that by optimizing number of nodes based on the number of cells to maximize throughput, the delay also is improved. We consider in our simulations, networks of sizes 9, 12, 16, 20, and 25 cells in the network. And for optimality, number of nodes are chosen to be 16, 20, 28, 34, and 44 respectively. For timeout duplicate removals we set the timeout value .
Here we show how BWAR works in the cellpartitioned network with the simplifying assumption that only one transmission is allowed per cell per time slot. Each time slot and for each cell we choose two nodes and and commodity such that:

and are in cell .

; for all , for all and in cell at time slot . This captures the maximization of queue differentials of the main queues.

If there exists in cell such that,
then . This captures the destination advantage. 
If there exists in cell and such that
and
or and then
. This captures the maximization of duplicate buffer differentials if there are some ties in main queue differentials.
The algorithm simply assigns a value of 1, and assigns all other a value of 0 such that in cell .
When a transmission is made from node to node of commodity at time slot and that transmission will make then this transmitted packet is duplicated and stored in the duplicate buffer of node making instead of . Duplicate packets are served only if there are no original packets to transmit. There is strict lower priority of duplicate packets compared to original packets.
IvB Protocol Variants
In the simulations, we implement and compare five different routing protocol variants. They are described as follows:

Regular Backpressure (RB): This is the basic backpressure scheduling and routing mechanism, where decisions are made purely based on queue differentials.

Regular Backpressure with Destination Advantage (RBDA): This is a slight modification in which packets corresponding to the destination are prioritized when the destination is encountered. As we show, this already yields significant delay improvements over regular backpressure.

BWAR with Ideal packet removal and original packets retained in the Main queue (BWARIM): This is our novel backpressure with adaptive redundancy in which the destination advantage is also holds. Here, when an original packet is duplicated the original packet remains in the main queue while the duplicate is stored in the duplicate buffer. We assume here whenever a packet reaches the destination, all of its duplicates are deleted including the original one in the main queue instantaneously.

BWAR with Ideal packet removal and original packets moved to Duplicate buffer upon copy (BWARID): This is very similar to BWARIM. The only difference is that whenever an original packet is duplicated both the original packet and the duplicate are stored in the duplicate buffer (of course in two different nodes one in the receiver and the other in the sender respectively).

BWAR with Timeout based packet removal and original packets moved to Duplicate buffer upon copy (BWARTD): This is a practical implementation of BWAR in which duplicates are deleted from the duplicate buffer after a predefined timeout value has passed since the first time the original packet is admitted to the network. However, the original packet that is kept in duplicate buffer is flagged and will not be deleted when a timeout occurred. It is only deleted if it gets acknowledged directly by the destination if its already received or otherwise it moved back to the main queue when it encounters the destination.

Spray and Wait (S&W): This is not a backpressure based mechanism. Spray and Wait is presented by T. Spyropoulos et al. [14] which is a state of the art routing scheme in intermittently connected mobile networks. S&W creates a predefined fixed number of copies (spraying) of the packet when admitted to the network. Those copies are distributed to distinct nodes and then each copy waits until it encounters the destination. We implemented S&W for comparison with BWAR. Our results show that BWAR outperforms S&W especially in high load scenarios.
The evaluations are conducted using a custom simulator written in C++ (for repeatability, we make our code available online at http://anrg.usc.edu/downloads/). Each simulation runs for one million time slots.
In figure 1(a), we show average delay of all above protocol variants as number of nodes vary for low load out of the per node capacity region . Delay is reduced significantly when BWAR is used. For this low load scenario all BWAR variants have almost the same average delay and they perform slightly better than Spray and Wait. Figure 1(a) also shows the great dramatic delay improvement of destination advantage without any redundancy in RBDA compared to regular backpressure RB.
Figure 1(b) compares the average delay of all variants of backpressurebased protocols as we vary the load. As expected, as the load increases the delay improvement of BWAR declines compared to RBDA. Figure 1(b) also shows how BWARID performs much better compared to BWARIM beyond some threshold of load(). This shows how moving the duplicated original packet to the duplicate buffer has great delay enhancement for high load scenarios.
In Figure 2, results show how BWAR mechanism outperforms Spray and Wait (S&W) delay performance for high load. It shows also how BWAR supports almost twice the capacity region of S&W.
Surprisingly in figure 3, BWARIM has a better total number of transmissions compared to regular backpressure RBDA for low load despite the flooding duplicates nature of BWAR at low load. Spray and Wait has superior energy consumption performance compared to all backpressurebased protocol variants considered. For future work, we intend to study the possibility of having both power optimization and adaptive redundancy features to be enabled on backpressure.
Figure 4 studies the effect of timeout value of BWARTD for removing duplicates under different load scenarios and compares its delay performance with ideal duplicate removals in BWARID.
V Related Work
The first theoretical work on backpressure scheduling is the classic result by Tassiulas and Ephremides in 1992, proving that this queuedifferential based scheduling mechanism is throughput optimal (i.e., it can stabilize any feasible rate vector in a network) [1]. Since then, researchers have combined the basic backpressure mechanism with utility optimization to provide a comprehensive approach to stochastic network optimization [2, 21, 22].
Of most relevance to this work are papers on delay enhancements to backpressure. A number of papers [23, 24, 25] address the utilitydelay tradeoff in optimizationoriented backpressure, to obtain a tradeoff based on a parameter such that the utility is improved by a factor of while the delay is made to be polylogarithmic in . Such a tradeoff has been shown to be practically achievable using LIFO queueing in [26], at the cost of a small probability of dropping packets. The firstever implementation of dynamic backpressure routing aimed for wireless sensor networks (BCP) [9] uses such a LIFO mechanism. As our focus in this work is not on utility optimization, the techniques presented in these works are somewhat orthogonal to the redundancy approach we develop here. Another set of papers [27, 3, 28] consider the use of shortest path routing in conjunction with backpressure to improve the delay performance. These techniques are well suited for static networks in which such paths can be computed; however, since our focus is on encounter based networks with limited connectivity, such an approach is not applicable.
In [29], the authors present a mechanism whereby only one real queue is maintained for each neighbor, along with virtual counters/shadow queues for all destinations, and show that this yields delay improvements. And in [5], a novel variant of backpressure scheduling mechanism is proposed which uses head of line packet delay instead of queue lengths as the basis of the backpressure weight calculation for each link/commodity, also yielding enhanced delay performance. However, these works both assume the existence of static fixed routes. It would be interesting to explore in future work whether their techniques can be applied to intermittently connected encounterbased mobile networks, and if so, how these approach can be further enhanced by the use of the adaptive redundancy that we propose in this work.
Ryu et al. present two works on backpressure routing aimed specifically for clusterbased intermittently connected networks [30, 10]. In [30], the authors develop a twophase routing scheme, combining backpressure routing with source routing for clusterbased networks, separating intracluster routing from intercluster routing. They show that this approach results in large queues at only a subset of the nodes, yielding smaller delays than conventional backpressure. In [10], the authors implement the abovementioned algorithm in a real experimental network and show the delay improvements empirically. The key difference of these works from ours is that we do not make any assumption about the intermittently connected network being organized in a clusterbased hierarchy.
Dvir and Vasilakos [31] also consider backpressure routing for intermittently connected networks, with link weights similar to that used in BCP [9]. They evaluate Weighted Fair Queueing in addition to LIFO and show through simulations that it offers energy improvements. Their work does not explicitly address additional delay improvements needed for these kinds of networks.
There is a rich literature on routing in delay tolerant / intermittently connected encounter based mobile networks (see [32] for a comprehensive survey). Although there exist singlecopy routing mechanisms for such networks [13], it has been wellrecognized that replication is helpful in reducing delay. While basic epidemic routing [33] creates multiple message replicas for reliable, fast delivery, it incurs too high of a transmission cost. Smarter multicopy routing mechanisms have therefore been developed such as Spray and Wait [14], and SARP [34]. These works introduce redundant packet transmissions to improve delay. However, all of these approaches are not adaptive to the traffic and therefore will hurt the throughput performance of the network. This has been noted before, by the authors of [10], who write that “replicationbased algorithms such as epidemic routing for DTNs … result in lower throughput since multiple copies of a piece of data need to be forwarded and stored (and therefore not throughput optimal).” In fact, in [20], it has been theoretically proved that capacity of such schemes that use fixed redundancy is necessarily lower. In this work, we present the first backpressure algorithm that uses replication in an adaptive manner so as to maintain throughput optimality while reducing delay. We explicitly compare our BWAR scheme with Spray and Wait, and show through our evaluation that not only does it provide similar, even better, delay performance, it does so without hurting throughput optimality; specifically, we show that BWAR can handle much higher traffic load than Spray and Wait.
To summarize, this paper on BWAR is the first work that explicitly combines the best of both worlds: multicopy routing for intermittently connected networks and throughputoptimal backpressure scheduling. This combination yields better delay performance than traditional backpressure, particularly at low loads, and better ability to handle high traffic than traditional DTN/ICN routing schemes.
Vi Conclusion and Future Work
We have presented in this paper BWAR, an enhanced backpressure algorithm that introduces adaptive redundancy to improve delay performance. We have proved analytically that this algorithm is also throughput optimal while providing a better delay bound, particularly at low load settings. Through simulation results we have shown that BWAR outperforms both traditional backpressure (at low loads) and conventional DTNrouting mechanisms (at high loads) in encounterbased mobile networks.
There are a few open avenues for future work suggested by our study. First, we would like to undertake a more careful analysis of the delay improvements obtained, relating them more explicitly, for instance, to arrival process parameters and the underlying mobility model. Second, the improvements obtained by BWAR in terms of delay are obtained at the expense of greater number of transmissions due to the introduced redundancy. While this may be acceptable in some networks, for energyconstrained networks this could be a concern. We therefore plan to explore the design of energyefficient variants of BWAR in the future, in which the redundancy can be controlled to provide a tunable tradeoff between energy and delay. We would also like to investigate automated selfconfiguration of the timeout parameter for duplicate removal through a distributed mechanism, as this is currently statically configured in BWAR.
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