pith. sign in

arxiv: 2605.24235 · v1 · pith:H4I7FGW5new · submitted 2026-05-22 · 💻 cs.NI

Ant Backpressure Routing for Dynamic Wireless Multi-hop Networks with Mixed Traffic Patterns

Negar Erfaniantaghvayi , Zhongyuan Zhao , Kevin Chan , Ananthram Swami , Santiago Segarra This is my paper

Pith reviewed 2026-06-30 14:06 UTC · model grok-4.3

classification 💻 cs.NI
keywords ant backpressure routingwireless multi-hop networksmixed traffic patternsbackpressure routingant colony optimizationFIFO queuesdynamic networksrouting protocols
0
0 comments X

The pith

Ant-BP routing uses virtual shortest-path backpressure updates to set pheromone probabilities for per-neighbor FIFO forwarding in wireless networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes Ant Backpressure (Ant-BP) to apply congestion-aware multipath routing in wireless multi-hop networks carrying both long streaming flows and short bursty traffic. Standard backpressure and shortest-path-biased variants require per-commodity queues and frequent control that are hard to implement in many systems. Ant-BP runs periodic virtual SP-BP calculations to learn next-hop probabilities while real packets move through simple per-neighbor FIFO queues using probabilistic selection. This separation lets links share capacity across flows and prevents short flows from starving. Simulations show the approach delivers lower latency and higher delivery ratios than SP-BP and ant-colony baselines at comparable throughput, while adapting to link failures and mobility.

Core claim

Ant-BP is a periodic fully distributed scheme that builds pheromone-based forwarding probabilities from virtual SP-BP updates while forwarding actual packets through per-neighbor first-in-first-out queues with probabilistic next-hop selection. This architecture decouples route learning from packet forwarding, enables link-capacity sharing across commodities, mitigates starvation of short-lived traffic, and extends SP-BP benefits to per-neighbor FIFO architectures. Periodic virtual updates further allow adaptation to transient link failures and mobility-induced changes, with analysis showing higher-quality policies at lower overhead than conventional ACO routing.

What carries the argument

Pheromone probabilities derived from periodic virtual SP-BP updates that guide probabilistic next-hop selection on per-neighbor FIFO queues.

If this is right

  • Ant-BP improves latency and delivery ratio over SP-BP and ACO baselines under mixed streaming and bursty traffic.
  • Throughput remains comparable to SP-BP at low and medium traffic loads.
  • The scheme stays robust under mismatched virtual-traffic assumptions, transient link failures, and node mobility.
  • Virtual SP-BP updates produce higher-quality forwarding policies with lower overhead than conventional ACO routing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The FIFO-only data plane could allow deployment on legacy wireless devices that cannot maintain per-commodity state.
  • Periodic virtual updates may support routing in other environments with limited per-flow state at forwarding nodes.
  • The learning-forwarding split could be applied to additional routing algorithms to reduce data-plane complexity.

Load-bearing premise

Pheromone probabilities derived from virtual SP-BP updates will produce effective forwarding policies when actual packets use only per-neighbor FIFO queues without per-commodity state.

What would settle it

A simulation run with mixed streaming and bursty traffic in which Ant-BP shows no reduction in latency or increase in delivery ratio relative to SP-BP.

Figures

Figures reproduced from arXiv: 2605.24235 by Ananthram Swami, Kevin Chan, Negar Erfaniantaghvayi, Santiago Segarra, Zhongyuan Zhao.

Figure 1
Figure 1. Figure 1: Ant backpressure routing system diagram: queueing system design, operations, and timelines. and maintenance require the continuous transmission of payload-heavy physical scout ants that must traverse the network and return to their sources, these protocols suffer from prohibitively high control overhead and slow conver￾gence [35] in MANETs with transient link failures or node mobility. In parallel with the… view at source ↗
Figure 2
Figure 2. Figure 2: The average (a) end-to-end latency and (b) delivery ratio of tested routing policies as a function of bursty flow load 𝐿𝑏 in 10 random instances of wireless networks of 100 nodes under mixed traffic setting with a constant streaming load 𝐿𝑠 = 2.0. (c) The average delivery ratio of tested routing schemes in wireless networks of 100 nodes under mixed traffic with different loads shown in the x-axis. For Ant-… view at source ↗
Figure 3
Figure 3. Figure 3: Average network goodput (network-wide number of packets delivered per time slot) of routing schemes on wireless networks with 100 nodes under all streaming traffic as a function of traffic load 𝐿𝑠 . loads 𝐿𝑠 ∈ {0.5, 1, 2,…, 12}. As shown in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The average (a, b, c) end-to-end latency and (d, e, f) delivery ratio of tested routing policies as a function of bursty flow load 𝐿𝑏 in 10 random instances of wireless networks of 100 nodes under mixed traffic setting with a constant streaming load 𝐿𝑠 = 1.0. Subfigures (a, d), (b, e), and (c, f) correspond to the All-Links, BW-Persist, and Local-Persist link failure scenarios, respectively. average end-to… view at source ↗
Figure 5
Figure 5. Figure 5: The average (a) end-to-end latency of all packets as a function of mobility level (number of mobile nodes), (b) end-to-end latency of delivered packets as a function of packet arrival time (binned in ranges of 50), and (c) end-to-end latency of delivered packets as a function of packet delivery time (binned in ranges of 50) for tested routing policies in 10 random instances of wireless networks of 100 node… view at source ↗
read the original abstract

Backpressure (BP) routing and its shortest-path biased variant (SP-BP) provide powerful congestion-aware multipath resource allocation for wireless multi-hop networks, but they rely on per-commodity queueing and slot-by-slot control that may be difficult to realize under practical or legacy forwarding architectures. Moreover, even state-of-the-art SP-BP still suffers from the last-packet problem when short-lived traffic coexists with streaming flows. To address these limitations, we propose Ant Backpressure (Ant-BP), a periodic and fully distributed routing scheme that decouples route learning from packet forwarding. Ant-BP uses virtual SP-BP to construct pheromone-based forwarding probabilities, while actual packets are forwarded through per-neighbor first-in-first-out (FIFO) queues with probabilistic next-hop selection. This architecture enables link-capacity sharing across commodities, mitigates starvation of short-lived traffic, and extends the benefits of SP-BP to network architectures based on per-neighbor FIFO forwarding. Through periodic virtual updates, Ant-BP also adapts to transient link failures and mobility-induced topology changes. Our theoretical analysis and simulations show that, compared with conventional ant colony optimization (ACO) routing, virtual SP-BP enables Ant-BP to establish higher-quality forwarding policies with lower overhead. As a result, Ant-BP improves latency and delivery ratio over SP-BP and ACO-based baselines under mixed streaming and bursty traffic, achieves throughput comparable to SP-BP at low and medium traffic load, and remains robust to mismatched virtual-traffic assumptions, transient link failures, and node mobility.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes Ant Backpressure (Ant-BP), a distributed routing scheme for wireless multi-hop networks that decouples route computation from packet forwarding: periodic virtual SP-BP updates generate pheromone-based next-hop probabilities, while actual packets are forwarded using only per-neighbor FIFO queues with probabilistic selection. It claims this architecture enables capacity sharing across commodities, mitigates the last-packet problem for short-lived flows, extends SP-BP benefits to legacy FIFO architectures, and yields lower latency and higher delivery ratio than SP-BP and ACO baselines under mixed streaming/bursty traffic while remaining robust to mobility, link failures, and mismatched virtual traffic assumptions.

Significance. If the performance claims hold under the stated conditions, the work would be significant for practical wireless network design by bridging theoretical backpressure routing with implementable per-neighbor FIFO forwarding. The periodic virtual-update mechanism for adaptation is a concrete strength, and the explicit comparison to both SP-BP and ACO baselines provides a useful reference point for mixed-traffic scenarios.

major comments (3)
  1. [Architecture description] Architecture description (abstract and § on system model): the central claim that pheromone probabilities derived from virtual SP-BP updates remain effective proxies for congestion when actual forwarding uses only per-neighbor FIFO queues (without per-commodity state) is load-bearing for all latency, delivery-ratio, and capacity-sharing assertions, yet no formal approximation bound or error analysis is supplied showing that the mapping preserves the throughput-optimality or delay properties of SP-BP under mixed traffic.
  2. [Theoretical analysis section] Theoretical analysis section: the abstract states that theoretical analysis supports the performance claims, but the provided text gives no model assumptions, queueing dynamics, or proof sketch establishing that the virtual-update period and pheromone update rule suffice to control the deviation from per-commodity backpressure when real queues lack commodity differentiation.
  3. [Simulation results] Simulation results (abstract): robustness claims to mismatched virtual-traffic assumptions and transient failures are asserted, but without reported details on traffic generation, statistical significance, confidence intervals, or data-exclusion rules, it is impossible to verify whether the reported gains over SP-BP are statistically reliable or sensitive to the FIFO approximation.
minor comments (2)
  1. Notation for pheromone probabilities and virtual queue updates should be defined explicitly with symbols before first use to improve readability.
  2. The abstract mentions 'periodic virtual updates' but does not specify the update interval relative to packet arrival rates; a brief clarification would help readers assess overhead.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point-by-point below. We agree that the current version lacks a formal error analysis and expanded simulation statistics, and we will incorporate clarifications and additions in the revised manuscript.

read point-by-point responses

  1. Referee: [Architecture description] Architecture description (abstract and § on system model): the central claim that pheromone probabilities derived from virtual SP-BP updates remain effective proxies for congestion when actual forwarding uses only per-neighbor FIFO queues (without per-commodity state) is load-bearing for all latency, delivery-ratio, and capacity-sharing assertions, yet no formal approximation bound or error analysis is supplied showing that the mapping preserves the throughput-optimality or delay properties of SP-BP under mixed traffic.

    Authors: We acknowledge that the manuscript does not supply a formal approximation bound or error analysis quantifying how closely the pheromone probabilities track per-commodity backpressure under FIFO forwarding. The existing theoretical discussion focuses on the comparative advantage of virtual SP-BP over ACO for establishing high-quality policies with lower overhead. In revision we will add an explicit discussion of the approximation, including any available bounds derived from the virtual-update period, pheromone evaporation rate, and queueing deviation under mixed traffic. revision: yes

  2. Referee: [Theoretical analysis section] Theoretical analysis section: the abstract states that theoretical analysis supports the performance claims, but the provided text gives no model assumptions, queueing dynamics, or proof sketch establishing that the virtual-update period and pheromone update rule suffice to control the deviation from per-commodity backpressure when real queues lack commodity differentiation.

    Authors: The theoretical analysis section in the manuscript is limited to a comparative argument showing that virtual SP-BP yields superior forwarding policies than standard ACO at comparable overhead; it does not contain a full queueing model or proof sketch for bounded deviation under the FIFO approximation. We will expand this section in revision to state the model assumptions (periodic virtual updates, pheromone update rule, per-neighbor FIFO dynamics) and provide a high-level sketch relating update frequency to deviation from ideal per-commodity backpressure. revision: yes

  3. Referee: [Simulation results] Simulation results (abstract): robustness claims to mismatched virtual-traffic assumptions and transient failures are asserted, but without reported details on traffic generation, statistical significance, confidence intervals, or data-exclusion rules, it is impossible to verify whether the reported gains over SP-BP are statistically reliable or sensitive to the FIFO approximation.

    Authors: The full manuscript describes the traffic generation process (mixed streaming and bursty flows with explicit arrival rates and packet sizes), mobility and failure models, and reports averages over multiple independent simulation runs. We agree, however, that confidence intervals, statistical significance tests, and any data-exclusion criteria are not explicitly stated. In the revision we will add these details, including error bars and p-values where appropriate, to allow verification of the reported gains. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on external baselines and independent theoretical analysis

full rationale

The paper's central claims derive from simulations comparing Ant-BP against SP-BP and ACO baselines plus a stated theoretical analysis showing virtual SP-BP yields higher-quality policies than ACO. No equation or step reduces by construction to a fitted parameter renamed as prediction, a self-definition, or a load-bearing self-citation chain; the architecture (virtual updates feeding per-neighbor FIFO forwarding) is presented as an explicit design choice whose benefits are externally validated rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim rests on unstated modeling assumptions about virtual traffic and pheromone mapping that cannot be audited from the given text.

pith-pipeline@v0.9.1-grok · 5826 in / 1188 out tokens · 50667 ms · 2026-06-30T14:06:33.190153+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

66 extracted references · 12 canonical work pages · 1 internal anchor

  1. [1]

    Erfaniantaghvayi, Z

    N. Erfaniantaghvayi, Z. Zhao, K. Chan, G. Verma, A. Swami, S.Segarra, Antbackpressureroutingforwirelessmulti-hopnetworks with mixed traffic patterns, in: IEEE Military Communications Conference (MILCOM), Washington DC, USA, 2024, pp. 1174–

    2024

  2. [2]

    doi:10.1109/MILCOM61039.2024.10774011

    work page doi:10.1109/milcom61039.2024.10774011 2024

  3. [3]

    X.Lin,N.B.Shroff,R.Srikant, Atutorialoncross-layeroptimization in wireless networks, IEEE J. Sel. Areas Commun. 24 (2006) 1452– 1463

    2006

  4. [4]

    S. K. Sarkar, T. G. Basavaraju, C. Puttamadappa, Ad hoc Mobile Wireless Networks: Principles, Protocols and Applications, CRC Press, 2013

    2013

  5. [5]

    Patriciello, C

    N. Patriciello, C. A. Grazia, J. Núñez-Martínez, J. Baranda, J. Mangues-Bafalluy, M. Casoni, Performance evaluation of back- pressure routing in integrated satellite-terrestrial backhaul for PPDR networks, in: IEEE Intl. Conf. on Wireless and Mobile Computing, Netw. and Communs. (WiMob), 2016, pp. 1–8. doi:10.1109/WiMOB. 2016.7763187

    work page doi:10.1109/wimob 2016

  6. [6]

    A.Kott,A.Swami,B.J.West, Theinternetofbattlethings, Computer 49 (2016) 70–75

    2016

  7. [7]

    Large language model (LLM)-enabled reinforcement learning for wireless network optimization,

    M. Cudak, A. Ghosh, A. Ghosh, J. Andrews, Integrated access and backhaul: A key enabler for 5G millimeter-wave deployments, IEEE Communications Magazine 59 (2021) 88–94. doi:10.1109/MCOM.001. 2000690

    work page doi:10.1109/mcom.001 2021

  8. [8]

    I.F.Akyildiz,A.Kak,S.Nie, 6Gandbeyond:Thefutureofwireless communications systems, IEEE Access 8 (2020) 133995–134030

    2020

  9. [9]

    Tassiulas, A

    L. Tassiulas, A. Ephremides, Stability properties of constrained queueing systems and scheduling policies for maximum throughput inmultihopradionetworks, in:IEEEConf.onDecisionandControl, IEEE, 1990, pp. 2130–2132

    1990

  10. [10]

    J. Ryu, L. Ying, S. Shakkottai, Back-pressure routing for intermit- tently connected networks, in: 2010 Proceedings IEEE INFOCOM, IEEE, 2010, pp. 1–5

    2010

  11. [11]

    Georgiadis, M

    L. Georgiadis, M. J. Neely, L. Tassiulas, Resource allocation and cross-layer control in wireless networks, Foundations and Trends® in Networking 1 (2006) 1–144. Erfaniantaghvayi et al.:Preprint submitted to Elsevier Page 12 of 14 Ant Backpressure Routing for Dynamic Wireless Multi-hop Networks

    2006

  12. [12]

    M. J. Neely, E. Modiano, C. E. Rohrs, Dynamic power allocation and routing for time-varying wireless networks, IEEE J. Sel. Areas Commun. 23 (2005) 89–103. doi:10.1109/JSAC.2004.837349

    work page doi:10.1109/jsac.2004.837349 2005

  13. [13]

    Conf.onAcoustics,SpeechandSignalProcess.(ICASSP),2023,pp

    Z.Zhao,B.Radojicic,G.Verma,A.Swami,S.Segarra, Delay-aware backpressure routing using graph neural networks, in: IEEE Intl. Conf.onAcoustics,SpeechandSignalProcess.(ICASSP),2023,pp. 4720–4724

    2023

  14. [14]

    Z. Zhao, G. Verma, A. Swami, S. Segarra, Enhanced backpressure routing using wireless link features, in: IEEE Intl. Wrksp. Computat. Advances Multi-Sensor Adaptive Process. (CAMSAP), 2023, pp. 1–

    2023

  15. [15]

    doi:10.1109/CAMSAP58922.2023.10403470

    work page doi:10.1109/camsap58922.2023.10403470 2023

  16. [16]

    Z. Zhao, B. Radojičić, G. Verma, A. Swami, S. Segarra, Biased Backpressure routing using link features and graph neural networks, IEEE Transactions on Machine Learning in Communications and Networking (2024) 1424 – 1439

    2024

  17. [17]

    Z. Jiao, B. Zhang, W. Gong, H. Mouftah, A virtual queue-based back-pressure scheduling algorithm for wireless sensor networks, EURASIP J. on Wireless Commun. and Netw. 2015 (2015) 1–9

    2015

  18. [18]

    Moeller, A

    S. Moeller, A. Sridharan, B. Krishnamachari, O. Gnawali, Routing without routes: The backpressure collection protocol, in: Proceed- ings of the 9th ACM/IEEE International Conference on Information Processing in Sensor Networks, 2010, pp. 279–290

    2010

  19. [19]

    Alresaini, K.-L

    M. Alresaini, K.-L. Wright, B. Krishnamachari, M. J. Neely, Back- pressure delay enhancement for encounter-based mobile networks while sustaining throughput optimality, IEEE/ACM Trans. Netw. 24 (2016) 1196–1208. doi:10.1109/TNET.2015.2404331

    work page doi:10.1109/tnet.2015.2404331 2016

  20. [20]

    B. Ji, C. Joo, N. B. Shroff, Delay-based back-pressure scheduling in multihop wireless networks, IEEE/ACM Trans. Netw. 21 (2012) 1539–1552

    2012

  21. [21]

    Liaskos, K

    C. Liaskos, K. Alexandris, A. Das, S. Tang, L. Tassiulas, Analysis and evaluation of fully TCP-compatible backpressure-driven traffic engineering, IEEETrans.onNetw.ScienceandEng.10(2023)4056– 4070

    2023

  22. [22]

    C. Joo, N. B. Shroff, Local greedy approximation for scheduling in multihop wireless networks, IEEE Trans. Mobile Computing 11 (2011) 414–426

    2011

  23. [23]

    Z. Zhao, G. Verma, C. Rao, A. Swami, S. Segarra, Link scheduling using graph neural networks, IEEE Trans. Wireless Commun. 22 (2023) 3997–4012

    2023

  24. [24]

    Z. Zhao, Y. Ming, A. Swami, K. Chan, F. Dagefu, S. Segarra, Generalizing biased backpressure routing and scheduling to wire- less multi-hop networks with advanced air-interfaces, arXiv preprint arXiv:2504.21721, 2025. Preprint

    work page arXiv 2025

  25. [25]

    L. X. Bui, R. Srikant, A. Stolyar, A novel architecture for reduction of delay and queueing structure complexity in the back-pressure algorithm, IEEE/ACM Trans. Netw 19 (2011) 1597–1609. doi:10. 1109/TNET.2011.2126593

    work page arXiv 2011

  26. [26]

    Liaskos, K

    C. Liaskos, K. Alexandris, A. Das, S. Tang, L. Tassiulas, Analysis and evaluation of fully tcp-compatible backpressure-driven traffic engineering, IEEETransactionsonNetworkScienceandEngineering 10 (2023) 4056–4070. doi:10.1109/TNSE.2023.3282642

    work page doi:10.1109/tnse.2023.3282642 2023

  27. [27]

    J. T. Moy, OSPF: anatomy of an Internet routing protocol, Addison- Wesley Professional, 1998

    1998

  28. [28]

    McKeown, T

    N. McKeown, T. Anderson, H. Balakrishnan, G. Parulkar, L. Peter- son,J.Rexford,S.Shenker,J.Turner, Openflow:enablinginnovation in campus networks, ACM SIGCOMM computer communication review 38 (2008) 69–74

    2008

  29. [29]

    Kreutz, F

    D. Kreutz, F. M. Ramos, P. E. Verissimo, C. E. Rothenberg, S. Azodolmolky, S. Uhlig, Software-defined networking: A compre- hensive survey, Proceedings of the IEEE 103 (2014) 14–76

    2014

  30. [30]

    C.A.Oliveira,P.M.Pardalos,etal.,Mathematicalaspectsofnetwork routing optimization, volume 53, Springer, 2011

    2011

  31. [31]

    Abolhasan, T

    M. Abolhasan, T. Wysocki, E. Dutkiewicz, A review of routing protocols for mobile ad hoc networks, Ad hoc networks 2 (2004) 1–22

    2004

  32. [32]

    Chlamtac, M

    I. Chlamtac, M. Conti, J. J.-N. Liu, Mobile ad hoc networking: imperatives and challenges, Ad hoc networks 1 (2003) 13–64

    2003

  33. [33]

    I.T.Haque,N.Abu-Ghazaleh, Wirelesssoftwaredefinednetworking: Asurveyandtaxonomy, IEEECommunicationsSurveys&Tutorials 18 (2016) 2713–2737

    2016

  34. [34]

    Routing Protocols for Mobile and Vehicular Ad-Hoc Networks: A Comparative Analysis

    P. Vinayakray-Jani, S. Sanyal, Routing protocols for mobile and vehicular ad-hoc networks: A comparative analysis, arXiv preprint arXiv:1206.1918 (2012)

    work page internal anchor Pith review Pith/arXiv arXiv 1918

  35. [35]

    Aggarwal, S

    A. Aggarwal, S. Gandhi, N. Chaubey, Performance analysis of AODV, DSDV and DSR in MANETs, International Journal of Distributed and Parallel Systems 2 (2011)

    2011

  36. [36]

    Telecommunications 16 (2005) 443–455

    G.DiCaro,F.Ducatelle,L.M.Gambardella, AntHocNet:anadaptive nature-inspired algorithm for routing in mobile ad hoc networks, European Trans. Telecommunications 16 (2005) 443–455

    2005

  37. [37]

    Purkayastha, J

    P. Purkayastha, J. S. Baras, Convergence results for ant routing algo- rithmsviastochasticapproximation, ACMTrans.Auton.Adapt.Syst. 8 (2013). URL: https://doi.org/10.1145/2451248.2451251. doi:10. 1145/2451248.2451251

    work page doi:10.1145/2451248.2451251 2013

  38. [38]

    Zhang, X

    H. Zhang, X. Wang, P. Memarmoshrefi, D. Hogrefe, A survey of ant colony optimization based routing protocols for mobile ad hoc networks, IEEE Access 5 (2017) 24139–24161

    2017

  39. [39]

    Dorigo, T

    M. Dorigo, T. Stützle, Ant colony optimization: overview and recent advances, Springer, 2019

    2019

  40. [40]

    D. B. Johnson, D. A. Maltz, Dynamic source routing in ad hoc wireless networks, in: Mobile computing, Springer, 1996, pp. 153– 181

    1996

  41. [41]

    D.B.Johnson,D.A.Maltz,J.Broch,etal., Dsr:Thedynamicsource routing protocol for multi-hop wireless ad hoc networks, Ad hoc networking 5 (2001) 139–172

    2001

  42. [42]

    Leung, J

    R. Leung, J. Liu, E. Poon, A.-L. Chan, B. Li, Mp-dsr: a qos- awaremulti-pathdynamicsourceroutingprotocolforwirelessad-hoc networks, in:ProceedingsLCN2001.26thAnnualIEEEConference on Local Computer Networks, IEEE, 2001, pp. 132–141

    2001

  43. [43]

    S.-J. Lee, E. M. Belding-Royer, C. E. Perkins, Scalability study of the ad hoc on-demand distance vector routing protocol, International journal of network management 13 (2003) 97–114

    2003

  44. [44]

    T.Saravanan,N.Nithya, Modelingdisplacementanddirectionaware adhocon-demanddistancevectorroutingstandardformobileadhoc networks, Mobile Networks and Applications 24 (2019) 1804–1813

    2019

  45. [45]

    M. K. Marina, S. R. Das, On-demand multipath distance vector routing in ad hoc networks, in: Proceedings ninth international conferenceonnetworkprotocols.ICNP2001,IEEE,2001,pp.14–23

    2001

  46. [46]

    E. M. Royer, C. E. Perkins, Multicast operation of the ad-hoc on- demand distance vector routing protocol, in: Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking, 1999, pp. 207–218

    1999

  47. [47]

    A. A. Bhorkar, M. Naghshvar, T. Javidi, B. D. Rao, Adaptive opportunistic routing for wireless ad hoc networks, IEEE/ACM Transactions On Networking 20 (2011) 243–256

    2011

  48. [48]

    Zhang, R

    Z. Zhang, R. Krishnan, An overview of opportunistic routing in mobile ad hoc networks, in: MILCOM 2013-2013 IEEE Military Communications Conference, IEEE, 2013, pp. 119–124

    2013

  49. [49]

    Chakchouk, A survey on opportunistic routing in wireless com- municationnetworks, IEEECommunicationsSurveys&Tutorials17 (2015) 2214–2241

    N. Chakchouk, A survey on opportunistic routing in wireless com- municationnetworks, IEEECommunicationsSurveys&Tutorials17 (2015) 2214–2241

    2015

  50. [50]

    Biswas, R

    S. Biswas, R. Morris, Exor: Opportunistic multi-hop routing for wireless networks, in: Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications, 2005, pp. 133–144

    2005

  51. [51]

    Z.Wang,Y.Chen,C.Li, Corman:Anovelcooperativeopportunistic routing scheme in mobile ad hoc networks, IEEE journal on selected areas in communications 30 (2012) 289–296

    2012

  52. [52]

    Bhorkar, M

    A. Bhorkar, M. Naghshvar, T. Javidi, Opportunistic routing with congestion diversity in wireless ad hoc networks, IEEE/ACM Trans- actions on Networking 24 (2015) 1167–1180

    2015

  53. [53]

    Kathiravelu, N

    T. Kathiravelu, N. Ranasinghe, A. Pears, An enhanced congestion aware adaptive routing protocol for opportunistic networks, in: 2011 6th International Conference on Industrial and Information Systems, IEEE, 2011, pp. 210–215. Erfaniantaghvayi et al.:Preprint submitted to Elsevier Page 13 of 14 Ant Backpressure Routing for Dynamic Wireless Multi-hop Networks

    2011

  54. [54]

    M.Shelke,A.Malhotra,P.N.Mahalle,Congestion-awareopportunis- ticroutingprotocolinwirelesssensornetworks, in:SmartComputing andInformatics:ProceedingsoftheFirstInternationalConferenceon SCI 2016, Volume 1, Springer, 2017, pp. 63–72

    2016

  55. [55]

    Sharma, K

    I. Sharma, K. Ramkumar, A survey on aco based multipath routing algorithms for ad hoc networks, International Journal of Pervasive Computing and Communications 13 (2017) 370–385

    2017

  56. [56]

    S. U. Rehman, M. A. Khan, T. A. Zia, A. Y. Zomaya, Joint rate and queue based routing for vehicular ad-hoc networks, in: 2016 IEEE 41st Conference on Local Computer Networks Workshops (LCN Workshops), IEEE, 2016, pp. 165–172

    2016

  57. [57]

    Naseem, C

    M. Naseem, C. Kumar, Queue-based multiple path load balancing routingprotocolformanets, InternationalJournalofCommunication Systems 30 (2017) e3141

    2017

  58. [58]

    L. A. Maglaras, D. Katsaros, Delay efficient backpressure routing in wireless ad hoc networks, EAI Endorsed Transactions on Mobile Communications and Applications 1 (2014)

    2014

  59. [59]

    L. Hai, Q. Gao, J. Wang, H. Zhuang, P. Wang, Delay-optimal back- pressure routing algorithm for multihop wireless networks, IEEE Transactions on Vehicular Technology 67 (2018) 2617–2630

    2018

  60. [60]

    C. Shan, Y. Xia, Z. Guo, G. Wang, J. Zhang, Tsbs: A two-stage backpressureschedulingschemeovermultihopwirelessnetworks,Ad Hoc Networks 132 (2022) 102874

    2022

  61. [61]

    Kawadia, P

    V. Kawadia, P. R. Kumar, A cautionary perspective on cross-layer design, Wireless Commun. 12 (2005) 3–11. doi:10.1109/MWC.2005. 1404568

    work page doi:10.1109/mwc.2005 2005

  62. [62]

    J. Yang, S. C. Draper, R. Nowak, Learning the interference graph of a wireless network, IEEE Trans. Signal Inf. Process. Netw. 3 (2016) 631–646

    2016

  63. [63]

    Varaiya, Max pressure control of a network of signalized inter- sections, TransportationResearchPartC:EmergingTechnologies36 (2013) 177–195

    P. Varaiya, Max pressure control of a network of signalized inter- sections, TransportationResearchPartC:EmergingTechnologies36 (2013) 177–195

    2013

  64. [64]

    M. W. Levin, Max-pressure traffic signal timing: A summary of methodological and experimental results, Journal of Transportation Engineering, Part A: Systems 149 (2023) 03123001. doi:10.1061/ JTEPBS.TEENG-7578

    2023

  65. [65]

    on Wireless Com- mun

    C.Joo,G.Sharma,N.B.Shroff,R.R.Mazumdar, Onthecomplexity of scheduling in wireless networks, EURASIP J. on Wireless Com- mun. and Netw. 2010 (2010) 1–13

    2010

  66. [66]

    Neely, Stochastic network optimization with application to com- munication and queueing systems, Morgan & Claypool Publishers, 2010

    M. Neely, Stochastic network optimization with application to com- munication and queueing systems, Morgan & Claypool Publishers, 2010. Erfaniantaghvayi et al.:Preprint submitted to Elsevier Page 14 of 14

    2010