Performance Approximation for Highway Emergency Rescue Systems

Song Jianhui; Shu Xiaofeng; Zhong Jie; Jiang Lanqing; Zhang Wenchao; Shi Guoqing

doi:doi:10.11648/j.ajtte.20261101.11

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Performance Approximation for Highway Emergency Rescue Systems

Song Jianhui, Shu Xiaofeng, Zhong Jie, Jiang Lanqing^*, Zhang Wenchao, Shi Guoqing

Published in American Journal of Traffic and Transportation Engineering (Volume 11, Issue 1)

Received: 11 November 2025 Accepted: 9 December 2025 Published: 19 January 2026

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Abstract

Ensuring prompt responses to spatially uncertain traffic accidents is critical for highway emergency rescue systems, aiming to address emergencies and to prevent network-wide traffic disruptions. This paper develops an approximation model to characterize priority-based rescue systems for RV fleets. By representing each RV's state as either idle or busy, we formulate an approximation model in which the dispatch probability of an RV is dynamically influenced by the utilization of higher-priority RVs and its own availability. The proportionality constant governing this relationship is derived analytically from an M/M/N queuing model, incorporating a random server selection mechanism without replacement until the first available RV is identified. The system of equations is simplified into a tractable set of N linear simultaneous equations, enabling efficient computation of RV workloads. We further propose a solution algorithm to estimate critical performance metrics, including individual RV workloads, system response times, and cross-dispatch frequencies. A practical case study based on the G15 Highway (Sutong Bridge section) in China illustrates the model's applicability in quantifying performance measures such as individual RV response times, cross-regional dispatch ratios, and workload distribution under varying vehicle allocations and priority levels. The proposed model provides a practical and computationally efficient tool to support RV location planning, response section partitioning, and overall performance evaluation in highway emergency services, offering valuable insights for optimizing rescue efficiency and resource allocation.

Published in	American Journal of Traffic and Transportation Engineering (Volume 11, Issue 1)
DOI	10.11648/j.ajtte.20261101.11
Page(s)	1-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Highway Emergency, RV Deployment, RV Dispatch Priority, Rescue Work Intensity

References

[1]	Iannoni, A. P., & Morabito, R. (2007). A multiple dispatch and partial backup hypercube queuing model to analyze emergency medical systems on highways. Transp. Res. Part E Logist. Transp. Rev., 43(6), 755–771.
[2]	Nakata, H. (2012, January 6). Domestic robots failed to ride to rescue after No. 1 plant blew. The Japan Times. Retrieved November 18, 2018, from https://www.japantimes.co.jp/news/2012/01/06/national/domestic-robots-failed-to-ride-to-rescue-after-no-1-plant-blew
[3]	Andradóttir, S., Ayhan, H., & Down, D. G. (2003). Dynamic server allocation for queueing networks with flexible servers. Oper. Res., 51(6), 952–968.
[4]	Beojone, C. V., Máximo de Souza, R., & Iannoni, A. P. (2021). An efficient exact hypercube model with fully dedicated servers. Transp. Sci., 55(1), 222–237.
[5]	Larson, R. C. (1974). A hypercube queuing model for facility location and redistricting in urban emergency services. Comput. Oper. Res., 1(1), 67–95.
[6]	Larson, R. C., & Odoni, A. R. (1981). Urban operations research. Prentice-Hall.
[7]	Galvão, R. D., & Morabito, R. (2008). Emergency service systems: The use of the hypercube queueing model in the solution of probabilistic location problems. Int. Trans. Oper. Res., 15, 525–549.
[8]	Larson, R. C. (1975). Approximating the performance of urban emergency service systems. Oper. Res., 23(5), 845–868.
[9]	Jarvis, J. P. (1985). Approximating the equilibrium behavior of multi-server loss systems. Manage. Sci., 31(2), 235–239.
[10]	Larson, R. C., & McKnew, M. A. (1982). Police patrol-initiated activities within a system queueing model. Manage. Sci., 28(7), 759–774.
[11]	Atkinson, J. B., Kovalenko, I. N., Kuznetsov, N. Y., & Mikhalevich, K. V. (2008). A hypercube queueing loss model with customer-dependent service rates. Eur. J. Oper. Res., 191(1), 223–239.
[12]	Iannoni, A. P., Morabito, R., & Saydam, C. (2009). An optimization approach for ambulance location and the districting of the response segments on highways. Eur. J. Oper. Res., 195(2), 528–542.
[13]	Budge, S., Ingolfsson, A., & Erkut, E. (2009). Approximating vehicle dispatch probabilities for emergency service systems with location-specific service times and multiple units per location. Oper. Res., 57(1), 251–255.
[14]	Morabito, R., Chiyoshi, F., & Galvão, R. D. (2008). Non-homogeneous servers in emergency medical systems: Practical applications using the hypercube queueing model. Socioecon. Plann. Sci., 42(4), 255–270.
[15]	Iannoni, A. P., Morabito, R., & Saydam, C. (2011). Optimizing large-scale emergency medical system operations on highways using the hypercube queuing model. Socioecon. Plann. Sci., 45(3), 105–117.
[16]	Takeda, R. A., Widmer, J. A., & Morabito, R. (2007). Analysis of ambulance decentralization in an urban emergency medical service using the hypercube queueing model. Comput. Oper. Res., 34(3), 727–741.
[17]	Khoshgehbari, F., & Al-e, S. M. J. M. (2023). Ambulance location routing problem considering all sources of uncertainty: Progressive estimating algorithm. Comput. Oper. Res., 160, 106400.
[18]	Frichi, Y., Aboueljinane, L., & Jawab, F. (2025). Ambulance location and relocation under budget constraints: Investigating coverage-maximization models and ambulance sharing to improve emergency medical services performance. Health Care Manage. Sci., 1–24.
[19]	Grot, M., Nagel, L., Becker, T., Fiebrandt, P. M., & Werners, B. (2022). Fairness or efficiency-managing this conflict in emergency medical services location planning. Comput. Ind. Eng., 173, 108664.
[20]	Gago-Carro, I., Aldasoro, U., Lee, D. J., & Merino, M. (2025). Hierarchical compromise optimization of ambulance locations under stochastic travel times. Comput. Oper. Res., 107208.
[21]	Rautenstrauss, M., Martin, L., & Minner, S. (2023). Ambulance dispatching during a pandemic: Tradeoffs of categorizing patients and allocating ambulances. Eur. J. Oper. Res., 304(1), 239–254.
[22]	Mandelbaum, A., & Stolyar, A. L. (2004). Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res., 52(6), 836–855.
[23]	Tsai, Y. C., & Argon, N. T. (2008). Dynamic server assignment policies for assembly-type queues with flexible servers. Nav. Res. Logist., 55(3), 234–251.
[24]	Iannoni, A. P., Chiyoshi, F., & Morabito, R. (2015). A spatially distributed queuing model considering dispatching policies with server reservation. Transp. Res. Part E Logist. Transp. Rev., 75, 49–66.
[25]	Wang, J., Liu, H., An, S., & Cui, N. (2016). A new partial coverage locating model for cooperative fire services. Inf. Sci., 373, 527–538.
[26]	Rodrigues, L. F., Morabito, R., Chiyoshi, F. Y., Iannoni, A. P., & Saydam, C. (2017). Towards hypercube queuing models for dispatch policies with priority in queue and partial backup. Comput. Oper. Res., 84, 92–105.
[27]	Liu, H., Yin, H., Zhou, Y., & Li, M. (2021). Cooperative hypercube queuing model for emergency service systems. J. Adv. Transp., 2021(1), 6653573.
[28]	Gu, Y., Jiang, L., Liu, H., Zhang, X., Wei, S., & Qi, Q. (2025). Advancing road traffic safety through stochastic modeling: An innovative assessment of emergency road rescue systems with the mn hypercube queuing model. J. Adv. Transp., 2025(1), 8145358.
[29]	Geroliminis, N., Karlaftis, M. G., & Skabardonis, A. (2009). A spatial queuing model for the emergency vehicle districting and location problem. Transp. Res. Part B Methodol., 43(7), 798–811.
[30]	Geroliminis, N., Kepaptsoglou, K., & Karlaftis, M. G. (2011). A hybrid hypercube–genetic algorithm approach for deploying many emergency response mobile units in an urban network. Eur. J. Oper. Res., 210(2), 287–300.
[31]	Zhen, L., Wu, J., Chen, F., & Wang, S. (2024). Traffic emergency vehicle deployment and dispatch under uncertainty. Transportation Research Part E: Logistics and Transportation Review, 183, 103449.

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APA Style

Jianhui, S., Xiaofeng, S., Jie, Z., Lanqing, J., Wenchao, Z., et al. (2026). Performance Approximation for Highway Emergency Rescue Systems. American Journal of Traffic and Transportation Engineering, 11(1), 1-14. https://doi.org/10.11648/j.ajtte.20261101.11

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ACS Style

Jianhui, S.; Xiaofeng, S.; Jie, Z.; Lanqing, J.; Wenchao, Z., et al. Performance Approximation for Highway Emergency Rescue Systems. Am. J. Traffic Transp. Eng. 2026, 11(1), 1-14. doi: 10.11648/j.ajtte.20261101.11

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AMA Style

Jianhui S, Xiaofeng S, Jie Z, Lanqing J, Wenchao Z, et al. Performance Approximation for Highway Emergency Rescue Systems. Am J Traffic Transp Eng. 2026;11(1):1-14. doi: 10.11648/j.ajtte.20261101.11

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@article{10.11648/j.ajtte.20261101.11,
  author = {Song Jianhui and Shu Xiaofeng and Zhong Jie and Jiang Lanqing and Zhang Wenchao and Shi Guoqing},
  title = {Performance Approximation for Highway Emergency Rescue Systems},
  journal = {American Journal of Traffic and Transportation Engineering},
  volume = {11},
  number = {1},
  pages = {1-14},
  doi = {10.11648/j.ajtte.20261101.11},
  url = {https://doi.org/10.11648/j.ajtte.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtte.20261101.11},
  abstract = {Ensuring prompt responses to spatially uncertain traffic accidents is critical for highway emergency rescue systems, aiming to address emergencies and to prevent network-wide traffic disruptions. This paper develops an approximation model to characterize priority-based rescue systems for RV fleets. By representing each RV's state as either idle or busy, we formulate an approximation model in which the dispatch probability of an RV is dynamically influenced by the utilization of higher-priority RVs and its own availability. The proportionality constant governing this relationship is derived analytically from an M/M/N queuing model, incorporating a random server selection mechanism without replacement until the first available RV is identified. The system of equations is simplified into a tractable set of N linear simultaneous equations, enabling efficient computation of RV workloads. We further propose a solution algorithm to estimate critical performance metrics, including individual RV workloads, system response times, and cross-dispatch frequencies. A practical case study based on the G15 Highway (Sutong Bridge section) in China illustrates the model's applicability in quantifying performance measures such as individual RV response times, cross-regional dispatch ratios, and workload distribution under varying vehicle allocations and priority levels. The proposed model provides a practical and computationally efficient tool to support RV location planning, response section partitioning, and overall performance evaluation in highway emergency services, offering valuable insights for optimizing rescue efficiency and resource allocation.},
 year = {2026}
}

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TY  - JOUR
T1  - Performance Approximation for Highway Emergency Rescue Systems
AU  - Song Jianhui
AU  - Shu Xiaofeng
AU  - Zhong Jie
AU  - Jiang Lanqing
AU  - Zhang Wenchao
AU  - Shi Guoqing
Y1  - 2026/01/19
PY  - 2026
N1  - https://doi.org/10.11648/j.ajtte.20261101.11
DO  - 10.11648/j.ajtte.20261101.11
T2  - American Journal of Traffic and Transportation Engineering
JF  - American Journal of Traffic and Transportation Engineering
JO  - American Journal of Traffic and Transportation Engineering
SP  - 1
EP  - 14
PB  - Science Publishing Group
SN  - 2578-8604
UR  - https://doi.org/10.11648/j.ajtte.20261101.11
AB  - Ensuring prompt responses to spatially uncertain traffic accidents is critical for highway emergency rescue systems, aiming to address emergencies and to prevent network-wide traffic disruptions. This paper develops an approximation model to characterize priority-based rescue systems for RV fleets. By representing each RV's state as either idle or busy, we formulate an approximation model in which the dispatch probability of an RV is dynamically influenced by the utilization of higher-priority RVs and its own availability. The proportionality constant governing this relationship is derived analytically from an M/M/N queuing model, incorporating a random server selection mechanism without replacement until the first available RV is identified. The system of equations is simplified into a tractable set of N linear simultaneous equations, enabling efficient computation of RV workloads. We further propose a solution algorithm to estimate critical performance metrics, including individual RV workloads, system response times, and cross-dispatch frequencies. A practical case study based on the G15 Highway (Sutong Bridge section) in China illustrates the model's applicability in quantifying performance measures such as individual RV response times, cross-regional dispatch ratios, and workload distribution under varying vehicle allocations and priority levels. The proposed model provides a practical and computationally efficient tool to support RV location planning, response section partitioning, and overall performance evaluation in highway emergency services, offering valuable insights for optimizing rescue efficiency and resource allocation.
VL  - 11
IS  - 1
ER  -

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Author Information

Song Jianhui

Jiangsu Sutong Bridge Co., Ltd, Soochow, China
Shu Xiaofeng

Transportation Engineering Construction Bureau, Soochow, China
Zhong Jie

Jiangsu Sutong Bridge Co., Ltd, Soochow, China
Jiang Lanqing

Jiangsu Baisheng Information Technology Co., Ltd, Soochow, China

Contact Email
Zhang Wenchao

China Communications Tunnel Engineering Bureau Co., Ltd, Soochow, China
Shi Guoqing

China Communications Tunnel Engineering Bureau Co., Ltd, Soochow, China

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APA Style

Jianhui, S., Xiaofeng, S., Jie, Z., Lanqing, J., Wenchao, Z., et al. (2026). Performance Approximation for Highway Emergency Rescue Systems. American Journal of Traffic and Transportation Engineering, 11(1), 1-14. https://doi.org/10.11648/j.ajtte.20261101.11

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ACS Style

Jianhui, S.; Xiaofeng, S.; Jie, Z.; Lanqing, J.; Wenchao, Z., et al. Performance Approximation for Highway Emergency Rescue Systems. Am. J. Traffic Transp. Eng. 2026, 11(1), 1-14. doi: 10.11648/j.ajtte.20261101.11

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AMA Style

Jianhui S, Xiaofeng S, Jie Z, Lanqing J, Wenchao Z, et al. Performance Approximation for Highway Emergency Rescue Systems. Am J Traffic Transp Eng. 2026;11(1):1-14. doi: 10.11648/j.ajtte.20261101.11

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@article{10.11648/j.ajtte.20261101.11,
  author = {Song Jianhui and Shu Xiaofeng and Zhong Jie and Jiang Lanqing and Zhang Wenchao and Shi Guoqing},
  title = {Performance Approximation for Highway Emergency Rescue Systems},
  journal = {American Journal of Traffic and Transportation Engineering},
  volume = {11},
  number = {1},
  pages = {1-14},
  doi = {10.11648/j.ajtte.20261101.11},
  url = {https://doi.org/10.11648/j.ajtte.20261101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtte.20261101.11},
  abstract = {Ensuring prompt responses to spatially uncertain traffic accidents is critical for highway emergency rescue systems, aiming to address emergencies and to prevent network-wide traffic disruptions. This paper develops an approximation model to characterize priority-based rescue systems for RV fleets. By representing each RV's state as either idle or busy, we formulate an approximation model in which the dispatch probability of an RV is dynamically influenced by the utilization of higher-priority RVs and its own availability. The proportionality constant governing this relationship is derived analytically from an M/M/N queuing model, incorporating a random server selection mechanism without replacement until the first available RV is identified. The system of equations is simplified into a tractable set of N linear simultaneous equations, enabling efficient computation of RV workloads. We further propose a solution algorithm to estimate critical performance metrics, including individual RV workloads, system response times, and cross-dispatch frequencies. A practical case study based on the G15 Highway (Sutong Bridge section) in China illustrates the model's applicability in quantifying performance measures such as individual RV response times, cross-regional dispatch ratios, and workload distribution under varying vehicle allocations and priority levels. The proposed model provides a practical and computationally efficient tool to support RV location planning, response section partitioning, and overall performance evaluation in highway emergency services, offering valuable insights for optimizing rescue efficiency and resource allocation.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Performance Approximation for Highway Emergency Rescue Systems
AU  - Song Jianhui
AU  - Shu Xiaofeng
AU  - Zhong Jie
AU  - Jiang Lanqing
AU  - Zhang Wenchao
AU  - Shi Guoqing
Y1  - 2026/01/19
PY  - 2026
N1  - https://doi.org/10.11648/j.ajtte.20261101.11
DO  - 10.11648/j.ajtte.20261101.11
T2  - American Journal of Traffic and Transportation Engineering
JF  - American Journal of Traffic and Transportation Engineering
JO  - American Journal of Traffic and Transportation Engineering
SP  - 1
EP  - 14
PB  - Science Publishing Group
SN  - 2578-8604
UR  - https://doi.org/10.11648/j.ajtte.20261101.11
AB  - Ensuring prompt responses to spatially uncertain traffic accidents is critical for highway emergency rescue systems, aiming to address emergencies and to prevent network-wide traffic disruptions. This paper develops an approximation model to characterize priority-based rescue systems for RV fleets. By representing each RV's state as either idle or busy, we formulate an approximation model in which the dispatch probability of an RV is dynamically influenced by the utilization of higher-priority RVs and its own availability. The proportionality constant governing this relationship is derived analytically from an M/M/N queuing model, incorporating a random server selection mechanism without replacement until the first available RV is identified. The system of equations is simplified into a tractable set of N linear simultaneous equations, enabling efficient computation of RV workloads. We further propose a solution algorithm to estimate critical performance metrics, including individual RV workloads, system response times, and cross-dispatch frequencies. A practical case study based on the G15 Highway (Sutong Bridge section) in China illustrates the model's applicability in quantifying performance measures such as individual RV response times, cross-regional dispatch ratios, and workload distribution under varying vehicle allocations and priority levels. The proposed model provides a practical and computationally efficient tool to support RV location planning, response section partitioning, and overall performance evaluation in highway emergency services, offering valuable insights for optimizing rescue efficiency and resource allocation.
VL  - 11
IS  - 1
ER  -

Copy | Download