# Graph and Analytical Models for Emergency Evacuation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Graph Based Critical Sensor Assessment

^{2}.

**Algorithm 1—Identifying the Most Disruptive Fire Outbreak Locations**

**Figure 1.**The colours attributed to each node represent the optimal floor exit, e.g., nodes coloured in blue will see their occupants exit through the N-E stairs. The red Diamond shows the fire location, the stars show the building exits. (

**a**) shows the reference map when there is no fire; (

**b**) illustrates a fire outbreak at a non-critical area—causing very little changes compared with the reference map; (

**c**) illustrates a fire outbreak at a critical area—highlighted by the profound changes compared with the reference map.

**Algorithm 2—Determining the Busiest Nodes During an Evacuation**

**Figure 2.**Graphical representation of the output of Algorithm 2, where line thickness increases with visit count. The cyan star on the ground floor marks the exit. Results shown for a subset of all building locations.

#### 2.1. Improving the Critical Sensors

**Algorithm 1**is most effective in intricate graphs featuring staircases, corridors and partitioned space, where an evacuation plan must be decided early based on the designation of strategic areas.**Algorithm 2**is best suited for open spaces, where bypassing the fire is generally trivial and the critical decisions relate to the availability of exits and how to approach them.

## 3. Queueing Analysis

#### 3.1. Analytical Results

**Figure 4.**Time needed to reach the exit based on the time at which the node of interest was visited. The red line shows the steady-state value predicted by the queueing network analysis.

## 4. Conclusions

- Compare the performance of the graph-based algorithms in either flat open-space areas or intricate multi-storey buildings to validate the hypothesis that the algorithms presented are better suited to some types of graphs.
- Devise more complex evacuation scenarios so that the performance gap between optimal and realistic scenarios is widened. The relative ease of evacuating the building resulted in rather high performance in the worst-case scenario, meaning that there is only limited scope for improvement.

## References

- Wong, J.; Li, H.; Wang, S. Intelligent building research: A review. Autom. Constr.
**2005**, 14, 143–159. [Google Scholar] [CrossRef] - Gelenbe, E.; Wu, F.J. Large scale simulation for human evacuation and rescue. Comput. Math. Appl.
**2012**, 64, 3869–3880. [Google Scholar] [CrossRef] - Schor, L.; Sommer, P.; Wattenhofer, R. Towards a zero-configuration wireless sensor network architecture for smart buildings. In Proceedings of the First ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Buildings; ACM: New York, NY, USA, 3 November 2009; pp. 31–36. [Google Scholar]
- Agarwal, Y.; Balaji, B.; Gupta, R.; Lyles, J.; Wei, M.; Weng, T. Occupancy-driven energy management for smart building automation. In Proceedings of the 2nd ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Building; ACM: New York, NY, USA, 3–5 November 2010; pp. 1–6. [Google Scholar]
- Snoonian, D. Smart buildings. IEEE Spectr.
**2003**, 40, 18–23. [Google Scholar] [CrossRef] - Aguilar, J.; Gelenbe, E. Task assignment and transaction clustering heuristics for distributed systems. Inf. Sci.
**1997**, 97, 199–219. [Google Scholar] [CrossRef] - Desmet, A.; Gelenbe, E. Interoperating Infrastructures in Emergencies; Gelenbe, E., Lent, R., Eds.; Springer: London, UK, 2012; pp. 123–130. [Google Scholar]
- Hoblos, G.; Staroswiecki, M.; Aitouche, A. Optimal design of fault tolerant sensor networks. In Proceedings of the 2000 IEEE International Conference on Control Applications, Anchorage, AK, USA, 25–27 September 2000; pp. 467–472.
- Ali, Y.; Narasimhan, S. Sensor network design for maximizing reliability of linear processes. AIChE J.
**1993**, 39, 820–828. [Google Scholar] [CrossRef] - Wang, F.; Ramamritham, K.; Stankovic, J. Determining redundancy levels for fault tolerant real-time systems. IEEE Trans. Comput.
**1995**, 44, 292–301. [Google Scholar] [CrossRef] - Maquin, D.; Luong, M.; Ragot, J. Some ideas about the design of measurement system. In Proceedings of European Control Conference ECC’95, Rome, Italy, 5–8 September 1995; pp. 3178–3183.
- Lee, W.S.; Grosh, D.L.; Tillman, F.A.; Lie, C.H. Fault tree analysis, methods, and applications 2013: A review. IEEE Trans. Reliab.
**1985**, R-34, 194–203. [Google Scholar] [CrossRef] - Dimakis, N.; Filippoupolitis, A.; Gelenbe, E. Distributed building evacuation simulator for smart emergency management. Comput. J.
**2010**, 53, 1384–1400. [Google Scholar] [CrossRef] - Gorbil, G.; Gelenbe, E. Opportunistic communications for emergency support systems. Procedia Comput. Sci.
**2011**, 5, 39–47. [Google Scholar] [CrossRef] - Gelenbe, E.; Hussain, K.; Kaptan, V. Simulating autonomous agents in augmented reality. J. Syst. Softw.
**2005**, 74, 255–268. [Google Scholar] [CrossRef] - Filippoupolitis, A.; Gelenbe, E. A distributed decision support system for building evacuation. In Proceedings of 2nd Conference on Human System Interactions HSI ’09, Catania, Italy, 21–23 May 2009; pp. 320–327.
- Gelenbe, E.; Muntz, R.R. Probabilistic models of computer systems: Part I (exact results). Acta Inf.
**1976**, 7, 35–60. [Google Scholar] [CrossRef] - Gelenbe, E.; Pujolle, G. Introduction to Queueing Networks; John Wiley: London, UK, 1998. [Google Scholar]
- Gelenbe, E.; Mitrani, I. Analysis and Synthesis of Computer Systems; World Scientific: Singapore, 2010. [Google Scholar]
- Gelenbe, E.; Hussain, K.; Kaptan, V. Simulating autonomous agents in augmented reality. J. Syst. Softw.
**2005**, 74, 255–268. [Google Scholar] [CrossRef] - Kaptan, V.; Gelenbe, E. Fusing terrain and goals: Agent control in urban environments. In Proceedings of Multisource Information Fusion: Architectures, Algorithms, and Applications 2006, Kissimmee, FL, USA, 19–20 April 2006; Volume 6242, pp. 71–79.
- Smith, J.M. State-dependent queueing models in emergency evacuation networks. Transp. Res. Part B Methodol.
**1991**, 25, 373–389. [Google Scholar] [CrossRef] - Bakuli, D.L.; Smith, J.M. Resource allocation in state-dependent emergency evacuation networks. Eur. J. Oper. Res.
**1996**, 89, 543–555. [Google Scholar] [CrossRef] - Hasofer, A.; Odigie, D. Stochastic modelling for occupant safety in a building Fire. Fire Saf. J.
**2001**, 36, 269–289. [Google Scholar] [CrossRef] - Elms, D.; Buchanan, A.; Dusing, J. Modeling fire spread in buildings. Fire Technol.
**1984**, 20, 11–19. [Google Scholar] [CrossRef] - Gelenbe, E.; Hébrail, G. A probability model of uncertainty in data bases. In Proceedings of the Second International Conference on Data Engineering, Los Angeles, CA, USA, 5–7 February 1986; pp. 328–333.
- Nardelli, E.; Proietti, G.; Widmayer, P. Finding the most vital node of a shortest path. Theor. Comput. Sci.
**2003**, 1, 167–177. [Google Scholar] [CrossRef] - Gelenbe, E. Sensible decisions based on QoS. Comput. Manag. Sci.
**2003**, 1, 1–14. [Google Scholar] [CrossRef] - Gelenbe, E. Steps towards self-aware networks. Commun. ACM
**2009**, 52, 66–75. [Google Scholar] [CrossRef] - Gelenbe, E.; Stafylopatis, A. Global behaviour of homogeneous random neural systems. Appl. Math. Model.
**1991**, 15, 534–541. [Google Scholar] [CrossRef] - Atalay, V.; Gelenbe, E. Parallel algorithm for colour texture generation using the random neural network model. Int. J. Pattern Recognit. Artif. Intell.
**1992**, 6, 437–446. [Google Scholar] [CrossRef] - Fourneau, J.M.; Gelenbe, E. Random neural networks with multiple classes of signals. Neural Comput.
**1999**, 11, 953–963. [Google Scholar]

© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Desmet, A.; Gelenbe, E. Graph and Analytical Models for Emergency Evacuation. *Future Internet* **2013**, *5*, 46-55.
https://doi.org/10.3390/fi5010046

**AMA Style**

Desmet A, Gelenbe E. Graph and Analytical Models for Emergency Evacuation. *Future Internet*. 2013; 5(1):46-55.
https://doi.org/10.3390/fi5010046

**Chicago/Turabian Style**

Desmet, Antoine, and Erol Gelenbe. 2013. "Graph and Analytical Models for Emergency Evacuation" *Future Internet* 5, no. 1: 46-55.
https://doi.org/10.3390/fi5010046