Abstract
The generality and usefulness ofM/G/C/C state dependent queueing models for modelling pedestrian traffic flows is explored in this paper. We demonstrate that the departure process and the reversed process of these generalizedM/G/C/C queues is a Poisson process and that the limiting distribution of the number of customers in the queue depends onG only through its mean. Consequently, the models developed in this paper are useful not only for the analysis of pedestrian traffic flows, but also for the design of the physical systems accommodating these flows. We demonstrate how theM/G/C/C state dependent model is incorporated into the modelling of large scale facilities where the blocking probabilities in the links of the network can be controlled. Finally, extensions of this work to queueing network applications where blocking cannot be controlled are also presented, and we examine an approximation technique based on the expansion method for incorporating theseM/G/C/C queues in series, merge, and splitting topologies of these networks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Altiok, Approximate analysis of exponential tandem queues with blocking, Eur. J. Oper. Res. 11 (1982) 390–398.
T. Altiok and H.G. Perros, Open networks of queues with blocking: Split and merge configurations, IIE Trans. (1986) 251–261.
N. Ashford and M. O'Leary, Stochastic modeling of passenger and baggage flows through an airport terminal, Traffic. Engin. Control (1976) 207–210.
N. Chikhale and J.M. Smith, Sensitivity analysis in open finite queueing networks, Paper presented at the ORSA/TIMS Meeting, Las Vegas Nevada (1990).
J. Cheah, State dependent queueing models, Master's Thesis, Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, MA (1990).
S. Daskalaki and J.M. Smith, Real time routing in finite queueing networks, eds. H. Perros and T. Altiok, in:Queueing Networks with Blocking (1989) pp. 313–324.
J.J. Fruin,Pedestrian Planning and Design (Metropolitan Assoc. of Urban Des. and Env. Ping., New York, NY, 1971).
D. Gross and C.M. Harris,Fundamentals of Queueing Theory (Wiley, New York, 1985).
S. Jain and J.M. Smith, Optimization of queueing networks with parallel servers, paper presented at the ORSA/TIMS Conference, New York City (1989).
F. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).
C.J. Karbowicz and J.M. Smith, A K-shortest paths routing heuristic for stochastic network evacuation models, Eng. Optimiz. 7 (1984) 253–280.
L. Kerbache, Analysis of open finite queueing networks, Ph.D. Dissertation, Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, MA (1984).
L. Kerbache and J.M. Smith, Asymptotic behaviour of the expansion method for open finite queueing networks, Comp. Oper. Res. 15 (1988) 157–169.
L. Kerbache and J.M. Smith, The generalized expansion method for open finite queueing networks, Eur. J. Oper. Res. 32 (1987) 448–461.
L. Kleinrock,Queueing Systems, Vol. I: Theory (Wiley, New York, 1975).
J. Labetoulle and G. Pujolle, Isolation method in a network of queues, IEEE Trans. Software Eng. SE-6 (1980) 373–380.
A. Lee,Applied Queueing Theory (St. Marin's Press, New York, 1966).
H.G. Perros, Queueing networks with blocking: A bibliography, ACM Sigmetrics 12 (1984) 8–12.
H.G. Perros and T. Altiok, Approximate analysis of open networks of queues with blocking: Tandem configurations, IEEE Trans. Software Eng. SE-12 (1986) 450–461.
S. Ross,Stochastic Processes (Wiley, New York, 1983).
J.M. Smith, R.J. Graves and L. Kerbache, QNET: An open queueing network model for material handling system analysis, Material Flow 3 (1986) 225–242.
J.M. Smith and L. Kerbache, Design of large scale facilities with open finite queueing networks, in review (1989).
J.M. Smith and J. Cheah,M/G/C/C state dependent queues and queueing network models, Paper presented at the SIAM Meeting on Applied Probability, New Orleans, LA (1990).
J.M. Smith, State dependent queueing models in emergency evacuation networks, Transport. Res. B25 (1991) 373–389.
J.M. Smith, State dependent queues, facilities, and finite queueing network models, in review (1991).
J.M. Smith, Topological network design of Steiner trees having random flows, in review (1992).
P. Tregenza,The Design of Interior Circulation (Van Norstrand Reinhold, New York, NY, 1976).
X. Wang and J.M. Smith, On the application of a diffusion approximation forGI/G/1/N queues, paper presented at the ORSA/TIMS Meeting, New York City (1989).
S. Yuhaski and J.M. Smith, Modeling circulation systems in buildings using state dependent queueing models, Queueing Systems 4 (1989) 319–338.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cheah, J.Y., Smith, J.M. Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows. Queueing Syst 15, 365–386 (1994). https://doi.org/10.1007/BF01189246
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01189246