Approximate models of air transport queueing systems with partial mutual assistance between service channels

Cite item


Approximate analytical models are proposed for two types of multi-channel queuing systems with partial mutual assistance between channels and waiting in limited-size and unbounded queues. The incoming flow of requests is a superposition of several simplest flows. It is assumed that normative numbers of channels for servicing a customer that differ depending on the flow of incoming customer requests are established. In the systems of the first type the normative number of channels is not necessary: a customer is accepted for servicing if there are free channels in the system and the number of channels is smaller than the normative one. Service time is distributed exponentially with the average inversely proportional to the number of allocated channels. In systems of the second type the service of a customer is always performed by the channels of the normative number. Service time can be distributed arbitrarily (not only exponentially) with the average irrespective of the number of allocated channels. The paper presents the results of comparative analysis of the results of dealing with some tasks of designing service systems in a wide range of input data using simulation modelling and calculations based on approximate analytical models that allowed evaluating the application area of the latter and making a conclusion about their satisfactory accuracy. Examples of the use of models of technological processes of airport ground handling as queuing systems of the considered types are given.

About the authors

V. A. Romanenko

Samara National Research University

Author for correspondence.
ORCID iD: 0000-0003-3897-2238

Candidate of Science (Engineering), Associate Professor, Associate Professor of the Department of Transportation Management and Control

Russian Federation


  1. Bocharov P.P., Pechinkin A.V. Teoriya massovogo obsluzhivaniya [Queuing Theory]. Moscow: RUDN University Publ., 1995. 529 p.
  2. Andronov A.M., Khizhnyak A.N. Matematicheskie metody planirovaniya i upravleniya proizvodstvennoy deyatel'nost'yu predpriyatiy grazhdanskoy aviatsii [Mathematical methods for planning and managing the production activities of civil aviation enterprises]. Moscow: Transport Publ., 1977. 215 p.
  3. Kleinrock L. Queueing systems. V. I. Theory. New York: Wiley-Interscience Publ., 1974. 448 p.
  4. Naji M., Braytee A., Al-Ani A., Anaissi A., Goyal M., Kennedy P.J. Design of airport security screening using queueing theory augmented with particle swarm optimisation. Service Oriented Computing and Applications. 2020. V. 14, Iss. 2. P. 119-133. doi: 10.1007/s11761-020-00291-0
  5. Wang M.J. Application of the queuing theory in characterizing and optimizing the passenger flow at the airport security. Journal of Applied Mathematics and Physics. 2017. V. 5, Iss. 9. P. 1620-1628. doi: 10.4236/jamp.2017.59134
  6. Shone R., Glazebrook K., Zografos K.G. Resource allocation in congested queueing systems with time-varying demand: An application to airport operations. European Journal of Operational Research. 2019. V. 276, Iss. 2. P. 566-581. doi: 10.1016/j.ejor.2019.01.024
  7. Itoh E., Mitici M. Queue-based modeling of the aircraft arrival process at a single airport. Aerospace. 2019. V.6, Iss.10. doi: 10.3390/aerospace6100103
  8. Stolletz R. Analysis of passenger queues at airport terminals. Research in Transportation Business and Management. 2011. V. 1, Iss. 1. P. 144-149. doi: 10.1016/j.rtbm.2011.06.012
  9. Jawab F., Khachani M., Akoudad K., Moufad I., Frichi Y., Laaraj N., Zehmed K. Queuing model for improving airport passengers treatment process. Proceedings of the ICIEOM: International Conference on Industrial Engineering and Operations Management (July, 26-27, 2018, Paris, France). P. 2095-2107
  10. Satanaryana V.V., Shaik Dawood A.K., Karthikeyan R., Khan N. Application of queuing theory models for optimized service to airline passengers. International Journal of Current Research. 2015. V. 7, Iss. 09. P. 20544-20547
  11. Airport Development Reference Manual. 10th edition. International Air Transport Association. Montrea, 2014.
  12. Romanenko V.A. Optimizing technological process control of hub airport as queueing system with non-stationary flows and partial mutual assistance between channels. Large-Scale Systems Control. 2012. No. 36. P. 209-247. (In Russ.)
  13. Ovcharov L.A. Prikladnye zadachi teorii massovogo obsluzhivaniya [Applications of queuing theory]. Moscow: Mashinostroenie Publ., 1969. 324 p.
  14. Romanenko V.A. Matematicheskie modeli funktsionirovaniya uzlovykh aeroportov v usloviyakh sovremennogo aviatransportnogo rynka [Mathematical models of hub airport operation in the modern air transport market]. Samara: As Gard Publ., 2010. 244 p.

Copyright (c) 2023 VESTNIK of Samara University. Aerospace and Mechanical Engineering

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies