The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Queueing Theory

  • Matthew J. Sobel
Reference work entry


Queueing theory is about mathematical models of congestion and delay phenomena. Most of the models are stochastic and, until the 1970s, they described physical rather than economic characteristics. For example, there is more theory from which one could deduce the (probability) distribution of the number of items stored in an inventory system than there is to specify a pattern of tolls which is appropriate for a municipal road traffic network. Similarly, the theory for models of a single service facility, such as a post office, is more highly developed than the theory for networks of service facilities, such as a multi-access computer network. Recent and current research, often motivated by emerging technology in manufacturing and computer-based communication systems, is redressing the imbalances.

This is a preview of subscription content, log in to check access.


  1. Cohen, J.W. 1969. The single server queue. New York: Wiley.Google Scholar
  2. Cooper, R.B. 1981. Introduction to queueing theory, 2nd ed. New York: North-Holland.Google Scholar
  3. Crabill, T.B., D. Gross, and M.J. Magazine. 1977. A classified bibliography of research on optimal design and control of queues. Operations Research 15: 304–318.Google Scholar
  4. Disney, R.L., and D. Konig. 1985. Queueing networks – A survey of their random processes. SIAM Review 27(3): 335–403.CrossRefGoogle Scholar
  5. Godwin, H.J. 1964. Inequalities on distribution functions. London: Griffin.Google Scholar
  6. Gross, D., and C.M. Harris. 1985. Fundamentals of queueing theory, 2nd ed. New York: Wiley.Google Scholar
  7. Harrison, J.M. 1985. Brownian motion and stochastic flow systems. New York: Wiley.Google Scholar
  8. Heyman, D.P., and M.J. Sobel. 1982. Stochastic models in operations research, vol. I: Stochastic processes and operating characteristics. New York: McGraw-Hill.Google Scholar
  9. Kelley, F.P. 1979. Reversibility, and stochastic networks. New York: Wiley.Google Scholar
  10. Lu, F.V., and R. Serfozo. 1983. M/M/1 queueing decision processes with monotone hysteretic optimal policies. Operations Research 32(5): 1116–1132.CrossRefGoogle Scholar
  11. Mendelson, H. 1985. Pricing computer services: Queueing effects. Communications of the ACM 28(3): 312–321.CrossRefGoogle Scholar
  12. Neuts, M.F. 1981. Matrix-geometric solutions in stochastic models. Baltimore: Johns Hopkins University Press.Google Scholar
  13. Pinedo, M., and L. Schrage. 1982. Stochastic shop scheduling – A survey. In Deterministic and stochastic scheduling, ed. M.A.H. Dempster et al. Dordrecht: Reidel.Google Scholar
  14. Ramakrishnan, K.G., and D. Mitra. 1982. An overview of PANACEA, a software package for analyzing Markovian queuing networks. Bell System Technical Journal 61(10): 2849–2872.CrossRefGoogle Scholar
  15. Schassberger, R. 1978. Insensitivity of stationary probabilities in networks of queues. Advances in Applied Probability 10(4): 906–912.CrossRefGoogle Scholar
  16. Stidham Jr., S. 1970. On the optimality of single-server queueing systems. Operations Research 18: 708–732.CrossRefGoogle Scholar
  17. Stoyan, D. 1977. Bounds and approximations in queueing through monotonicity and continuity. Operations Research 25: 851–863.CrossRefGoogle Scholar
  18. Syski, R. 1960. Introduction to congestion theory in telephone systems. Edinburgh/London: Oliver & Boyd.Google Scholar
  19. Weiss, G. 1982. Multiserver stochastic scheduling. In Deterministic and stochastic scheduling, ed. M.A.H. Dempster et al. Dordrecht: Reidel.Google Scholar
  20. Whitt, W. 1983. The queuing network analyzer. Bell System Technical Journal 62(9): 2779–2816.CrossRefGoogle Scholar
  21. Whitt, W. 1974. Heavy traffic limit theorems for queues: A survey. In Mathematical methods in queueing theory, ed. A.B. Clarke. New York: Springer.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Matthew J. Sobel
    • 1
  1. 1.