Skip to main content Accessibility help

Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times

  • Patricia A. Jacobs (a1)


Models are given for sequences of correlated exponential interarrival and service times for a single-server queue. These multivariate exponential models are formed as probabilistic linear combinations of sequences of independent exponential random variables and are easy to generate on a computer. Limiting results for customer waiting time under heavy traffic conditions are obtained for these queues. Heavy traffic results are useful for analyzing the effect of correlated interarrival and service times in queues on such quantities as queue length and customer waiting time. They can also be used to check simulation results.


Corresponding author

Postal address: Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, U.S.A.


Hide All

Support from NSF grants ENG-77-09020 and ENG-79-01438 and ONR contract NR-42-284 is gratefully acknowledged.



Hide All
1. Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.
2. Boonsong, P. (1978) A Simulation Study of a Class of First-Come First-Served Queues with earma Correlation Structure. , Naval Postgraduate School, Monterey, California.
3. Jacobs, P. A. and Lewis, P. A. W. (1977) A mixed autoregressive-moving average exponential sequence and point process (earma 1, 1). Adv. Appl. Prob. 9, 87104.
4. Jacobs, P. A. (1978) A cyclic queueing network with dependent exponential service times. J. Appl. Prob. 15, 573589.
5. Kingman, J. F. C. (1962) On queues in heavy traffic. J. Roy. Statist. Soc. B 24, 383392.
6. Lewis, P. A. W. and Shedler, G. S. (1977) Analysis and modelling of point processes in computer systems. Bull. Int. Statist. Inst. 47, 193210.
7. Lewis, P. A. W. and Shedler, G. S. (1977) Analysis and modelling of point processes in computer systems. Naval Postgraduate School Technical Report NPS55-77-38.
8. Lindvall, T. (1973) Weak convergence of probability measures and random functions in the function space D[0, ∞). J. Appl. Prob. 10, 109121.
9. Loynes, R. M. (1962) The stability of a queue with non-independent interarrival and services. Proc. Camb. Phil. Soc. 58, 497520.
10. Rosenblatt, M. (1971) Markov Processes. Structure and Asymptotic Behavior. Springer-Verlag, Berlin.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed