Skip to main content
SpringerLink
Log in

Transient and asymptotic behavior of synchronization processes in assembly-like queues

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper analyzes the synchronization process of an assembly-like queueing system in which two distinct types of items/customers arrive at separate buffers, according to independent Poisson processes, so as to be synchronized into pairs at a synchronization node. Once a pair is synchronized it then queues up for service from a single server on a first-in-first-out basis as pairs. It is assumed that the service times of pairs are exponentially distributed and that the system has infinite capacity. Despite their practical significance, such queueing systems have not been adequately treated in the literature due to their transience or null recurrence. We first investigate the transient and asymptotic properties of the synchronization process’ first two moments, both analytically and numerically. Motivated by the observed asymptotic behavior, we then propose an M/M/1 approximation to describe the behavior of such assembly-like queueing systems. Finally, a numerical study of the proposed approximation reveals that it performs sufficiently well for practical applications.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramowitz, M., & Stegun, I. A. (1964). US national bureau of standards, applied mathematics series : Vol. 55. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover.

    Google Scholar 

  • Asmussen, S. (2000). Applied probability and queues (2nd ed.). New York: Springer.

    Google Scholar 

  • Baccelli, F., & Makowski, A. M. (1989). Queueing models for systems with synchronization constraints. Proceedings of the IEEE, 77(1), 138–161.

    Article  Google Scholar 

  • Bhat, U. N. (1986). Finite capacity assembly-like queues. Queueing Systems, 1(1), 85–101.

    Article  Google Scholar 

  • Bonomi, F. (1987). An approximate analysis for a class of assembly-like queues. Queueing Systems, 1(3), 289–309.

    Article  Google Scholar 

  • Burke, P. (1956). The output of a queuing system. Operations Research, 4(5), 699–704.

    Article  Google Scholar 

  • Duenyas, I., & Hopp, W. J. (1993). Estimating the throughput of an exponential CONWIP assembly system. Queueing Systems, 14(1–2), 137–157.

    Google Scholar 

  • Foster, F. G. (1959). A unified theory of stock, storage and queue control. Operational Research Quarterly, 10(3), 121–130.

    Article  Google Scholar 

  • Fukuda, A., Sato, S., & Mukumoto, K. (1988). Parallel queues with common service process and their input control. Electronics and Communications in Japan, Part 1: Communications, 71(4), 1–14.

    Article  Google Scholar 

  • Harrison, J. M. (1973). Assembly-like queues. Journal of Applied Probability, 10(2), 354–367.

    Article  Google Scholar 

  • Hopp, W. J., & Simon, J. T. (1989). Bounds and heuristics for assembly-like queues. Queueing Systems, 4(2), 137–155.

    Article  Google Scholar 

  • Kashyap, B. R. K. (1966). The double-ended queue with bulk service and limited waiting space. Operations Research, 14(5), 822–834.

    Article  Google Scholar 

  • Keblis, M. F., & Duenyas, I. (1999). Control of an assembly system with processing time and subassembly-type uncertainty. Queueing Systems, 11(4), 353–370.

    Google Scholar 

  • Kendall, D. G. (1951). Some problems in the theory of queues. Journal of the Royal Statistical Society, Series B, 13(2), 151–185.

    Google Scholar 

  • Lipper, E. H., & Sengupta, B. (1986). Assembly-like queues with finite capacity: bounds, asymptotics and approximations. Queueing Systems, 1(1), 67–83.

    Article  Google Scholar 

  • Prabhakar, B., Bambos, N., & Mountford, T. S. (2000). The synchronization of Poisson processes and queueing networks with service and synchronization nodes. Advances in Applied Probability, 32(3), 824–843.

    Article  Google Scholar 

  • Sasieni, M. W. (1961). Double queues and impatient customers with and application to inventory theory. Operations Research, 9(6), 771–781.

    Article  Google Scholar 

  • Som, P., Wilhelm, W. E., & Disney, R. L. (1994). Kitting process in a stochastic assembly system. Queueing Systems, 17(3–4), 471–490.

    Article  Google Scholar 

  • Takahashi, M., Ōsawa, H., & Fujisawa, T. (2000). On a synchronization queue with two finite buffers. Queueing Systems, 36(1–3), 107–123.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Finance and Quantitative Analysis, University of Otago, P.O. Box 56, Dunedin, 9054, New Zealand

    David R. Alexander & I. M. Premachandra

  2. Graduate School of Economics and Business Administration, Hokkaido University, Nishi 7, Kita 9, Kita-ku, Sapporo, 060-0809, Japan

    Toshikazu Kimura

Authors
  1. David R. Alexander
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. M. Premachandra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Toshikazu Kimura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David R. Alexander.

Additional information

T. Kimura is supported in part by the Japan Society for the Promotion of Science under Grant 20241037.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alexander, D.R., Premachandra, I.M. & Kimura, T. Transient and asymptotic behavior of synchronization processes in assembly-like queues. Ann Oper Res 181, 641–659 (2010). https://doi.org/10.1007/s10479-010-0796-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-010-0796-9

Keywords

Search

Navigation