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On the output dynamics of production systems subject to blocking

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  • Barış Tan
  • Svenja Lagershausen

Abstract

Analyzing the output dynamics of a production system gives valuable information for operation and performance evaluation of a production system. In this article, we present an analytical method to determine the autocorrelation of the inter-departure times in queueing networks subject to blocking that can be represented by a Continuous-Time Markov Chain. We particularly focus on production systems that are modeled as open or closed queueing networks, and where stations have phase-type service time distributions. We use the analytical results for the mean and the variance of the time to produce a given number of products in queueing networks to determine the correlation of inter-departure times with different lags. We present a computationally efficient recursive method to determine the correlation of the inter-departure times in open and closed queueing networks. The method also yields closed-form expressions for the correlations of a two-station production line with exponential servers and a finite buffer. We show how the correlations develop with increasing lags subject to different processing time distributions, buffer capacities, and number of stations, in both open and closed queueing networks. As a result, we propose the analytical method given in this study as a tool to study the effects of design and control parameters on the output dynamics of production systems.

Suggested Citation

  • Barış Tan & Svenja Lagershausen, 2017. "On the output dynamics of production systems subject to blocking," IISE Transactions, Taylor & Francis Journals, vol. 49(3), pages 268-284, March.
    • Handle: RePEc:taf:uiiexx:v:49:y:2017:i:3:p:268-284
    DOI: 10.1080/0740817X.2016.1222470
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    Cited by:

    1. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    2. Khayyati, Siamak & Tan, Barış, 2020. "Data-driven control of a production system by using marking-dependent threshold policy," International Journal of Production Economics, Elsevier, vol. 226(C).
    3. Nima Manafzadeh Dizbin & Barış Tan, 2019. "Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 1042-1076, December.

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