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Estimating variance of output from cyclic exponential queueing systems

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Abstract

Production systems, particularly those making use of a “pull” production control mechanism, are well-modeled as closed queueing networks. Average throughput is clearly one important performance measure for these systems. However, many control decisions require information concerning the variability of the output process as well as throughput. Because of this, the standard deviation of the number of outputs during a specified interval is a practical performance measure for production systems.

In this paper, we consider the standard deviation of the number of outputs during a time interval from a closed queueing network consisting ofM single server exponential queues. Because computing this quantity exactly is extremely cumbersome, we introduce a simple approximation that makes use of (1) known results for the variance of the time a marked job takes to complete a round trip and (2) an approximate correction term for the covariance between successive round trips. We show through comparisons with simulation that our method is quite accurate under a variety of conditions.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, 60208, Evanston, IL, USA

    Izak Duenyas & Wallace J. Hopp

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  1. Izak Duenyas
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  2. Wallace J. Hopp
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Duenyas, I., Hopp, W.J. Estimating variance of output from cyclic exponential queueing systems. Queueing Syst 7, 337–353 (1990). https://doi.org/10.1007/BF01154550

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  • DOI: https://doi.org/10.1007/BF01154550

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