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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/199216
- The variance of production counts over a long time horizon
- Nazarathy, Yoni
- Consider a production process. Once the throughput is known, knowledge of the variability can allow managers to allocate storage and transportation resources more effectively. This has led some researchers over the past years to develop computational models for assessing the variability of complex production systems. Since the variance of the number of items produced during the time interval [0,t] typically grows linearly for large t, a natural quantity of interest is the asymptotic variance rate - this is the asymptotic slope of the variance of the number of items produced during [0,t]. Quite surprisingly, the asymptotic variance of more elementary models such as the single server queue has not received attention until recently. For such models it is quite clear that the asymptotic variance rate is determined by the arrivals for under-loaded systems and is determined by the services for over-loaded systems. In the case of critically loaded systems both the arrivals and services play a role. In this case, we have discovered that the asymptotic variance rate is often reduced by a factor of about 30% compared to the average of the arrival and service processes!!! We call this phenomena BRAVO - Balancing Reduces Asymptotic Variance of Outputs. While it is so far proved only for single station queuing models, we believe that this phenomenon holds in great generality and should thus be made known to managers of production systems and supply chains. This presentation is based on some joint works with Ahmad Al-Hanbali, Yoav Kerner, Michel Mandjes, Ward Whitt and Gideon Weiss.
- Publication type
- Conference paper
- Paper presented at the EURANDOM Workshop on Stochastic Models of Manufacturing Systems, Eindhoven, Netherlands, 24-25 June 2010
- Publication year
- Asymptotic variance rate; Production systems
- European Institute for Statistics, Probability, Stochastic Operations Research and its Applications
- Publisher URL
- Copyright © 2010.