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  • 1
    Electronic Resource
    Electronic Resource
    On the steady-state queue size distribution of the discrete-timeGeo/G/1 queue with repeated customers (1995)
    Springer
    Queueing systems 21 (1995), S. 199-215 
    Details
    ISSN: 1572-9443
    Keywords: Discrete-time queues ; generating functions ; recursive computation ; retrial queues ; stochastic decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, we study the steady-state queue size distribution of the discrete-timeGeo/G/1 retrial queue. We derive analytic formulas for the probability generating function of the number of customers in the system in steady-state. It is shown that the stochastic decomposition law holds for theGeo/G/1 retrial queue. Recursive formulas for the steady-state probabilities are developed. Computations based on these recursive formulas are numerically stable because the recursions involve only nonnegative terms. Since the regularGeo/G/1 queue is a special case of theGeo/G/1 retrial queue, the recursive formulas can also be used to compute the steady-state queue size distribution of the regularGeo/G/1 queue. Furthermore, it is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/1 retrial queue by dividing the time into small intervals of equal length and the approximation approaches the exact when the length of the interval tends to zero. This relationship allows us to apply the recursive formulas derived in this paper to compute the approximate steady-state queue size distribution of the continuous-timeM/G/1 retrial queue and the regularM/G/1 queue.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158581
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  • 2
    Electronic Resource
    Electronic Resource
    A Probability-Based Renewal Rainfall Model for Flow Forecasting (1997)
    Springer
    Natural hazards 15 (1997), S. 51-70 
    Details
    ISSN: 1573-0840
    Keywords: flood warning ; rainfall forecasting ; Markov chain ; transition probability matrix ; transfer function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In real-time flood warning systems, sufficient lead-time is important for people to take suitable actions. Rainfall forecasting is one of the ways commonly used to extend the lead-time for catchments with short response time. However, an accurate forecast of rainfall is still difficult for hydrologists using the present deterministic model. Therefore, a probability-based rainfall forecasting model, based on Markov chain, was proposed in this study. The rainfall can be forecast one to three hours in advance for a specified nonexceeding probability using the transition probability matrix of rainfall state. In this study, the nonexceeding probability, which was hourly updated on the basis of development or decay of rainfall processes, was taken as a dominant variable parameter. The accuracy of rainfall forecasting one to three hours in advance is concluded from the application of this model to four recording rain gauges. A lumped rainfall-runoff forecasting model derived from a transfer function was further applied in unison with this rainfall forecasting model to forecast flows one to four hours in advance. The results of combination of these two models show good performance with agreement between the observed and forecast hydrographs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007946628274
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