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The authors propose two multirate teletraffic loss models in a two‐link system that accommodates Poisson arriving calls from different service‐classes with different bandwidth‐per‐call requirements. Each link has two thresholds which refer to the number of in‐service calls in the link. The lowest threshold named support threshold, defines up to which point the link can support calls offloaded from the other link. The highest threshold, named offloading threshold, defines the point where the link starts offloading calls to the other link. Two different bandwidth sharing policies are considered: (i) the complete sharing policy, in which a call can be accepted in a link if there exist enough available bandwidth units and (ii) the bandwidth reservation policy, in which an integer number of bandwidth units is reserved to benefit calls of high bandwidth requirements. The two models do not have a product form solution for the steady state probabilities. However, they propose approximate formulas for the calculation of call blocking probabilities. The accuracy of the formulas is verified through simulation and found to be quite satisfactory. [ABSTRACT FROM AUTHOR]

Drought is a slow and creeping phenomenon that occurs more frequently in arid and semi-arid regions. In recent decades, among natural disasters influencing human societies the number or frequency of drought event has increased more than others. In this context, the prediction of drought intensity, duration and frequency can help to take the necessary precautions and reduce drought risk. This study employs Markov chains of different orders (0, 1, 2 and 3) to analyze hydrological drought characteristics. Hydrological drought is identified based on the streamflow drought index (SDI) at 3-, 6-, 9- and 12-month time scales using data from 21 hydrometric stations located in the Karkheh River Basin in Iran. According to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), first-order Markov chain models are adequate to reproduce the statistical structure of SDI-based hydrological droughts. Moreover, the steady state probabilities and expected residence time of drought severity for all time scales increase as the degree of severity decreases. The results also indicate that the expected frequency of drought occurrence is higher for smaller time scales (i.e., 3-month and 6-month). [ABSTRACT FROM AUTHOR]

A reduced system is a smaller system derived in the process of analyzing a larger system. In solving for steady state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability (or rate) matrix. Following Lal (1981), a Markov chain can be categorized as standard or nonstandard depending on the location of an invertible submatrix necessary for an efficient solution in a transition probability (or rate) matrix. In this paper, algorithms for the determination of steady state probabilities are developed by using (i) a backward recursion which is efficient for standard systems and (ii) a forward recursion which is efficient for nonstandard systems. It is also shown that the backward recursion can be used for finding the first passage time distribution and its mean and variance. [ABSTRACT FROM AUTHOR]