Queuing models create lot of interest due to their ready applicability in the analysis of several congestion control systems. In this paper, we develop and analyze K-parallel and series queuing systems which is connected in a single network. Here, it is assumed that there are 'K' queues Q 1 , Q 2 , …, Q k which are connected in parallel and connected in series to another queue Q k?1 . Here the arrivals are in bulk and follows a compound Poisson process. It is assumed that the service completions in K nodes is load dependent and follow Poisson processes. Using the difference differential equations the joint probability generating function of number of customers in each queue is derived. The system performance measures such as average number of customers in each queue, the probability of the system emptiness, the average waiting time of a customer, throughput of the queues and the variability of system size distribution in each queue are derived and analyzed through numerical illustrations. The utility of this model in queue line control is demonstrated through applying it at Tirumala Tirupati Devasthanam which deals with pilgrims is also discussed. It is observed that the load dependent strategy reduces the congestion in queues and mean delays.
Castor is treated as an important non-edible oil crop among Mahua, Karanja and Jatropha. India occupies a leading position in the production of castor followed by China and Brazil. Castor has been used in various purposes from thousands of years ago which has important characteristics. The main objectives of current work are i) Identification of change point and ii) Trend analysis with respect to area, yield and production of castor for the period from 1961 to 2016 in India. The non-parametric statistical methods such as Pettitt's, Standard Normal Homogeneity (SNH) and Buishand’s Range tests have conceded to detect the mutation point whereas the magnitude of trend is measured and analysed with the help of Sen’s slope estimator and their significance is tested by Mann-Kendall test. The results revealed that the change is identified by mutation point at initially 1988. Interestingly the maximum growth is captured in the second sub-time series on the basis of time scale and area, yield and production. However, the production of castor cannot meet up its annual enormous demand for India.
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