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In this paper, we study a single server queuing model with retention of reneging customers. The transient solution of the model is derived using probability generating function technique. The time-dependent mean and variance of the model are also obtained. Some important special cases of the model are derived and discussed. Finally, based on the numerical example, the transient performance analysis of the model is performed.

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In this paper, we study a finite capacity single server queuing model with balking and correlated reneging and discuss its application in queues at health care facilities. The reneging considered so far in the queuing literature is a function of system-state. In many practical situations, reneging may depend on factors other than the system-state. For instance, in health care systems the reneging of patients at two consecutive time marks may be correlated in a sense that if a patient reneges at a time mark then there is a probability that a patient may renege at the next time mark due to the factors like improper check-up, sluggish management, unnecessary costly prescription by doctors, etc. The steady-state solution of the model is derived by using matrix-decomposition method. Finally, the transient performance analysis of the model is performed using Runge-Kutta method. [ABSTRACT FROM AUTHOR]

In this paper, a finite capacity two heterogeneous servers' queuing system with retention of reneging customers is studied. The explicit transient probabilities of system size are obtained using matrix method. Further, the time-dependent mean and variance are presented. Finally, a numerical example is provided to show the behavior of the system. [ABSTRACT FROM AUTHOR]

In this paper we consider a Markovian queuing system with heterogeneous servers, balking and catastrophes. The time-dependent behavior of the system is analyzed by using generating function technique. The expressions for mean and variance of the system are obtained in transient state. At last, some special cases of the model are derived and discussed. [ABSTRACT FROM AUTHOR]

In present era, to preserve a security and sovereignty of the country, it is necessary to spend a significant amount of national income on defense sector. This study instigates the increasing demand of defense expenditure and also to study the growth performance of India's with special focus on the efficacy of defense expenditure on economic growth. This study adopts an Autoregressive Distributed Lag and Toda-Yamamoto granger non-causality model during the period 1961 to 2017. Overall, the results suggest that India is affected both internally and externally issues and also verifies that defense expenditure and economic growth are positively and significantly affect to each other in both period short run and long run. It advocates that increment in defense expenditure by 1% in current period will help to boost economic growth by 1.15 per cent in the long run. For to the directional relationship the Toda-Yamamoto Granger causality outcomes suggest that causality running form DE to GDP which means shows the unidirectional relationship. Accordingly, this designates that defense sector has a crucial efficacy in the development of Indian economies. [ABSTRACT FROM AUTHOR]

The use of efficient bio-inoculants in chickpea is the best way to increase crop productivity under rainfed conditions. To assess the combined effect of bio-inoculants on crop yield, field experiments were conducted during Rabi seasons at Research Station, Punjab Agricultural University, Ballowal Saunkhri, Punjab, India. The application of different bio-inoculants significantly improved number of pods, grain and straw yield of chickpea over the un-inoculated treatment. The combined application of Rhizobium + PSB + AM fungi + azotobactor inoculums as seed treatment with 75% of recommended phosphorus produced highest grain yield. The nodule count, nodule weight, per cent root colonization of AM fungi and different enzymes activities in soil were also highest in combined bio-inoculants treatment. The present study concluded that combined application of bio-inoculants (Rhizobium, PSB, AM fungi and azotobactor) can save 25% of recommended phosphorus by sustaining the crop yield and improving the soil health. [ABSTRACT FROM AUTHOR]

In this paper, the transient solution of a Markovian queuing system with two heterogeneous servers and retention of reneging customers is obtained. The explicit transient probabilities of system size are obtained using probability generating function technique. The corresponding steady-state probabilities are also derived. Further, the time-dependent mean and variance are obtained. Finally, a numerical example is provided to study the behavior of the system. The numerical results show that the heterogeneous system performs better than its homogeneous counterpart. [ABSTRACT FROM AUTHOR]

In this paper, we study an infinite capacity multi-server Markovian queuing system with balking and retention of reneging customers. The transient analysis of the model is performed. The probability generating function technique along with Bessel function properties is used to derive the time-dependent state probabilities explicitly. [ABSTRACT FROM PUBLISHER]

In this paper, a finite capacity Markovian single-server queuing system with discouraged arrivals, reneging, and retention of reneging customers is studied. The time-dependent probabilities of the queuing system are obtained by using a computational technique based on the 4th order Runge-Kutta method. With the help of the time-dependent probabilities, we develop some important measures of performance of the system, such as expected system size, expected reneging rate, and expected retention rate. The time-dependent behavior of the system size probabilities and the expected system size is also studied. Further, the variations in the expected system size, the expected reneging rate, and the expected retention rate with respect to the probability of retaining a reneging customer are also studied. Finally, the effect of discouragement in the same model is analyzed. [ABSTRACT FROM AUTHOR]