Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems

The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during its service time. The optimal allocation problem is formulated as a Markov-decision one. We show numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix expressions for performance measures of the system and compare the main model with alternative simplified queuing systems which are analysed for the arbitrary number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model by calculating the mean number of customers in the system. Moreover, using the preemptive and non-preemptive queueing models with the faster server first policy the lower and upper bounds are calculated for this mean value.

MICRONUTRIENT STATUS OF TISTA MEANDER FLOODPLAIN SOILS UNDER MAJOR CROPPING PATTERNS IN MITHAPUKUR UPAZILA

Soil micronutrients from their finite source are strongly affected by the inclusion of high-yielding crop cultivars in the cropping patterns and their fertilization practices. A study was conducted to identify the dominant cropping patterns and to evaluate their impacts on soil micronutrients’ (Zn, B, Cu, Fe, Mn) status in Tista Meander Floodplain Soils at Mithapukur upazila of Rangpur district, Bangladesh. The study revealed that potato-rice-rice (P-R-R) (18.26%), rice-fallow-rice (R-F-R) (15.65%), and maize-fallow-rice (M-F-R) (13.91%) were the most prevalent among the existing cropping patterns. Zn and B fertilizers are used by 35% and 23% of farmers. The concentrations of Zn, B, and Mn increased while Cu and Fe decreased under all dominant patterns. The highest accumulation of Zn by 281.63%, B by 139.36%, and Mn by 83.13% were obtained under P-R-R while, the highest depletion of Cu by 52.58% and Fe by 24.48% were obtained under P-R-R and M-F-R cropping patterns, respectively. An increasing trend of soil toxicity index (STI) values was observed with Zn, B, and Mn. A deleterious shift of B from lower to higher STI class was obtained under the P-R-R and R-F-R patterns while an ameliorating shift of Cu from higher to lower class was obtained under P-R-R and M-F-R patterns. The recent STI status of Fe and Mn under all cropping patterns rendered in the ‘highly toxic’ class. This investigation emphasizes that the concentrations of selected micronutrients were found above their respective critical limits and that the studied micronutrients except Zn imposed toxicity in the soil.