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This paper we constructs the N-policy FM/FM/1 vacation queueing system with server start-up and time-out by using fuzzy control chart based on Zedeh extension law to transform fuzzy queues into family of crisp queues. Arrival rate, service rate and vacation times will all be made by fuzzy nature. We derive the membership functions of the parameters of the control chart corresponding to the expected system length L and also confirmed the parameters of the control chart for fuzzy. We have also set an numerical example. [ABSTRACT FROM AUTHOR]

In this study, the process of finding performance measures of N* is the optimal threshold, L is the expected system length and T(N*) is the minimum expected cost for an optimal strategy analysis of N-policy FM / FM / 1 Vacation Queueing system with server Start-up and Time-out, in which the arrival rate and service rate triangular and trapezoidal fuzzy numbers are proposed. By using L-R method the L-R method is smaller and more convenient differentiate to alpha-cuts method. The cogency of the model is study by numerical example. [ABSTRACT FROM AUTHOR]

In present study, MIKE 11NAM rainfall runoff(R-R) and MIKE BASIN models were used to develop R–R relationship and to analyze the water availability status of the Shipra river basin under changing hydrological conditions. The model was developed using discharge data observed for 9 years at the Ujjain G/d site. The coefficient of determination(R2) values for NAM R-R model calibration and validation were 0.685 and 0.642, respectively, indicating good agreement between the simulated and observed runoff. As the Shipra River is subjected to a number of hydrological interventions, the MIKE BASIN model was used to develop various scenarios to study the influence of river diversion, on-stream dam, river interlinking on water availability in different time-scale at desired locations. Scenario analysis of MIKEBASIN results indicated that the Khan diversion, which was executed to avoid entry of contaminated Khan river water into Shipra has reduced the water availability in the Shipra river. However, the simulation results indicated that the water availability in Shipra has been improved due to Narmada-Shipra link, a minimum of 1.7 m3/s flow is available at Ujjain even during the low-flow period. Gambhir reservoir was developed to evaluate how demand deficit can be fulfilled through proper reservoir operation during a drought period. [ABSTRACT FROM AUTHOR]