Performance Evaluation Of An M/M(A,B)/C Queueing Model With Setup Time, Multiple Adaptive Vacation And Parallel Service

Abstract

This paper studies an M/M(a,b)/c queueing system with identical servers, setup time, and multiple adaptive vacations. Customer arrival follows a Poisson process, and service times are exponentially distributed within the interval (a,b). When the queue size falls below the threshold level a, servers enter an adaptive vacation mode . After returning, if the queue length remains below a, the server stays idle or continues its vacation until the thresholdvalue  is reached. Before starting service, each server undergoes an exponentially distributed setup period. The generating function of the queue length distribution and key performance measures are obtained. The cost model is used to analyze system performance under different traffic intensities. This model can be effectively applied in Smart Agriculture and IoT-based monitoring systems, where soil moisture sensors require adaptive scheduling, efficient resource utilization, and reduced response time for better agricultural management.