Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service

The paper investigates the M/M/s retrial queueing system with servers prone to breakdown and with voluntary service. During a phone call, if the caller finds a free call line, then it connects immediately to the call agent, considered as server. Those who finds the call busy either join the orbit for retrial or disconnect the call. After receiving the essential service either caller leaves the system or requests for voluntary service. The miniature used in the queueing system employs a quasi-birth-and-death process. The stationary probabilities are derived using matrix-analytic approach and then performance measures are calculated using these stationary probabilities. The impact of system parameters on performance measures is illustrated using graphs and tables. Total system cost is calculated as a function of orbit capacity, repair rate of breakdown and two different service rates. The optimization methodology is demonstrated using various cases. Further the Genetic algorithm is used to find the optimum value of both essential and optional service rates, rate of breakdown and orbit capacity to minimize the overall cost. The study of consistency of retrial queue with server prone to breakdowns and repairs is of great significance because of inadequate capability of repairs and strong impact of the breakdowns on the performance measures.