An unreliable M~X/G/l retrial Queue with multi optional stages of service and delay in repair

摘要

Unreliable vacation retrial queue and multi stages of service delay in repair is studied. After completion of the i~(th) (i=l,2, ...k) stage of service, the unit may have the option to choose (i+1)~(th) stage of service with probability θ_i, or with p_i, may join into orbit to give feedback or may leave the station with probability q_i, = 1 —p_i—6., (7 = 1,2,...k-1) and q = 1—p_i (i = k) After service completion if the orbit has no units, server takes avacation.During repair, the unit waiting in the system to complete the remaining service (delay time) is discussed. We analyzed the system using the method of supplementary variable. Simulation results are given using MATLAB.