An unreliable MX/G/1 queueing system with k phases of heterogeneous service and random feedback

摘要

This paper considers an unreliable MX/G/1 queueing system with k phases of heterogeneous service and random feedback. In the system,after the completion of the i-th phase service the customers may receive the (i+1)-th phase service with probability θi,or may feedback to the tail of the queue with probability pi,or leave the system with probability qi=1-pi-θi,for i=1,2,…,k-1. After the completion of the k-th phase service,the customers may feedback to the tail of the queue with probability pk,or leave the system with probability qk=1-pk. By the method of supplementary variables,we obtain the probability generating functions of the steady-state queue length distribution,the mean queue size and some performance measures of the sever.