Queuing Model with Variable Input Rate and Service Rate and with Error Service

This paper discusses that the arrived customers enter M /M /1 /m queuing system with the probability α κ,that service rate of service window is changing with the queuing length and that system service can make mistakes,obtains that the customer flow entering into the system is a Poisson process and that the customer number in the system is birth-death process,and gets the stable distribution of this model,the average input rate of the customers,the average queuing length,the average length of the system,the average staying time of the customers,and the average waiting time of the customers.