Strong stability of the embedded Markov chain in an GI/M/1 queue with negative customers

This paper is devoted to the investigation for sufficient conditions of the strong stability of the embedded Markov chain in GI/M/1 queueing system with negative customers. After perturbing the occurrence rate of the negative customers, we prove the strong stability of the considered Markov chain with respect to a convenient weight variation norm. Furthermore, we estimate the deviation of its transition operators and provide an upper bound to the approximation error. This results allow us to understand how the negative customers will affect the system’s level of performance.