A retrial queue with multiple vacation and two-phase services is studied, in which the server is restarted after the vacation. Customers arriving in batches form a generalized Poisson process with the parameter \lambda. They are provided with two phase of service: the essential service and the optional service, and there are many services to choose from the second phase services. Firstly, the existence conditions of system stability are obtained by embedding Markov chains. Then the probability distribution and some performance measures of the system to be steady are obtained by introducing supplementary variables. Finally, under the definition of generalized vacation, the stochastic decomposition of the system is proved.
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程慧慧,田中连. 具有多重休假和两阶段服务的MX/G/1重试排队系统[J]. 科学技术与工程, 2020, 20(32): 13091-13098. CHENG Hui-Hui, TIAN Zhong-lian. Mx/G/1 Retrial Queuing System with Multiple Vacation and Two-phase Services[J]. Science Technology and Engineering,2020,20(32):13091-13098.