Analytical solutions for state-dependent M/M/c/c+r retrial queues with Bernoulli abandonment

Authors:
Tuan Phung-Duc;Hiroyuki Masuyama;Shoji Kasahara;Yutaka Takahashi
Affiliations:
Kyoto University, Sakyo-ku, Kyoto, Japan;Kyoto University, Sakyo-ku, Kyoto, Japan;Kyoto University, Sakyo-ku, Kyoto, Japan;Kyoto University, Sakyo-ku, Kyoto, Japan
Venue:
Proceedings of the 4th International Conference on Queueing Theory and Network Applications
Year:
2009

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Abstract

This paper considers a state-dependent M/M/c/c + r retrial queue with Bernoulli abandonment, where the number of servers is equal to c, the capacity of the buffer is equal to r and that of the virtual waiting room for retrial customers is infinite. We call the virtual waiting room by orbit hereafter. We assume that the arrival and service rates depend on the number of customers in the system (the servers and buffer). Such retrial queues cover conventional M/M/c/c retrial queues without abandonment, as special cases. By a continued fraction approach, we derive analytical solutions for the stationary joint distribution of the queue length in the system and that in the orbit, assuming that the capacity of the system is less than or equal to 4. We also show that our analytical solutions can be numerically computed with any accuracy.