Busy Period

In this chapter, we study the length of the busy period, denoted by L, and related performance measures for the M/G/1 and M/M/c retrial queues. This seems that the existing numerical inversion techniques would be inadequate to handle. For this reason, alternative approaches are needed, and Subsection 4.1.1 concentrates on methods based on the principle of maximum entropy and on the truncation of the orbit capacity for the M/G/1 retrial queue. Subsections 4.1.2 and 4.1.3 complete the analysis of the single server model by studying the recursive computation of the number of customers served and the maximum orbit size during a busy period. In Section 4.2, we consider the M/M/c retrial queue. In particular, Subsection 4.2.1 discusses the length of a busy period and the computation of its moments. The algorithms presented involve the approximating models X^W, X^F and X^NR, which were introduced in Section 3.4. In Subsection 4.2.2, we briefly show how to extend the analysis to the number of customers served. The exact computation of the maximal queue length is presented in Subsection 4.2.3. Finally, bibliographical remarks are given in Section 4.3.