The departure process from a GI/G/1 queue and its applications to the analysis of tandem queues

In this paper we characterize exactly the departure process of a GI/G/1 queue and use this characterization to propose a new algorithm for the analysis of single server tandem queues with general distributions. We first establish a close connection of the departure process with the idle time and obtain that in steady state interdeparture times are identically distributed but they are not independent. Using the Hilbert factorization combined with complex analysis methods, we find exactly the Laplace transform of the stationary interval, determine exactly the correlation of the departure times and characterise the counting proces of the departure process. We then use these results to propose a new approaimate algorithm for the steady-state analysis of tandem queues. We implemented the algorithm and we found that the answers produced by the aarismn. are very close to those produced by simulation. We believe that the plra ofr the algorithm rests in the direct exploitation of the characteristics of T:depatub process. We report several computational results. · Dimitrd Betaims, Sloan School of Management and Operations Reseach Center, MIT, Camnbridge, Ma 02139. The research of the author was partially supported by grants from the Leaders for Manufacturin program at MIT and from Draper Laboratory. tDaisuhe Nakasato, Operations Research Center, MIT, Cambridge, MA 02139.