Abstract
AbstractStudies on the analysis of M/G/1 and GI/M/1 using the supplementary variable approach have already been reported. However, there has been no study which analyzed consistently the systems from the transient state to the steady state.Using the remaining service time of a customer being served in the M/G/1 and the residual interarrival time in the GI/M/1 as supplementary variables, we derive the basic equations of state probability density functions and state transition probability density functions which describe the behavior of the systems and the transient distributions of characteristic quantities, such as queue length, virtual waiting time, etc. the transient solution is derived as a solution of certain initial‐value‐ and boundary‐value problems. Using this solution, the transient solutions of the characteristic quantities (including queue length, virtual waiting time, mean queue length, mean virtual waiting time, etc.) are derived. Furthermore, by applying the final value theorem of Laplace transform to these results, we obtain stationary distributions of the characteristic quantities which equal those results obtained by imbedded Markov chain analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Electronics and Communications in Japan (Part I: Communications)
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
