A new model approximating M/PH/1 queuing systems during the transient period

Abstract

This paper presents an efficient approximation for M/PH/1 queuing systems based on the replacement of the majority of the vector valued state probabilities by a diffusion approximation. The strength of the new approximation is that it gives more accurate results than the current diffusion approximations at both high and low traffic intensities and at little extra computational cost. The accuracy of the new approximation during the transient is shown by comparing it numerically with solutions to the M/PH/1 system and current approaches based on the diffusion approximation.

Straipsnyje pateikta efektyvi masinio aptarnavimo sistemos M/PH/1 aproksimacija, kuri gaunama naudojant daugumos būsenu tikimybiu difuzine aproksimacija. Šios aproksimacijos privalumas tas, kad gaunami tikslesni rezultatai, negu naudojant iprastines difuzines aproksimacijas, tiek esant mažiems, tiek dideliems paraišku intensyvumui. Be to, pakanka mažiau skaičiavimu. Šios naujos aproksimacijos tikslumas perejimo būsenoje parodomas lyginant sistemos M/PH/1 sprendinius su sprendiniais, kurie gaunami naudojant iprastine difuzine aproksimacija.