Large Deviations for the Single-Server Queue and the Reneging Paradox

Rami Atar, Amarjit Budhiraja, Paul Dupuis, Ruoyu Wu

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים

תקציר

For theM/M/1+Mmodel at the law-of-large-numbers scale, the long-run reneging count per unit time does not depend on the individual (i.e., per customer) reneging rate. This paradoxical statement has a simple proof. Less obvious is a large deviations analogue of this fact, stated as follows: The decay rate of the probability that the long-run reneging count per unit time is atypically large or atypically small does not depend on the individual reneging rate. In this paper, the sample path large deviations principle for the model is proved and the rate function is computed. Next, large time asymptotics for the reneging rate are studied for the case when the arrival rate exceeds the service rate. The key ingredient is a calculus of variations analysis of the variational problem associated with atypical reneging. A characterization of the aforementioned decay rate, given explicitly in terms of the arrival and service rate parameters of themodel, is provided yielding a precise mathematical description of this paradoxical behavior.

שפה מקוריתאנגלית
עמודים (מ-עד)232-258
מספר עמודים27
כתב עתMathematics of Operations Research
כרך47
מספר גיליון1
תאריך מקוון מוקדם21 יולי 2021
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - פבר׳ 2022

ASJC Scopus subject areas

  • ???subjectarea.asjc.1700.1706???
  • ???subjectarea.asjc.2600.2600???
  • ???subjectarea.asjc.1800.1803???

טביעת אצבע

להלן מוצגים תחומי המחקר של הפרסום 'Large Deviations for the Single-Server Queue and the Reneging Paradox'. יחד הם יוצרים טביעת אצבע ייחודית.

פורמט ציטוט ביבליוגרפי