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

Rami Atar, Amarjit Budhiraja, Paul Dupuis, Ruoyu Wu

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

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.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)232-258
عدد الصفحات27
دوريةMathematics of Operations Research
مستوى الصوت47
رقم الإصدار1
تاريخ مبكر على الإنترنت21 يوليو 2021
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - فبراير 2022

All Science Journal Classification (ASJC) codes

  • !!Computer Science Applications
  • !!General Mathematics
  • !!Management Science and Operations Research

بصمة

أدرس بدقة موضوعات البحث “Large Deviations for the Single-Server Queue and the Reneging Paradox'. فهما يشكلان معًا بصمة فريدة.

قم بذكر هذا