RENEWAL CONVERGENCE RATES FOR DHR AND NWU LIFETIMES

This article studies the geometric convergence rate of a discrete renewal sequence with decreasing hazard rate or, more generally, new worse than used lifetimes. Several variants of these structural orderings are considered. The results are derived from power series methods; roots of generating functions are the prominent issue. Optimality of the rates are considered. Examples demonstrating the utility of the results, as well as applications to Markov chains, are presented.

Geometric renewal convergence rates from hazard rates

This paper studies the geometric convergence rate of a discrete renewal sequence to its limit. A general convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to extract a good convergence rate when the lifetimes are ordered in the sense of new better than used or increasing hazard rate. A bound for the best possible geometric convergence rate is derived for lifetimes having a finite support. Examples demonstrating the utility and sharpness of the results are presented. Several of the examples study convergence rates for Markov chains.

Geometric renewal convergence rates from hazard rates

This paper studies the geometric convergence rate of a discrete renewal sequence to its limit. A general convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to extract a good convergence rate when the lifetimes are ordered in the sense of new better than used or increasing hazard rate. A bound for the best possible geometric convergence rate is derived for lifetimes having a finite support. Examples demonstrating the utility and sharpness of the results are presented. Several of the examples study convergence rates for Markov chains.

The behavior of the renewal sequence in case the tail of the waiting-time distribution is regularly varying with index −1

A second-order asymptotic result for the probability of occurrence of a persistent and aperiodic recurrent event is given if the tail of the distribution of the waiting time for this event is regularly varying with index −1.

The behavior of the renewal sequence in case the tail of the waiting-time distribution is regularly varying with index −1

A second-order asymptotic result for the probability of occurrence of a persistent and aperiodic recurrent event is given if the tail of the distribution of the waiting time for this event is regularly varying with index −1.

Heavy traffic theory for queues with several servers. I

Queues with several servers are examined here, in which arrivals are assumed to form a renewal sequence and successive service times to be mutually independent and independent of the arrival times. The first-come-first-served queue discipline only is considered. An asymptotic formula for the equilibrium waiting time distribution is obtained under conditions of heavy traffic.