Moment problems and their applications to the stability of queueing models

✍ Scribed by George Anastassiou; Svetlozar T. Rachev

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 846 KB
• Volume: 24
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(92)90201-r

✦ Synopsis

A.bstractmThis paper deals with the following question: "Will the proposed determln;itic queueing model yield a satisfactory approximation to the real qtteueing system under c(mslderation and if so, within which limits?" At first, we analyze the degree of approximation of the random real model by a deterministic one. This is achieved by estimating the Prokhorov distance betweea the output sequences of both models. The right-hand sides of the obtained estimates depend (m the Prokhorov or Ky Fan distances between the inputs of the underlined models. To estimate the latter distances we evaluate the Ky Fan radius of a set of l~obabillty measures satlsfying basic moment conditions involving line&r combinatious of {t,t 2 ) or {cos t, sin t}. In particular, the last results lead to quantitative criteria for the weak convergence of probability meaiures to a point mass.