SOONER AND LATER WAITING TIME PROBLEMS BASED ON A DEPENDENT SEQUENCE

QING HAN* AND SIGEO AKI

Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan

(Received July 30, 1998; revised February 15, 1999)

Abstract. This paper introduces a new concept: a binary sequence of order (k, r), which is an extension of a binary sequence of order k and a Markov dependent sequence. The probability functions of the sooner and later waiting time random variables are derived in the binary sequence of order (k, r). The probability generating functions of the sooner and later waiting time distributions are also obtained. Extensions of these results to binary sequence of order (g, h) are also presented.

Key words and phrases: Binary sequence of order (k, r), binary sequence of order k, sooner and later waiting time problems, probability function, probability generating function.