A Random Walk with Exponential Travel Times

Subject Areas : International Journal of Industrial Mathematics

R.  Kazemi ¹ (Department of Statistics, Imam Khomeini International University, Qazvin, Iran)

Received: 2013-11-14 Accepted : 2013-11-14 Published : 2014-12-01

Keywords: Smallest path, Random Walk, Pure birth process, Random recursive trees,

Abstract :

Consider the random walk amongN places with N(N- 1)/2 transports. We attach an exponential random variableXij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probabilityp and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point logN as Np is large.