Characteristics of Transient and Stationary Waiting Times in Poisson Driven (max,+) Linear Systems

Abstract

In their 1997 paper, Baccelli, Hasenfuss and Schmidt provide explicit expressions for the expected value of the waiting time of the nth customer in a given subarea of a (max,+) linear system. Using similar analysis, we present explicit expressions for the moments, Laplace transform and the tail probability of transient waiting times in Poisson driven (max,+) linear systems. Furthermore, starting with these closed form expressions, we also derive explicit expressions for the moments, Laplace transform and tail probability of stationary waiting times in a class of (max,+) linear systems with deterministic service times. An example pertaining to queueing theory is given to illustrate the results.