The conditional and residual waiting time distributions of the M/G/1 queue

A single-server queuing system with arrivals according to a Poisson process and general service times is considered. The system is assumed to be in steady state. Using linear algebraic techniques only, alternate derivations are given for the moments of the waiting time distributions and the Pollaczek-Khinchine transform equation for this queue. An explicit form is given for the residual response time and conditional waiting times. The first moment and the squared coefficient of variation of these distributions are derived, and lower bounds are given