Certain volterra integral equations arising in queueing

The linear Volterra integral equation is studied especially a form arising in many queueing problems. New methods of solution are given depending on the Laplace transform. Also, the solution of certain forms of nonlinear Volterra equations is discussed. A method of numerical solution is also given and illustrated with an example. Inequalities are proved which are useful in error estimation and in comparisons of systems. New comparison results are obtained for the emptiness probabilities in certain M/G/1 systems.