On some boundary value problems in queueing theory (Q1063340)

This paper treats the difference equation \[ (\partial /\partial t)[u(x,t)]=\sum^{m}_{i=1}a_ iu(x+y_ i,t), \] where \(x,y_ 1,y_ 2,...,y_ m\) are points in \({\mathbb{R}}^ n\). Some initial and boundary value problems are studied, one of which represents a generalization of the classical ruin problem. Another variant describes a random walk with jumps forming a Poisson process; for this, an expression is obtained for the probability of arriving at a specified point at a time t. The title of the paper implies a fuller reference to queueing theory than is actually given.