SITA queues were introduced in [4] as a means for reducing job size variance at individual hosts in a server farm. It turns out that SITA queues are mathematically very interesting. For example, they satisfy a duality that is typical of automorphic forms in number theory. This leads to useful queueing theoretic insights, [1] and is also related to interesting number theoretic questions, [7], [5]. In this paper we will consider other aspects of SITA queues which turn out to be related to two dimensional Lorentzian geometry. In particular we will be interested in the behavior of SITA queues as h → ∞. The tail of the waiting time function was studied in detail in [8]. We will concentrate on the average waiting time E(W ), rather than the tail since it leads to some interesting analogy and insights. A SITA queue consists of h hosts, numbered 1, ..., h and a set of cutoffs 0 = s0 1 such that tj(x)/t1(x) = cj for all x. In this case, we again take t1 to be the identity (job sizes are measured by the time they take on host 1).