Large deviation analysis of the single server queue

Certain corrections are needed in this paper concerning the definition and properties of the weak topology on 12. Instead of characterising it in terms of converging sequences as on p. 7, one should define the weak topology as the coarsest topology for which the evaluations f --+ f o h(t)dr(t), f E ]2, are continuous for all continuous h(t) of compact support. With this topology, 12 is a Tihonov, i.e., completely regular, topological space, however it is not metrisable as is erroneously claimed at the beginning of p. 8 which follows by Theorem 17 in Dudley [1]. Hence, the topology induced on 12 by the metric Pv introduced in the appendix is different from the weak topology. On the other hand, Dudley's Theorem 18 implies that Pv metrizes the weak topology on 12+ and 12+. Therefore, in part 1 of Theorem A.1 one should change 12 to 12+ which is enough for the applications in the paper. It is also interesting to note that the assertion of Theorem 1.1 holds for both the weak topology (as in the paper) and the topology induced by Pv. Finally, the remark preceding the statement of Theorem 1.1 is erroneous, it is correct with 12 replaced by either l) + or 12 +.