Corrigendum to: Single class queueing networks with discrete and fluid customers on the time interval ℝ

Abstract

Publication [1] contains a number of inaccuracies. Particularly point 9 below justifies a correction, since the concerned Lemma 20 forms an essential part in our work [2]: 1. Page 408, first paragraph of Sect. 2: It should be “d := limt→−∞ d(t)/t” and “d := limt→∞ d(t)/t”. I want to thank an anonymous referee for indicating this typo. 2. Page 411, Lemma 1: “w = 0” and “idR− y ∈ I” should be added to statement 2, and “q = 0” and “idR − y ∈ I” to statement 3. 3. Page 413, Corollary 3: w = 0 and idR − y ∈ I is missing in statement 2, and q = 0 and idR − y ∈ I in statement 3. 4. Page 413, paragraph after Corollary 3: It should be “x = Xs,a,r(y)”. 5. Page 414, proof of Theorem 4: In the display “u′t < c(t) < d(t) < v′t” the second “<” should be “ ”. The sentence between page 414 and 415 should be “Since y(−2) is Lipschitz continuous with constant one and y(+2) non-decreasing, . . . ”. 6. Page 417, Theorem 7: The proof contains a couple of typos and gaps. Instead of a detailed correction we refer to the proof of the more general Theorem 2 in [2]. 7. Page 419, fourth line in Sect. 6: It should be x < s. 8. Page 423: In line 5 and in the first line of the proof of Lemma 16 it should be “an absolute vector norm” instead of “a vector norm,” since the monotonicity of the vector norm is implicitly used in the proof of Lemma 16. Moreover, in the second display in the proof both terms “diag(s−σ)” should be “diag(s−σ)−1”. 9. Page 427, Lemma 20: In assumption 2, the words “random variable” should be dropped and the prerequisite a(0)= 0 and r(0)= 0 added.