This note is to provide results for and give hints on applying stochastic network calculus to service guarantee analysis say of wireless networks. At this moment of writing, the focus is on single hop networks. At the end of the note, potential research topics are discussed. 1 Preliminaries 1.1 Model and Notation We consider discrete-time single cell wireless networks. All nodes share a wireles...

⋆ Group: (G, γ) where G is a set and γ a binary operation γ : G×G → G. If γ is clear from the context the group is simply denoted by G. ◦ In place of γ(f, g) write fγg or simply fg when there is no ambiguity, as in most of what follows. ◦ Example: G = Z = {. . .− 2,−1, 0, 1, 2 . . .}, γ = +, γ(f, g) = f + g. • For G to be a group three conditions must be satisfied: (i) γ is associative: γ(f, γ(...

and Applied Analysis 3 In contrast to the modified Roper-Suffridge extension operator in the unit ball, it is natural to ask if we can modify the Roper-Suffridge extension operator on the Reinhardt domains. In this paper, we will introduce the following modified operator: F z ⎛ ⎝f z1 f ′ z1 n ∑ j 2 ajz pj j , ( f ′ z1 2z2, . . . , ( f ′ z1 nzn ⎞ ⎠ ′ 1.5 on the Reinhardt domainΩn,p2,...,pn . Wew...

In this short paper we deal with the stability analysis problem of non-autonomous non-linear systems, in cascade. In particular we give suucient conditions to guarantee that: (i) a globally uniformly stable (GUS) nonlinear time-varying (NLTV) system remains GUS when it is perturbed by the output of a globally uniformly asymptotically stable (GUAS) NLTV system, under the assumption that the pert...

This article is concerned with characteristic Sturmian words of slope α and 1−α (denoted by cα and c1−α respectively), where α ∈ (0, 1) is an irrational number such that α = [0; 1 + d1, d2, . . . , dn] with dn ≥ d1 ≥ 1. It is known that both cα and c1−α are fixed points of non-trivial (standard) morphisms σ and σ̂, respectively, if and only if α has a continued fraction expansion as above. Accor...

In this paper, we study the inverse first-crossing problem. This problem originates from the Merton’s structural model [7] for credit risk management, derived as follows. Consider a company whose asset value and debt at time t ≥ 0 are denoted by A(t) and D(t) respectively. Assume the following: (1) D(0) ≤ A(0) and the company is in default at a time t > 0 if A(t) < D(t). (2) {A(t)} is a log-nor...