Chapter 6 brings attention to another important feature of ultra-dense networks, i.e. the surplus of the number of small cell base stations with respect to the amount of user equipment. Building on this fact and looking ahead at next generation small cell base stations, the ability to go into idle mode, transmit no signalling meanwhile, and thus mitigate inter-cell interference is presented in this chapter, as a key tool to enhance ultra-dense network performance and combat the previously presented caveats. Special attention is paid to the upgraded modelling and analysis of the idle mode capability at the small cell base stations.

Chapter 5 studies in detail – and also from a theoretical perspective – yet another and more important caveat towards a satisfactory network performance in the ultra-dense regime, i.e. that of the impact of the antenna height difference between the user equipment and the small cell base stations. Similarly as in the previous chapter, such antenna-related modelling upgrades, the new derivations in a three-dimensional space and the new obtained results are carefully presented and discussed in this book chapter for the better understanding of the readers. Moreover, several small cell deployment and configuration guidelines are provided to improve the network performance.

For the case where the jump distributions vary regularly at infinity (slow decay), for the sake of completeness we present without proof a number of results from A. A. Borovkov and K. A. Borovkov,Asymptotic Analysis of Random Walks. Vol. I: Slowly Decaying Jump Distributions (in Russian; Moscow: Fizmatlit, 2008).

We obtain limit theorems describing sharp asymptotics in boundary crossing problems for CRPs.

Chapter 2 introduces the need for wireless network performance analysis tools to drive optimal network deployments and set optimal parameter values and describes the main building blocks and models of any wireless network performance analysis tool. In more details, it focuses on i) the system-level simulation and ii) the theoretical performance analysis concepts used in this book, paying particular attention to stochastic geometry frameworks.

We introduce the objects of study and outline the contents of the book.

We study the nature of the distributions of CRPs in the large deviation zone and establish the corresponding LDPs. We clarify the relation of the distribution of a CRP with the renewal measure for the sequence {Tn, Zn}. We investigate some properties of the deviation functions of the renewal measures that appear in this problem. We prove the LDPs for the CRPs Z(t). The definition of the fundamental function is given, and we also study its properties and relations to the deviation functions. We present several results on LDPs for the process Y(t) and for Markov additive processes.

We continue the study of large deviation principles for compound renewal processes. We are mostly concerned with probabilities of large deviations of the trajectories of CRPs. We establish "partial" LDPs (local LDPs applicable only in the space of absolutely continuous functions). "Complete" LDPs are obtained under rather restrictive conditions. It proves possible to obtain LDPs for boundary crossing problems under broader conditions and with explicit deviation functional. A moderately large deviation principle for CRPs is established.

We present the basic limit theorems for CRPs in the domain of normal deviations (with the functional limit theorems), including the case of infinite variance of the jumps of the process. We also present the law of the iterated logarithm and its analogs.

We extend the invariance principle for CRPs to the domain of moderately large and small deviations. The results in this chapter turn out to be new for random walks as well.