This paper presents a set of new results on wireless channel capacity by exploring its special characteristics. An appealing discovery is that the instantaneous and cumulative capacity distributions of typical fading channels are lighttailed. An implication of this property is that these distributions and subsequently the distributions of delay and backlog for constant arrivals can be upper-bounded by some exponential functions, which is often assumed but not justified in the literature of wireless network performance analysis. In addition, three representative dependence structures of the capacity process are studied, namely comonotonicity, independence, and Markovian, and bounds are derived for the cumulative capacity distribution and delay-constrained capacity. To help gain insights in the performance of a wireless channel whose capacity process may be too complex or detailed dependence information is lacking, stochastic orders are introduced to the capacity process, based on which, comparison results of delay and delay-constrained capacity are obtained. Moreover, the impact of self-interference in communication, which is an open problem in stochastic network calculus (SNC), is investigated and original results are derived. These results complement the SNC literature, easing its application to wireless networks and its extension towards a calculus for wireless networks.

This paper aims to initiate the research on dependence control, which transforms the dependence structure of a stochastic process in the system through dependence manipulation, to improve the system performance. Specifically, we develop a dependence control theory for wireless channels, focusing on three principles in dependence control: (i) the asymptotic decay rates of delay and backlog in the system are the measures for dependence comparison and ordering, (ii) the dependence in the arrival process and the service process have a dual potency to influence the system performance, and (iii) the manipulation of the dependence in the free dimensions of the arrival or service process transforms the dependence structure of the arrival or service process. In addition, we apply the theory to the Markov additive process, which is a general model for a class of arrival processes and a versatile model for wireless channel capacity, and derive a set of results for various performance measures, including delay, backlog, and delayconstrained capacity. To demonstrate the use of the theory, we focus on dependence manipulation in wireless channel capacity, where we use copula to represent the dependence structure of the underlying Markov process of wireless channel capacity. We show that, based on a priori information of the temporal dependence of the uncontrollable parameters and the spatial dependence between the uncontrollable and controllable parameters, we can construct a sequence of temporal copulas of the Markov process and obtain a sequence of transition matrices of the controllable parameters to achieve the demanded dependence properties of the wireless channel capacity. This dependence manipulation technique is validated by simulation.

This paper aims to present a mathematical tool useful for quantum key distribution network configuration. In particular, the paper studies the throughput of secret key distribution in a quantum key distribution network with trusted repeaters. In addition, the backlog of secret keys at a trusted repeater is also investigated. The analysis is based on the queueing principle of secret keys in the trusted repeater, implied by that the transmission of secret keys in the network is store-andforward. The obtained results are applied to a discrete-variable protocol with weak coherent pulse sources, where realistic system parameters are integrated in the analysis. It is shown that, if the secret key rates on the transmission path are different, the transient throughput of secret key distribution through the network also vary, located between an upper bound and a lower bound on the secrete key distribution rate.

Future wireless communication calls for exploration of more efficient use of wireless channel capacity to meet the increasing demand on higher data rate and less latency. However, while the ergodic capacity and instantaneous capacity of a wireless channel have been extensively studied, they are in many cases not sufficient for use in assessing if data transmission over the channel meets the quality of service (QoS) requirements. To address this limitation, we advocate a set of wireless channel capacity concepts, namely "cumulative capacity", "maximum cumulative capacity", "minimum cumulative capacity", and "range of cumulative capacity", and for each, study its properties by taking into consideration the impact of the underlying dependence structure of the corresponding stochastic process. Specifically, their cumulative distribution function (CDFs) are investigated extensively, where copula is adopted to express the dependence structures. Results considering both generic and specific dependence structures are derived. In particular, in addition to i.i.d., a specially investigated dependence structure is comonotonicity, i.e, the time series of wireless channel capacity are increasing functions of a common random variable. Appealingly, copula can serve as a unifying technique for obtaining results under various dependence assumptions, e.g. i.i.d. and Markov dependence, which are widely seen in stochastic network calculus. Moreover, some other characterizations of cumulative capacity are also studied, including moment generating function, Mellin transform, and stochastic service curve. With these properties, we believe QoS assessment of data transmission over the channel can be further performed, e.g. by applying analytical techniques and results of the stochastic network calculus theory.

Summary We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, and for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, that is, backlog, delay, and throughput.