Approximations for the Moments of Nonstationary and State Dependent Birth-Death Queues

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed. Using new weighted discrete Sobolev spaces, we derive explicit error bounds of the transition probabilities and new weak a priori estimates for approximating the moments of the Markov processs using a truncated form of the expansion. Using our error bounds and estimates, we are able to show that our approximations converge to the true stochastic process as we add more terms to the expansion and give explicit bounds on the truncation error. As a result, we are the first paper in the queueing literature to provide error bounds and estimates on the performance of a moment closure approximation. Lastly, we perform several numerical experiments for some important models in the queueing theory literature and show that our expansion techniques are accurate at estimating the moment dynamics of these Markov process with only a few terms of the expansion

The Value-of-Information in Matching with Queues

We consider the problem of \emph{optimal matching with queues} in dynamic systems and investigate the value-of-information. In such systems, the operators match tasks and resources stored in queues, with the objective of maximizing the system utility of the matching reward profile, minus the average matching cost. This problem appears in many practical systems and the main challenges are the no-underflow constraints, and the lack of matching-reward information and system dynamics statistics. We develop two online matching algorithms: Learning-aided Reward optimAl Matching ($\mathtt{LRAM}$) and Dual-$\mathtt{LRAM}$ ($\mathtt{DRAM}$) to effectively resolve both challenges. Both algorithms are equipped with a learning module for estimating the matching-reward information, while $\mathtt{DRAM}$ incorporates an additional module for learning the system dynamics. We show that both algorithms achieve an $O(\epsilon+\delta_r)$ close-to-optimal utility performance for any $\epsilon>0$, while $\mathtt{DRAM}$ achieves a faster convergence speed and a better delay compared to $\mathtt{LRAM}$, i.e., $O(\delta_{z}/\epsilon + \log(1/\epsilon)^2))$ delay and $O(\delta_z/\epsilon)$ convergence under $\mathtt{DRAM}$ compared to $O(1/\epsilon)$ delay and convergence under $\mathtt{LRAM}$ ($\delta_r$ and $\delta_z$ are maximum estimation errors for reward and system dynamics). Our results reveal that information of different system components can play very different roles in algorithm performance and provide a systematic way for designing joint learning-control algorithms for dynamic systems

Optimal Cross Slice Orchestration for 5G Mobile Services

5G mobile networks encompass the capabilities of hosting a variety of services such as mobile social networks, multimedia delivery, healthcare, transportation, and public safety. Therefore, the major challenge in designing the 5G networks is how to support different types of users and applications with different quality-of-service requirements under a single physical network infrastructure. Recently, network slicing has been introduced as a promising solution to address this challenge. Network slicing allows programmable network instances which match the service requirements by using network virtualization technologies. However, how to efficiently allocate resources across network slices has not been well studied in the literature. Therefore, in this paper, we first introduce a model for orchestrating network slices based on the service requirements and available resources. Then, we propose a Markov decision process framework to formulate and determine the optimal policy that manages cross-slice admission control and resource allocation for the 5G networks. Through simulation results, we show that the proposed framework and solution are efficient not only in providing slice-as-a-service based on the service requirements, but also in maximizing the provider's revenue.Comment: 6 pages, 6 figures, WCNC 2018 conferenc

Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks

Recently, it has been shown that CSMA-type random access algorithms can achieve the maximum possible throughput in ad hoc wireless networks. However, these algorithms assume an idealized continuous-time CSMA protocol where collisions can never occur. In addition, simulation results indicate that the delay performance of these algorithms can be quite bad. On the other hand, although some simple heuristics (such as distributed approximations of greedy maximal scheduling) can yield much better delay performance for a large set of arrival rates, they may only achieve a fraction of the capacity region in general. In this paper, we propose a discrete-time version of the CSMA algorithm. Central to our results is a discrete-time distributed randomized algorithm which is based on a generalization of the so-called Glauber dynamics from statistical physics, where multiple links are allowed to update their states in a single time slot. The algorithm generates collision-free transmission schedules while explicitly taking collisions into account during the control phase of the protocol, thus relaxing the perfect CSMA assumption. More importantly, the algorithm allows us to incorporate mechanisms which lead to very good delay performance while retaining the throughput-optimality property. It also resolves the hidden and exposed terminal problems associated with wireless networks.Comment: 12 page

Optimal Random Access and Random Spectrum Sensing for an Energy Harvesting Cognitive Radio with and without Primary Feedback Leveraging

We consider a secondary user (SU) with energy harvesting capability. We design access schemes for the SU which incorporate random spectrum sensing and random access, and which make use of the primary automatic repeat request (ARQ) feedback. We study two problem-formulations. In the first problem-formulation, we characterize the stability region of the proposed schemes. The sensing and access probabilities are obtained such that the secondary throughput is maximized under the constraints that both the primary and secondary queues are stable. Whereas in the second problem-formulation, the sensing and access probabilities are obtained such that the secondary throughput is maximized under the stability of the primary queue and that the primary queueing delay is kept lower than a specified value needed to guarantee a certain quality of service (QoS) for the primary user (PU). We consider spectrum sensing errors and assume multipacket reception (MPR) capabilities. Numerical results show the enhanced performance of our proposed systems.Comment: ACCEPTED in EAI Endorsed Transactions on Cognitive Communications. arXiv admin note: substantial text overlap with arXiv:1208.565