Naoto Miyoshi

A Cellular Network Model with Ginibre Configured Base Stations

Stochastic geometry models for wireless communication networks have recently attracted much attention. This is because the performance of such networks critically depends on the spatial configuration of wireless nodes and the irregularity of the node configuration in a real network can be captured by a spatial point process. However, most analysis of such stochastic geometry models for wireless networks assumes, owing to its tractability, that the wireless nodes are deployed according to homogeneous Poisson point processes. This means that the wireless nodes are located independently of each other and their spatial correlation is ignored. In this work we propose a stochastic geometry model of cellular networks such that the wireless base stations are deployed according to the Ginibre point process. The Ginibre point process is one of the determinantal point processes and accounts for the repulsion between the base stations. For the proposed model, we derive a computable representation for the coverage probability—the probability that the signal-to-interference-plus-noise ratio (SINR) for a mobile user achieves a target threshold. To capture its qualitative property, we further investigate the asymptotics of the coverage probability as the SINR threshold becomes large in a special case. We also present the results of some numerical experiments.

A scalable and lightweight QoS monitoring technique combining passive and active approaches

To make a scalable and lightweight QoS monitoring system, we have proposed a new QoS monitoring technique, change-of-measure based passive/active monitoring (CoMPACT monitor), which is based on change-of-measure framework and is an active measurement transformed by using passively monitored data. This technique enables us to measure detailed QoS information for individual users, applications, and organizations, in a scalable and lightweight manner. In this paper, we present the mathematical foundation of CoMPACT monitor. In addition, we show its characteristics through simulations in terms of typical implementation issues for inferring the delay distributions. The results show that CoMPACT monitor gives accurate QoS estimations with only a small amount of extra traffic for active measurement.

Fluid limit analysis of FIFO and RR caching for independent reference models

We study the fluid limit analysis of random replacement (RR) caching for the independent reference model. Applying the limit theorem for the mean field interaction model, we derive the fluid limit of fault probability in the transient state as well as in the steady state. Since the stationary fault probability for the RR cache is identical to that for the first-in first-out (FIFO) cache, our results on the stationary fault probability are available for the FIFO caching. We see that the fluid limit of stationary fault probability that we obtain is coincident with the existing heuristic approximation of stationary fault probability. That is, our fluid limit analysis gives a rigorous theoretical foundation to the heuristic approximation.

Scale free interval graphs

Scale free graphs have attracted attention by their non-uniform structure that can be used as a model for various social and physical networks. In this paper, we propose a natural and simple random model for generating scale free interval graphs. The model generates a set of intervals randomly under a certain distribution, which defines a random interval graph. The main advantage of the model is its simpleness. The structure/properties of generated graphs are analyzable by relatively simple probabilistic and/or combinatorial arguments, which is different from many other models. Based on such arguments, we show for our random interval graph that its degree distribution follows a power law, and that it has a large average clustering coefficient.

Uplink cellular network models with Ginibre deployed base stations

Stochastic geometry models have been attracting attention as tractable models of wireless communication networks. Most prior studies on such models assume that the wireless nodes are placed according to homogeneous Poisson point processes (PPPs); that is, their spatial correlation is ignored. Recently, a stochastic geometry model of downlink cellular networks was proposed in which the wireless base stations (BSs) are deployed according to the Ginibre point process (GPP). The GPP can express repulsion between BSs. On the other hand, the uplink analysis is more complicated than the downlink one since the transmit power of each mobile user depends on its location. In this study, we propose two approximation models for uplink cellular networks in which BSs are deployed according to the GPP. For these models, we derive computable representations for two performance indices and investigate the impact of varying the power control parameter on the network performance.

Downlink coverage probability in a cellular network with Ginibre deployed base stations and Nakagami-m fading channels

Recently, spatial stochastic models based on determinantal point processes (DPP) are studied as promising models for analysis of cellular wireless networks. Indeed, the DPPs can express the repulsive nature of the macro base station (BS) configuration observed in a real cellular network and have many desirable mathematical properties to analyze the network performance. However, almost all the prior works on the DPP based models assume the Rayleigh fading while the spatial models based on Poisson point processes have been developed to allow arbitrary distributions of fading/shadowing propagation effects. In order for the DPP based model to be more promising, it is essential to extend it to allow non-Rayleigh propagation effects. In the present paper, we propose the downlink cellular network model where the BSs are deployed according to the Ginibre point process, which is one of the main examples of the DPPs, over Nakagami-m fading. For the proposed model, we derive a numerically computable form of the coverage probability and reveal some properties of it numerically and theoretically.

Padé approximation for coverage probability in cellular networks

Coverage probability is one of the most important metrics for evaluating the performance of wireless networks. However, the spatial stochastic models for which a computable expression of the coverage probability is available are restricted (such as the Poisson based or α-Ginibre based models). Furthermore, even if it is available, the practical numerical computation may be time-consuming (in the case of α-Ginibre based model). In this paper, we propose the application of Padé approximation to the coverage probability in the wireless network models based on general spatial stationary point processes. The required Maclaurin coefficients are expressed in terms of the moment measures of the point process, so that the approximants are expected to be available for a broader class of point processes. Through some numerical experiments for the cellular network model, we demonstrate that the Padé approximation is effectively applicable for evaluating the coverage probability.

Optimal service control of a station connected with two parallel substations

The optimization problem is studied for a queueing network consisting of one station and two parallel subordinate stations. After service completion at the first station, the job is divided into two subjobs and each of them enters one of the subordinate stations. The service rate at the first station is controlled in order to minimize the expected total discounted cost or the long-run average expected cost. >

Cellular Networks with \(\alpha \)-Ginibre Configurated Base Stations

We consider a cellular network model with base stations configurated according to the \(\alpha \)-Ginibre point process with \(\alpha \in (0,1]\), which is one of the determinantal point processes. In this model, we focus on the asymptotic behavior of the so-called coverage probability (or link success probability) as the threshold value tends to \(0\) and \(\infty \), and discuss the Pade approximation of the coverage probability at \(0\) and the dependence on \(\alpha \in (0,1]\) of the asymptotic constant at \(\infty \) both numerically and theoretically.

A Change-of-Measure Approach to Per- Flow Delay Measurement Combining Passive and Active Methods: Mathematical Formulation for CoMPACT Monitor

One problem with active measurement is that, while it is suitable for measuring time-average network performance, it is difficult to measure per-flow quality of service (QoS), which is defined as the average over packets in the flow. To achieve such per-flow QoS measurement, the authors proposed a new technique, called the change- of- measure-based passive/active monitoring (CoMPACT Monitor), which is based on the change-of-measure framework in probability/measure theory and transforms actively obtained information by using passively monitored data. This technique enables us to concurrently measure one-way delay information about individual users, applications, and organizations in detail in a lightweight manner. This paper presents the mathematical formulation for the CoMPACT Monitor and verifies that it works well under some weak conditions. In addition, we investigate its characteristics regarding several implementation issues through simulation and actual network experiments. The results reveal that our technique provides highly qualified estimates involving only a limited amount of extra traffic from active probes.