arXiv subjects

Yoshiaki Inoue

Publications and source records attributed to Yoshiaki Inoue.

12 recordsLinked to original sources

arXiv2026

Computing transient probabilities in Markovian queues with balking conditional on a fixed number of joined customers

We analyze the transient behavior of a Markovian queue with balking, conditional on exactly $K$ customers joining the system in a finite time interval $[0, T]$. A key quantity of interest is the cumulative number of balking customers, for which we consider the probability generating function (PGF) and derive an equation it satisfies. This approach circumvents the computational burden arising from dealing with high-dimensional Markovian system, which arises when attempting to directly compute the joint distribution of the cumulative number of balking customers together with the total number of joining customers and the number of customers in the system. To compute state transitions in $(t, T]$ efficiently, we examine the conditional state probability at time $T$ given the system state at time $T - u$, and show that it satisfies a linear differential equation in $u$. For piecewise-constant arrival rates, we develop a numerical procedure for evaluating the moment of the total number of balking customers, jointly with the cumulative number of joining customers and the number of customers in the system, under the condition that $K$ customers joined. We also present numerical examples that highlight counterintuitive behaviors arising from this conditioning, along with explanations of the underlying mechanisms.

math.PR↗

arXiv2025

A Two-Stage Scheduling Method for Nurse Scheduling and Its Practical Application

The creation of nurses' schedules is a critical task that directly impacts the quality and safety of patient care as well as the quality of life for nurses. In most hospitals in Japan, this responsibility falls to the head nurse of each ward. The physical and mental burden of this task is considerable, and recent challenges such as the growing shortage of nurses and increasingly diverse working styles have further complicated the scheduling process. Consequently, there is a growing demand for automated nurse scheduling systems. Technically, modern integer programming solvers can generate feasible schedules within a practical timeframe. However, in many hospitals, schedules are still created manually. This is largely because tacit knowledge, considerations unconsciously applied by head nurses, cannot be fully formalized into explicit constraints, often resulting in automatically generated schedules that are not practically usable. To address this issue, we propose a novel "two-stage scheduling method." This approach divides the scheduling task into night shift and day shift stages, allowing head nurses to make manual adjustments after the first stage. This interactive process makes it possible to produce nurse schedules that are suitable for real-world implementation. Furthermore, to promote the practical adoption of nurse scheduling, we present case studies from acute and chronic care hospitals where systems based on the proposed method were deployed. We also discuss the challenges encountered during implementation and the corresponding solutions.

math.OC↗

arXiv2025

Effects of the Auto-Correlation of Delays on the Age of Information: A Gaussian Process Framework

The age of information (AoI) has been studied actively in recent years as a performance measure for systems that require real-time performance, such as remote monitoring systems via communication networks. The theoretical analysis of the AoI is usually formulated based on explicit system modeling, such as a single-server queueing model. However, in general, the behavior of large-scale systems such as communication networks is complex, and it is usually difficult to express the delay using simple queueing models. In this paper, we consider a framework in which the sequence of delays is composed from a non-negative continuous-time stochastic process, called a virtual delay process, as a new modeling approach for the theoretical analysis of the AoI. Under such a framework, we derive an expression for the transient probability distribution of the AoI and further apply the theory of stochastic orders to prove that the high dependence of the sequence of delays leads to the degradation of AoI performance. We further consider a special case in which the sequence of delays is generated from a stationary Gaussian process, and we discuss the sensitivity of the AoI to second-order statistics of the delay process through numerical experiments.

cs.PF↗

arXiv2024

Time-dependent queue length distribution in queues fed by $K$ customers in a finite interval

We consider queueing models, where customers arrive according to a continuous-time binomial process on a finite interval. In this arrival process, a total of $K$ customers arrive in the finite time interval $[0,T]$, where arrival times of those $K$ customers are independent and identically distributed according to an absolutely continuous distribution defined by its probability density function $f(t)$ on $(0,T]$. To analyze the time-dependent queue length distribution of this model, we introduce the auxiliary model with non-homogeneous Poisson arrivals and show that the time-dependent queue length distribution in the original model is given in terms of the time-dependent joint distribution of the numbers of arrivals and departures in the auxiliary model. Next, we consider a numerical procedure for computing the time-dependent queue length distribution in Markovian models with piecewise constant $f(t)$. A particular feature of our computational procedure is that the truncation error bound can be set as the input. Some numerical examples are also provided.

math.PR↗

arXiv2024

Characterizing the Age of Information with Multiple Coexisting Data Streams

In this paper we analyze the distribution of the Age of Information (AoI) of a tagged data stream sharing a processor with a set of other data streams. We do so in the highly general setting in which the interarrival times pertaining to the tagged stream can have any distribution, and also the service times of both the tagged stream and the background stream are generally distributed. The packet arrival times of the background process are assumed to constitute a Poisson process, which is justified by the fact that it typically is a superposition of many relatively homogeneous streams. The first main contribution is that we derive an expression for the Laplace-Stieltjes transform of the AoI in the resulting GI+M/GI+GI/1 model. Second, we use stochastic ordering techniques to identify tight stochastic bounds on the AoI, leading to an explicit lower and upper bound on the mean AoI. In addition, when approximating the tagged stream's inter-generation times through a phase-type distribution (which can be done at any precision), we present a computational algorithm for the mean AoI. As illustrated through a sequence of numerical experiments, the analysis enables us to assess the impact of background traffic on the AoI of the tagged stream. It turns out that the upper bound on the mean AoI is remarkably close to its true value, which yields an explicit expression (in terms of the model parameters) for an accurate proxy of the AoI-minimizing generation rate.

cs.NI↗

arXiv2024

Exact Analysis of the Age of Information in the Multi-Source M/GI/1 Queueing System

We consider a situation that multiple monitoring applications (each with a different sensor-monitor pair) compete for a common service resource such as a communication link. Each sensor reports the latest state of its own time-varying information source to its corresponding monitor, incurring queueing and processing delays at the shared resource. The primary performance metric of interest is the age of information (AoI) of each sensor-monitor pair, which is defined as the elapsed time from the generation of the information currently displayed on the monitor. Although the multi-source first-come first-served (FCFS) M/GI/1 queue is one of the most fundamental model to describe such competing sensors, its exact analysis has been an open problem for years. In this paper, we show that the Laplace-Stieltjes transform (LST) of the stationary distribution of the AoI in this model, as well as the mean AoI, is given by a simple explicit formula, utilizing the double Laplace transform of the transient workload in the M/GI/1 queue.

cs.NI↗

arXiv2023

Evaluation of Large Language Models for Decision Making in Autonomous Driving

Various methods have been proposed for utilizing Large Language Models (LLMs) in autonomous driving. One strategy of using LLMs for autonomous driving involves inputting surrounding objects as text prompts to the LLMs, along with their coordinate and velocity information, and then outputting the subsequent movements of the vehicle. When using LLMs for such purposes, capabilities such as spatial recognition and planning are essential. In particular, two foundational capabilities are required: (1) spatial-aware decision making, which is the ability to recognize space from coordinate information and make decisions to avoid collisions, and (2) the ability to adhere to traffic rules. However, quantitative research has not been conducted on how accurately different types of LLMs can handle these problems. In this study, we quantitatively evaluated these two abilities of LLMs in the context of autonomous driving. Furthermore, to conduct a Proof of Concept (POC) for the feasibility of implementing these abilities in actual vehicles, we developed a system that uses LLMs to drive a vehicle.

cs.CV↗

arXiv2022

Estimating customer impatience in a service system with unobserved balking

This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every customer has a patience threshold and they balk if the observed delay is above the threshold. The main objective is to estimate the parameters of the customers' patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication, and distinguishing feature of our setup, lies in the fact that customers who decide not to join are not observed, remarkably, we manage to devise a procedure to estimate the underlying patience and arrival rate parameters. The model is a multi-server queue with a Poisson stream of customers, enabling evaluation of the corresponding likelihood function of the state-dependent effective arrival process. We establish strong consistency of the MLE and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution.

math.PR↗

arXiv2022

Stochastic Image Transmission with CoAP for Extreme Environments

Communication in extreme environments is an important research topic for various use cases including environmental monitoring. A typical example is underwater acoustic communication for 6G mobile networks. The major challenges in such environments are extremely high-latency and high-error rate. They make real-time image transmission difficult using existing communication protocols. This is partly because frequent retransmission in noisy networks increases latency and leads to serious deterioration of real-timeness. To address this problem, this paper proposes a stochastic image transmission with Constrained Application Protocol (CoAP) for extreme environments. The goal of the proposed idea is to achieve approximate real-time image transmission without retransmission using CoAP over UDP. To this end, an image is divided into blocks, and value is assigned for each block based on the requirement. By the stochastic transmission of blocks, the reception probability is guaranteed without retransmission even when packets are lost in networks. We implemented the proposed scheme using Raspberry Pi 4 to demonstrate the feasibility. The performance of the proposed image transmission was confirmed from the experimental results.

cs.NI↗

arXiv2021

Queueing Analysis of GPU-Based Inference Servers with Dynamic Batching: A Closed-Form Characterization

GPU-accelerated computing is a key technology to realize high-speed inference servers using deep neural networks (DNNs). An important characteristic of GPU-based inference is that the computational efficiency, in terms of the processing speed and energy consumption, drastically increases by processing multiple jobs together in a batch. In this paper, we formulate GPU-based inference servers as a batch service queueing model with batch-size dependent processing times. We first show that the energy efficiency of the server monotonically increases with the arrival rate of inference jobs, which suggests that it is energy-efficient to operate the inference server under a utilization level as high as possible within a latency requirement of inference jobs. We then derive a closed-form upper bound for the mean latency, which provides a simple characterization of the latency performance. Through simulation and numerical experiments, we show that the exact value of the mean latency is well approximated by this upper bound. We further compare this upper bound with the latency curve measured in real implementation of GPU-based inference servers and we show that the real performance curve is well explained by the derived simple formula.

cs.PF↗

arXiv2020

Global Optimization of Relay Placement for Seafloor Optical Wireless Networks

Optical wireless communication is a promising technology for underwater broadband access networks, which are particularly important for high-resolution environmental monitoring applications. This paper focuses on a deep sea monitoring system, where an underwater optical wireless network is deployed on the seafloor. We model such an optical wireless network as a general queueing network and formulate an optimal relay placement problem, whose objective is to maximize the stability region of the whole system, i.e., the supremum of the traffic volume that the network is capable of accommodating. The formulated optimization problem is further shown to be non-convex, so that its global optimization is non-trivial. In this paper, we develop a global optimization method for this problem and we provide an efficient algorithm to compute an optimal solution. Through numerical evaluations, we show that a significant performance gain can be obtained by using the derived optimal solution.

cs.NI↗

arXiv2019

A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues

This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update systems. The formula indicates that the stationary distribution of the AoI is given in terms of the stationary distributions of the system delay and the peak AoI. To demonstrate its applicability and usefulness, we analyze the AoI in single-server queues with four different service disciplines: first-come first-served (FCFS), preemptive last-come first-served (LCFS), and two variants of non-preemptive LCFS service disciplines. For the FCFS and the preemptive LCFS service disciplines, the GI/GI/1, M/GI/1, and GI/M/1 queues are considered, and for the non-preemptive LCFS service disciplines, the M/GI/1 and GI/M/1 queues are considered. With these results, we further show comparison results for the mean AoI's in the M/GI/1 and GI/M/1 queues under those service disciplines.

cs.PF↗