Yoshiaki Inoue

Analysis of the loss probability in the M/G/1+G queue

We consider the loss probability in the stationary M/G/1+G queue, i.e., the stationary M/G/1 queue with impatient customers whose impatience times are generally distributed. It is known that the loss probability is given in terms of the probability density function v(x) of the virtual waiting time and that v(x) is given by a formal series solution of a Volterra integral equation. In this paper, we show that the series solution of v(x) can be interpreted as the probability density function of a random sum of dependent random variables and we reveal its dependency structure through the analysis of a last-come first-served, preemptive-resume M/G/1 queue with workload-dependent loss. Furthermore, based on this observation, we show some properties of the loss probability.

The stationary distribution of the age of information in FCFS single-server queues

We consider the stationary distributions of the age of information (AoI) and the peak AoI in information update systems. We first derive an invariant relation among the distributions of the AoI, the peak AoI, and the system delay, which holds for a wide class of information update systems. Based on this result, we next obtain several formulas for the stationary distributions of the AoI and the peak AoI in the first-come first-served (FCFS) GI/GI/1 queue, which is a general model of FCFS information update systems. Finally, we derive explicit formulas for the Laplace-Stieltjes transforms of the stationary distributions of the AoI and the peak AoI in FCFS M/GI/1 and GI/M/1 queues.

Behavior analysis of self-evolving botnets

Machine learning techniques have been achieving significant performance improvements in various kinds of tasks, and they are getting applied in many research fields. While we benefit from such techniques in many ways, they can be a serious security threat to the Internet if malicious attackers become able to utilize them to detect software vulnerabilities. This paper introduces a new concept of self-evolving botnets, where computing resources of infected hosts are exploited to discover unknown vulnerabilities in non-infected hosts. We propose a stochastic epidemic model that incorporates such a feature of botnets, and show its behaviors through numerical experiments and simulations.

The M/D/1+D queue has the minimum loss probability among M/G/1+G queues

We consider the loss probability P loss in the stationary M/G/1 queue with generally distributed impatience times (M/G/1+G queue). Recently, it was shown that P loss increases with service times in the convex order. In this paper, we show that P loss also increases with impatience times in the excess wealth order. With these results, we show that P loss in the M/D/1+D queue is smallest among all M/G/1+G queues with the same and finite arrival rate, mean service time, and mean impatience time.

A computational algorithm for the loss probability in the M/G/1+PH queue

ABSTRACT This article develops a computational algorithm for the loss probability in the stationary M/G/1 queue with impatient customers whose impatience times follow a phase-type distribution (M/G/1+PH). The algorithm outputs the loss probability, along with an upper-bound of its numerical error due to truncation, and it is readily applicable to the M/D/1+PH, M/PH/1+PH, and M/Pareto/1+PH queues.

Analysis of \(\hbox {M}^{\mathrm {x}}/\hbox {G}/1\) queues with impatient customers

This paper considers a batch arrival (hbox {M}^{mathrm {x}}/hbox {G}/1) queue with impatient customers. We consider two different model variants. In the first variant, customers in the same batch are assumed to have the same patience time, and patience times associated with batches are i.i.d. according to a general distribution. In the second variant, patience times of customers in the same batch are independent, and they follow a general distribution. Both variants are related to an M/G/1 queue in which the service time of a customer depends on its waiting time. Our main focus is on the virtual and actual waiting times, and on the loss probability of customers.

Stochastic modeling of self-evolving botnets with vulnerability discovery

Abstract Machine learning techniques have been actively studied and achieved significant performance improvements in various kinds of tasks. While we benefit from such techniques in many ways, they can be a serious security threat to the Internet if malicious attackers become able to utilize them to discover unknown software vulnerabilities. This paper introduces a new concept of self-evolving botnets, where computing resources of infected hosts are exploited to discover unknown vulnerabilities in non-infected hosts and the botnets evolve autonomously. We provide a stochastic epidemic model for the self-evolving botnets, and show its behaviors through numerical and simulation experiments.