Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams

This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular feature of this queue is that service time distributions of customers may be different for different arrival streams. After briefly discussing the actual waiting time distributions of customers from respective arrival streams, we derive a formula for the vector generating function of the time-average joint queue length distribution in terms of the virtual waiting time distribution. Further assuming the discrete phase-type batch size distributions, we develop a numerically feasible procedure to compute the joint queue length distribution. Some numerical examples are provided also

Cell loss dynamics and output process in a finite-buffer discrete-time queue with correlated arrivals

This paper analyzes the performance of an ATM switching node considering cell arrival correlation. An ATM switching node is modeled as a discrete-time finite-buffer queue. Cell arrivals are assumed to follow a semi-Markovian process, where the number of cell arrivals in a lot depends on the states of the underlying (M-state) Markov chain in the current and previous slots. This paper presents analyses for various characteristics of the cell loss, as well as the distribution function of the cell output process from an ATM switching node. Obtained results include the cell loss probability, the consecutive loss probability, the distribution of loss period lengths, the joint distribution of successive cell interdeparture times, and the distribution of busy and idle periods. Through the numerical results, it is shown that both the correlation and the variation of cell arrivals significantly affect the cell loss and the output process characteristics

Inferring Traffic Flow Characteristics from Aggregated-flow Measurement

In the Internet, a statistical perspective of global traffic flows has been considered as an important key to network operations and management. Nonetheless, it is expensive or sometime difficult to measure statistics of each flow directly. Therefore, it is of practical importance to infer unobservable statistical characteristics of individual flows from characteristics of the aggregated-flows, which are easily observed at some links (e.g., router interfaces) in the network. In this paper, we propose a new approach to such inference problems based on finding an inverse function from (observable) probabilities of some states on aggregated-flows to (unobservable) probabilities of some states on flows on a discrete state model, and provide a method inferring arrival rate statistics of individual flows (the OD traffic matrix inference). Our method is applicable to cases not covered by the existing normal-based methods for the OD traffic matrix inference. We also show simulation results on several flow topologies, which indicate potential of our approach

ALGORITHMIC COMPUTATION OF THE TRANSIENT QUEUE LENGTH DISTRIBUTION IN THE BMAP/D/c QUEUE

Abstract This paper proposes a numerically feasible algorithm for the transient queue length distribution in the BMAP/D/c queue. The proposed algorithm ensures the accuracy of the computational result and it is applicable not only to the stable case but also to the unstable case. This paper also discusses a numerical procedure to compute moments of the transient queue length distribution. Finally, some numerical examples are presented to demonstrate the applicability of the proposed algorithm

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

Inferring Link Loss Rates from Unicast-Based End-to-End Measurement

In the Internet, because of huge scale and distributed administration, it is of practical importance to infer network-internal characteristics that cannot be measured directly. In this paper, based on a general framework we proposed previously, we present a feasible method of inferring packet loss rates of individual links from end-to-end measurement of unicast probe packets. Compared with methods using multicast probes, unicast-based inference methods are more flexible and widely applicable, whereas they have a problem with imperfect correlation in concurrent events on paths. Our method can infer link loss rates under this problem, and is applicable to various path-topologies including trees, inverse trees and their combinations. We also show simulation results which indicate potential of our unicast-based method