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

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

A discrete-time HOL priority queue with multiple traffic classes.

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Delay analysis for CBR traffic under static-priority scheduling

We examine the delay performance of packets from constant-bit-rate (CBR) traffic whose delay is affected by non-real-time traffic. The delay performance is analyzed by solving the nD/D/1 queue with vacations. We obtain an exact and closed form solution, hence obviating the need of any approximations or numerical Laplace inversions. We then provide various numerical results for low-bit-rate transmission links, in which packets can experience large delay. From our quantitative evaluation, we conclude that there exists an optimum packet size for a given delay bound. In extremely slow links, such as modem links, transmission control protocol (TCP) packets should be segmented to reduce the CBR delay. We therefore investigate the delay impact of TCP packet sizes as wel

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