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

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

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

Matrix product-form solution for an LCFS-PR single-server queue with multiple arrival streams governed by a Markov chain.

This paper considers a stationary single-server queue with multiple arrival streams governed by a Markov chain, where customers are served on an LCFS preemptive-resume basis. Service times of customers from each arrival stream are generally distributed and service time distributions for different arrival streams may be different. Under these assumptions, it is shown that the stationary distribution of queue strings representing from which arrival stream each customer in the system arrived has a matrix product-form solution, where rate matrices constituting the matrix product-form solution are given in terms of the infinitesimal generator of a certain Markov chain. Compared with the previous works, the result in this paper is more general in the sense that general service time distributions are allowed, and it has the advantage of computational efficiency

Queue Length Distribution In A Fifo Single-Server Queue With Multiple Arrival Streams Having Different Service Time Distributions

This paper considers the queue length distribution in a class of FIFO single-server queues with (possibly correlated) multiple arrival streams, where the service time distribution of customers from each arrival stream may differ from one another among streams. It is widely recognized that the queue length distribution in a FIFO queue with multiple non-Poissonian arrival streams having different service time distributions is very hard to analyze, since we have to keep track of the complete order of customers in the queue to describe the queue length dynamics. In this paper, we provide an alternative way to solve the problem for a class of such queues. We characterize the stationary joint queue length distribution in terms of the joint probability generating function, by considering the joint distribution of the number of customers arriving from each stream during the stationary attained waiting time. Further we provide recursion formulas to compute the stationary joint queue length dist..