Journal ArticleDOI
The Single Server Queue with Periodic Arrival Process and Deterministic Service Times
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TLDR
An algorithm is derived for computing the exact delay distribution for the following first-come-first-served single server queue: the idealized queueing model above, which analyzes the worst-delay situation for this problem when the incoming trunks are fully utilized and the packets are maximum sized.Abstract:
We derive an algorithm for computing the exact delay distribution for the following first-come-first-served single server queue. The arrival process is the superposition of N + 1 independent equivalent deterministic arrival streams, and the service times are deterministic. Numerical results are used to compare this system with an approximating system which has been used in the absence of exact results: the M/D/1 queue (Poisson input, deterministic service time). A comparison with a finite source model is also given. This study was motivated by the following issue germane to packet switching data networks. There are N + 1 packet processes, arriving over identical trunks, which must share the transmission capacity of a single high-speed trunk in a store-and-forward manner. The idealized queueing model above analyzes the worst-delay situation for this problem when the incoming trunks are fully utilized and the packets are maximum sized. The results indicate that an M/D/1 approximation can be quite pessimistic in predicting the performance of such a system.read more
Citations
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Journal ArticleDOI
The superposition of variable bit rate sources in an ATM multiplexer
TL;DR: In this paper, the authors analyzed the burst component of the considered superposition queuing process in a variable-bit-rate constant-output-rate (COR) fluid system.
Journal ArticleDOI
The superposition of periodic cell arrival streams in an ATM multiplexer
James Roberts,Jorma Virtamo +1 more
TL;DR: The authors consider the queue arising in a multiservice network using ATM (asynchronous transfer mode) when a superposition of periodic streams of constant-length cells is multiplexed on a high-speed link, and derive an exact closed formula for the queue length distribution.
Journal ArticleDOI
Managing bandwidth in ATM networks with bursty traffic
TL;DR: A bandwidth management and congestion control scheme for asynchronous transfer mode (ATM) networks that supports both point-to-point and one- to-many multicast virtual circuits is proposed and it is shown that the method can handle fully heterogeneous traffic and can be effectively implemented.
Proceedings ArticleDOI
Analysis of the delay and jitter of voice traffic over the Internet
Mansour J. Karam,Fouad A. Tobagi +1 more
TL;DR: It is concluded that priority queuing is the most appropriate scheduling scheme for the handling of voice traffic, while preemption of non-voice packets is strongly recommended for sub-10 Mbit/s links.
Proceedings ArticleDOI
Fractal analysis and modeling of VoIP traffic
TL;DR: It is argued that the call hold times follow heavy-tailed distributions rather than exponential distributions and the generalized Pareto distribution is proposed for modeling the call holding times.
References
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Book
A first course in stochastic processes
Samuel Karlin,Howard M. Taylor +1 more
TL;DR: In this paper, the Basic Limit Theorem of Markov Chains and its applications are discussed and examples of continuous time Markov chains are presented. But they do not cover the application of continuous-time Markov chain in matrix analysis.
Journal ArticleDOI
A Proof for the Queuing Formula: L = λW
TL;DR: In this paper, it was shown that if the three means are finite and the corresponding stochastic processes strictly stationary, and if the arrival process is metrically transitive with nonzero mean, then L = λW.
Journal ArticleDOI
Superimposed renewal processes and storage with gradual input
TL;DR: In this article, the storage process at the buffer may be considered as a queueing process with gradual input, being a process which until now has been hardly studied, and the present study provides for several models of this type an analytic description, it shows that existing results of queueing theory can be used.
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