Discrete Time Networks with Product Form Steady States

Daduna, Hans

doi:10.1007/978-1-4419-6472-4_6

Cited by 2 publications

(1 citation statement)

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“…In a network, the joint distribution of queue lengths and delays as well as the end-to-end delay are useful measures of network performance but have proved Volume 13, Number 6, 2022 to be hard problems to solve [2]. Analogous to the analysis of their continuous time counterparts, decomposition of the stationary joint distribution of the queue lengths at different queues in a discrete time network into a product of marginal distributions is shown for a large class of networks [6]. To employ this for obtaining the delays, one needs to establish arrival theorems which are known for only special models of networks [7].…”

Section: Introductionmentioning

confidence: 99%

Delay Distributions in Discrete Time Multiclass Tandem Communication Network Models

Gangadhar

Kadambi

2022

Int. j. electr. comput. eng. syst. (Online)

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An exact computational algorithm for the solution of a discrete time multiclass tandem network with a primary class and cross-traffic at each queue is developed. A sequence of truncated Lindley recursions is defined at each queue relating the delays experienced by the first packet from consecutive batches of a class at that queue. Using this sequence of recursions, a convolve-and-sweep algorithm is developed to compute the stationary distributions of the delay and inter-departure processes of each class at a queue, delays experienced by a typical packet from the primary class along its path as well as the mean end-to-end delay of such a packet. The proposed approach is designed to handle the non-renewal arrival processes arising in the network. The algorithmic solution is implemented as an abstract class which permits its easy adaptation to analyze different network configurations and sizes. The delays of a packet at different queues are shown to be associated random variables from which it follows that the variance of total delay is lower bounded by the sum of variances of delays at the queues along the path. The developed algorithm and the proposed lower bound on the variance of total delay are validated against simulation for a tandem network of two queues with three classes under different batch size distributions.

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Section: Introductionmentioning

confidence: 99%