Percentile Delay Calculation for the Infinite Population Nonpersistent CSMA/CD

Kiyoshi YONEDA  

IEICE TRANSACTIONS (1976-1990)   Vol.E68    No.6    pp.371-375
Publication Date: 1985/06/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Data Transmission

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A model for computation of the transmission delay distribution in infinite population nonpersistent CSMA/CD is presented, together with computational approximations. Recent extensions of the use of CSMA/CD to heavy load realtime applications, such as packet voice communication and process control, motivated this work. The realtime condition demands quantiles of packet delay distributions, which in turn requires that the entire distribution be calculated rather than representative values such as mean delay and coefficient of variation. The model decomposes into two submodels describing channel state and delay distribution, respectively. The channel model is of infinite population justifying the assumption that the channel behavior affects an individual station's behavior, whereas the converse does not take place. The formulation is by discrete time Markov chain; time is grained into slots or backoff unit time. An arbitrary packet size distribution is allowed. The solution is obtained in closed form; measures such as throughput and probability of trial success are also available in closed form. The delay model assumes that channel access trials are independent of each other; the calculation consists of convolutions and weighted sum of distributions. Because this computation is rather heavy, approximations are included.