Estimates of distributions of random variables for certain computer communications traffic models
Proceedings of the first ACM symposium on Problems in the optimization of data communications systems
Communication nets; stochastic message flow and delay
Communication nets; stochastic message flow and delay
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Integrating two different message switching systems into one with the resultant integrated system having the combined channel capacity, need not necessarily result in improved performance. This segregated system vs. integrated system question has been adequately answered in a recent communication for the specific case when the message arrivals are Poisson processes and the message lengths for the two systems are (separately) exponentially distributed. While the Poisson assumption is probably adequate for message arrivals, recent investigations indicate that in computer communications traffic, a better approximation of the message lengths is provided by the geometric distribution. This paper presents a new algorithm which establishes the relative superiority of the segregated or the integrated system for the geometrically distributed message lengths. In order to make an equitable comparison, the average delay per message for the segregated systems is computed after making an optimum reallocation of the total available channel capacity. This is done by numerically solving a sixth order equation. The first and the second moments of the combined traffic, which need not necessarily have a geometric distribution, is then computed. Using this statistics and the combined channel capacity, the delay for the integrated system is obtained. A comparison between the performances of the segregated and the integrated systems is then effected.