THE ECONOMICS OF SEGREGATED AND INTEGRATED SYSTEMS IN DATA COMMUNICATION WITH GEOMETRICALLY DISTRIBUTED MESSAGE LENGTHS P. K. Verma and A. M. Rybczynski Bell Canada Computer Communications Ottawa, Canada ABSTRACT 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 arri- vals are Poisson processes and the message lengths for the two systems are (separately) exponentially distributed. While the Polsson assumption is pro- bably adequate for message arrivals, recent investigations indicate that in computer communications traffic, a better approxima- tion 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 neallocatlon 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. INTRODUCTION A computer communication system is characterized by a set of nodes connected to each other by communication links or channels in order to effect the transmission of messages from one node to another. Both the lengths of the messages as well as the time between successive arrivals are random quantities. The resulting stochastic flow of the message traffic gives rise to queues at the nodes and an analysis of this process is an essential part of the successful design of any computer communication system. $8 The average delay encountered by a message in passing through a communication net is the criterion commonly employed as a measure of its performances 1,2 Since the transmission costs can be considered to be most heavily dependent upon the channel capacity required,3 system optimization consists essentially in minimizing the average delay under the constraint of a fixed channel capacitp~ Generally speaking, an increase in the size of a message switching system with~ the utilization factor 0* held constant, results in improved performance in the sense of obtaining a lower average message delay. However, integrating two different message switching systems into one with the resul- tant integrated system having the combined channel capacity need not necessarily result in improved performance. This segregated system vs. integrated system question has been the subject of recent investigations2, 4 and must be carefully analyzed for every computer communication system catering to more than one class of traffic. Rudin 2 has obtained appropriate results for the specific case when the message arrivals are Poisson processes and the message lengths for the two systems are (separately) exponentially distributed. ~a Silva 4 has introduced priorities in the two classes of users and has established a critical value of message length ratio such that a lesser disparity in message lengths will lead to the integrated system being superior in performance, da Silva's analysis also assumes exponentially distributed message lengths. The Poisson assumption is probably adequate for message arrivals but recent investigation on computer communication traffic models indicate that a better appro- ximation to message lengths is provided by the geometric distributionS, 6 While the mathematical complexity of the geometric distribution defies a closed form solution, it is nevertheless essential to obtain an *The utilization factor 0 of a link can be defined as the ratio of the average number of bits transmitted per second to the channel capacity of the link in bits per second.