On Distributed Communications Series

III. Determination of Path-Lengths in a Distributed Network

Appendix A

Program Description

A listing of a collection of SCAT-encoded computer routines designed to operate under the aegis of a usercomposed supervisory routine is contained in Appendix B. The collection includes routines for defining networks in terms of pertinent parameters, for assigning and re-assigning parameter values, for performing Monte Carlo simulations on networks, for applying Model A and Model B to networks, and for displaying results of simulations and model-runs. The routines are operative on the IBM 7090, require the RAND versions of SOS[1] for that machine, and are well-described by the listing of Appendix B.

Supervisory routines to perform network calculations must be encoded in SCAT and should use the macro-directives described on p. 4 of the listing. Figure 11 contains an example of a supervisory routine, suitably annotated. The general procedure is to first assign parameter values, then to simulate or model, and finally to display or interrogate results and, perhaps, iterate the procedure. Network parameters are described in Fig. 12; the "normal" values there listed remain in effect until changed by the supervisory program. Much of Figs. 11 and 12, and the macro-directive listing in Appendix B, is self-explanatory.

The parameter WEAVE, which specifies network connectivity, is defined by Fig. 13. The parameter GRAIN defines the ratio of message-unit length (time required to insert a message into a link) to the time required by a station to route a message. Since message-routing time is equivalent to simulation cycle time, GRAIN defines the "coarseness" of the simulation. Note that simulations may be halted and then continued; during these "pauses" the user may display results of the simulation and may change the values of certain parameters. Parameters which may be changed during the course of a simulation are indicated in Fig. 12 with an asterisk. Sources and sinks may be defined, deleted, or have their weights changed during a simulation. Deletion of a source or sink is accomplished by assigning a zero weight. One further restriction exists: the impairment factor, IMPAIR, may not be reset to a value greater than that which held at the initiation of the simulation; this, however, is not a real restriction, since the simulator can be initiated for a zero-time run.

Execution times for application of the two models are negligible. Simulation times are a function of the size and connectivity of the net being simulated and of the traffic density. A reasonable approximation to execution times for an n x m net of redundancy r is given by:

where is the loading factor described in Sec. III.

Computer storage required is a function of net size and connectivity, of traffic density, and of other desiderata. An n x m net of redundancy-r requires approximately

words of computer storage, 24,000 words being available. A 10x10 network of redundancy-four, or a 10 x 10 network of redundancy-three can be accommodated.


[1] Bryan, G. E., Ed., The RAND-SHARE Operating System Manual for the IBM 7090 Computer, The RAND Corporation, RM-3327-PR, September 1962.

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