**Estimation of an Average Interconnection Length**

**Alexander Y. Tetelbaum **
Department of Electrical Engineering

Michigan State University

East Lansing, MI 48824

and

International Solomon University, Kiev, Ukraine

This paper describes some new results with respect to the problem of the estimation of the average interconnection length. These estimations are based on new rules T1, T2 for the component-to-pin
ratio which are generalizations of Rent's Rule. Estimations of average interconnection lengths for 1D- and 2D-cases are deduced. The impact of optimal placement on interconnection length is considered. The new estimations have been found to produce very satisfactory results on test and industrial circuits.
The described method was implemented in the program ANALYZER. The ANALYZER was implemented in C language on a SUN 3/50 workstation running Unix 4.2BSD. We tested the ANALYZER using ten random generated systems and circuits, two benchmarks: Primary 1 and Primary 2, and several example circuits. Experimental results of the length prediction for these examples are represented. The estimations of ANALYZER are quite comparable to the best real results.

The experimental investigation of the ANALYZER for nMOS integrated circuits and bipolar integrated circuits on the base of the master slice has shown that in many cases its results are quite lose to the manual design. Comparison our predictions with manual designs is also summarized.

The new T1, T2-Rules, provided a basis for direct estimation of the interconnection length which is not possible with Rent's Rule. Numerous experiments have been done to secure comparative data: theoretical results versus empirical data. We learned that:

- Results generated by the new estimates are 6.3% more accurate in
average than estimates based upon Rent's Rule.
- The length estimations obtained from the T1- and T2-Rules are very
close to each other.
- The difference between the real interconnection length and the
theoretical estimation did not exceed 7.4%. The average difference was 3.2%.