Modeling short-range ballistic missile defense and Israel's Iron Dome system

This paper develops a model of short-range ballistic missile defense and uses it to study the performance of Israel’s Iron Dome system. The deterministic base model allows for inaccurate missiles, unsuccessful interceptions, and civil defense. Model enhancements consider the trade-offs in attacking the interception system, the difficulties faced by militants in assembling large salvos, and the effects of imperfect missile classification by the defender. A stochastic model is also developed. Analysis shows that system performance can be highly sensitive to the missile salvo size, and that systems with higher interception rates are more “fragile” when overloaded. The model is calibrated using publically available data about Iron Dome’s use during Operation Pillar of Defense in November 2012. If the systems performed as claimed, they saved Israel an estimated 1778 casualties and $80 million in property damage, and thereby made preemptive strikes on Gaza about 8 times less valuable to Israel. Gaza militants could have inflicted far more damage by grouping their rockets into large salvos, but this may have been difficult given Israel’s suppression efforts. Counter-battery fire by the militants is unlikely to be worthwhile unless they can obtain much more accurate missiles.

List of Employees to be involved in the extension of the Port Dalhousie and Thorold Railway

List of Employees to be involved in the extension of the Port Dalhousie and Thorold Railway (1 page, handwritten). This is signed by S.D. Woodruff, Nov. 25, 1856.

Letter of estimate sent to S.D. Woodruff for the total cost of construction and equipment of the extension of the line to Port Colborne

Letter of estimate sent to S.D. Woodruff for the total cost of construction and equipment of the extension of the line to Port Colborne [this is unsigned]. There is an envelope with this letter that suggests that it is from Mr. Shanly, Mar. 12, 1857.

Chart of estimate of cost of Port Dalhousie and Thorold Railway extension Line no. 1

Chart of estimate of cost of Port Dalhousie and Thorold Railway extension Line no. 1 signed by Mr. Shanly, Mar. 12, 1857.

Report sent to the President and Director of the Port Dalhousie and Thorold Railway stating that the location of the line extension of the railway is completed

Report sent to the President and Director of the Port Dalhousie and Thorold Railway stating that the location of the line extension of the railway is completed. The distance from Thorold Station to Port Colborne is 20 miles. The estimate provides for construction of a permanent structure across the Chippewa and Welland River. Estimates for building a first class road, culverts and bridges will be of permanent and durable masonry. This includes estimates for various station buildings such as a warehouse in Port Colborne and a warehouse in Port Dalhousie. Surveys and plans are ready and will be registered this week. This is signed by S.D. Woodruff (2 copies) [one appears to be a rough copy] (The rough copy is 5 pages, handwritten and the other copy is 6 pages, handwritten), Apr. 8, 1857.

Voucher #2 from the Engineer Department of Port Dalhousie and Thorold Railway Extension paid to Daniel Plumsteel, Dec. 31, 1856

Voucher #2 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for surveys, paid to Daniel Plumsteel, Dec. 31, 1856.

Voucher #3 from the Engineer Department of Port Dalhousie and Thorold Railway Extension paid to Thomas Woods, Dec. 31, 1856

Voucher #3 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for sinking test pits, paid to Thomas Woods, Dec. 31, 1856.

Voucher #5 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to George Forbes for surveys, Jan. 31, 1857

Voucher #5 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to George Forbes for surveys, Jan. 31, 1857.

Voucher #6 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to Thomas Woods for surveys, Jan. 31, 1857

Voucher #6 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to Thomas Woods for surveys, Jan. 31, 1857.

Voucher #7 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to W.G. Thompson accompanied by an abstract of vouchers and summaries of account paid by W.G. Thompson for surveys, Jan. 31, 1857

Voucher #7 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to W.G. Thompson accompanied by an abstract of vouchers and summaries of account paid by W.G. Thompson for surveys, Jan. 31, 1857.

Pay roll voucher #8 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for surveys in the month of February, Feb. 28, 1857

Pay roll voucher #8 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for surveys in the month of February, Feb. 28, 1857.

Voucher #9 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to W. G. Thompson accompanied by an abstract of vouchers for surveys, Feb. 28, 1857

Voucher #9 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to W. G. Thompson accompanied by an abstract of vouchers for surveys, Feb. 28, 1857

Pay roll voucher #10 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for the engineer corps. , Mar. 31, 1857

Pay roll voucher #10 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for the engineer corps. , Mar. 31, 1857.

Voucher #15 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to A. H. Armour for office supplies, Apr. 1, 1857

Voucher #15 from the Engineer Department of Port Dalhousie and Thorold Railway Extension to A. H. Armour for office supplies, Apr. 1, 1857.

Pay roll voucher #12 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for the office approved by F. Shanly, chief engineer, April, 1857

Pay roll voucher #12 from the Engineer Department of Port Dalhousie and Thorold Railway Extension for the office approved by F. Shanly, chief engineer, April, 1857.