Risk Analysis, Vol. 31, No. 10, 2011 DOI: 10.1111/j.1539-6924.2011.01593.x Defense Resource Distribution Between Protection and Redundancy for Constant Resource Stockpiling Pace Gregory Levitin 1,2 and Kjell Hausken 3, * The article considers the optimal resource distribution in a parallel system between increas- ing protection and providing redundancy in a situation when the attacker’s and defender’s resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time proba- bility is uniformly distributed along this horizon. The defender optimizes the resource distri- bution in order to minimize the system destruction probability during the time horizon. First, we find the optimal pace of construction of the new redundant elements assuming that the construction must start in the initial stage of the stockpiling process. We show that starting construction of new elements in the beginning of the system’s existence results in its high ini- tial vulnerability. Introducing the time delay before starting the construction can reduce the initial system vulnerability and the entire system destruction probability. The problem of op- timization of time delay and new element construction pace is considered with and without constraint on the initial system vulnerability. Examples illustrating the methodology of the optimal defense strategy analysis are presented. KEY WORDS: Attack; contest success function; defense; delay; protection; redundancy; stockpiling; vulnerability 1. INTRODUCTION Classical reliability theory considers providing redundancy and improving reliability of elements as measures of system reliability enhancement. (1,2) When survivability of systems exposed to intentional attacks is concerned, deploying separated redundant elements and protection of these elements against malicious impacts become essential elements of the defense strategy. (3−5) The defender must decide how 1 Collaborative Autonomic Computing Laboratory, School of Computer Science, University of Electronic Science and Tech- nology of China. 2 The Israel Electric Corporation Ltd., P.O. Box 10, Haifa 31000, Israel. 3 Faculty of Social Sciences, University of Stavanger, N-4036 Sta- vanger, Norway. ∗ Address correspondence to Kjell Hausken, Faculty of Social Sci- ences, University of Stavanger, N-4036 Stavanger, Norway; tel: +47 51 831632; fax: +47 51 831550; kjell.hausken@uis.no. to distribute system defense resources among differ- ent defensive measures. The theory of defense against intentional attacks has attracted increasing efforts over the last years. Several contributions have been made that consider the optimal allocation of the defense resources. Most such contributions consider static situa- tions. Bier et al. (6) assume that a defender allocates defense to a collection of locations while an attacker chooses a location to attack. They show that the de- fender sometimes leaves a location undefended and sometimes prefers a higher vulnerability at a partic- ular location even if a lower risk could be achieved at zero cost. Dighe et al. (7) consider secrecy in de- fensive allocations as a strategy for achieving more cost-effective attacker deterrence. See also Bier, (8) Carayon et al., (9) Phimister et al. (10) The conflict literature (11−14) has mostly also con- sidered static situations in the form of static contests 1632 0272-4332/11/0100-1632$22.00/1 C  2011 Society for Risk Analysis