Maintaining Secure and Reliable Distributed Control Systems

We consider the role of security in the maintenance of an automated system, controlled by a network of sensors and simple computing devices. Such systems are widely used in transportation, utilities, healthcare, and manufacturing. Devices in the network are subject to traditional failures that can lead to a larger system failure if not repaired. However, the devices are also subject to security breaches that can also lead to catastrophic system failure. These security breaches could result from either cyber attacks (such as viruses, hackers, or terrorists) or physical tampering. We formulate a stochastic model of the system to examine the repair policies for both real and suspected failures. We develop a linear programming-based model for optimizing repair priorities. We show that, given the state of the system, the optimal repair policy follows a unique threshold indicator (either work on the real failures or the suspected ones). We examine the behavior of the optimal policy under different failure rates and threat levels. Finally, we examine the robustness of our model to violations in the underlying assumptions and find the model remains useful over a range of operating assumptions.

[1]  P. Whittle Restless Bandits: Activity Allocation in a Changing World , 1988 .

[2]  Adam Wierman,et al.  Multi-Server Queueing Systems with Multiple Priority Classes , 2005, Queueing Syst. Theory Appl..

[3]  Kevin D. Glazebrook,et al.  An index policy for a stochastic scheduling model with improving/deteriorating jobs , 2002 .

[4]  James E. Eckles,et al.  Optimum Maintenance with Incomplete Information , 1968, Oper. Res..

[5]  J. McCall Operating Characteristics of Opportunistic Replacement and Inspection Policies , 1963 .

[6]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[7]  Tom Burr,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 2001, Technometrics.

[8]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[9]  Kevin D. Glazebrook,et al.  Index policies for the maintenance of a collection of machines by a set of repairmen , 2005, Eur. J. Oper. Res..

[10]  Hongzhou Wang,et al.  A survey of maintenance policies of deteriorating systems , 2002, Eur. J. Oper. Res..

[11]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[12]  José Niño-Mora,et al.  Computing a Classic Index for Finite-Horizon Bandits , 2011, INFORMS J. Comput..

[13]  Z. A. Lomnicki,et al.  Mathematical Theory of Reliability , 1966 .

[14]  Dimitris Bertsimas,et al.  Restless Bandits, Linear Programming Relaxations, and a Primal-Dual Index Heuristic , 2000, Oper. Res..

[15]  M. Klein Inspection—Maintenance—Replacement Schedules Under Markovian Deterioration , 1962 .

[16]  Winfried K. Grassmann,et al.  Matrix Analytic Methods , 2000 .

[17]  Howard Kunreuther,et al.  Near‐Miss Incident Management in the Chemical Process Industry , 2003, Risk analysis : an official publication of the Society for Risk Analysis.

[18]  Richard H. Davis Waiting-Time Distribution of a Multi-Server, Priority Queuing System , 1966, Oper. Res..

[19]  Dietmar Wagner Analysis of a Finite Capacity Multiserver Model with Nonpreemptive Priorities and Nonrenewal Input , 1996 .

[20]  Kevin D. Glazebrook,et al.  Multi-Armed Bandit Allocation Indices: Gittins/Multi-Armed Bandit Allocation Indices , 2011 .

[21]  José Niòo-Mora A Faster Index Algorithm and a Computational Study for Bandits with Switching Costs , 2008 .

[22]  John K. Jackman,et al.  Interval Coverage in Multiclass Queues Using Batch Mean Estimates , 1996 .

[23]  van Geert-Jan Geert-Jan Houtum,et al.  Reducing costs of repairable inventory supply systems via dynamic scheduling , 2013 .

[24]  Matthieu van der Heijden,et al.  On the interaction between maintenance, spare part inventories and repair capacity for a k , 2006, Eur. J. Oper. Res..

[25]  Lani Haque,et al.  A survey of the machine interference problem , 2007, Eur. J. Oper. Res..

[26]  Lajos Takács,et al.  Priority queues , 2019, The Art of Multiprocessor Programming.

[27]  Dimitris Bertsimas,et al.  Conservation laws, extended polymatroids and multi-armed bandit problems: a unified approach to ind exable systems , 2011, IPCO.

[28]  Alan Cobham,et al.  Priority Assignment in Waiting Line Problems , 1954, Oper. Res..

[29]  Dimitris Bertsimas,et al.  Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; A Polyhedral Approach to Indexable Systems , 1996, Math. Oper. Res..

[30]  José Niño-Mora A Faster Index Algorithm and a Computational Study for Bandits with Switching Costs , 2008, INFORMS J. Comput..

[31]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[32]  Christian M. Ernst,et al.  Multi-armed Bandit Allocation Indices , 1989 .

[33]  José Niòo-Mora Computing a Classic Index for Finite-Horizon Bandits , 2011 .

[34]  Dietmar Wagner,et al.  A finite capacity multi-server multi-queueing priority model with non-renewal input , 1998, Ann. Oper. Res..

[35]  Matthieu van der Heijden,et al.  An Exact Solution for the State Probabilities of the Multi-Class, Multi-Server Queue with Preemptive Priorities , 2005, Queueing Syst. Theory Appl..