Melike Baykal-Gürsoy

Modeling traffic flow interrupted by incidents

A steady-state M/M/c queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where servers work at a reduced service rate. We analyze this system in steady-state and present a scheme to obtain the stationary number of vehicles on a link. For those links with large c values, the closed-form solution of M/M/[infinity] queues under batch service interruptions can be used as an approximation. We present simulation results that show the validity of the queueing models in the computation of average travel times.

Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates

Motivated by the need to study transportation systems in which incidents cause traffic to slow down, we consider an M/M/∞ queueing system subject to random interruptions of exponentially distributed durations. System breakdowns, where none of the servers work, as well as partial failures, where all servers work with lower efficiency, are investigated. In both cases, it is shown that the number of customers present in the system in equilibrium is the sum of two independent random variables. One of these is the number of customers present in an ordinary M/M/∞ queue without interruptions.

Allocation sequences of two processes sharing a resource

We study a Petri net model of a system composed of two processes sharing a resource. Conflicts may occur over the usage of the shared resource, thus making the system nondeterministic. Therefore, in the context of minimax algebra, it cannot be formulated as a linear system in order to compute its performance measures. However, if the sequence by which the resource is allocated to the two processes is known, we can transform the system into a decision-free net. For this system with an imposed constraint on the resource allocation frequencies, we show that the optimal allocation sequence is the most regular integer sequence satisfying that constraint. We also discuss the periodic behavior of this system under no constraints on the resource allocation frequencies. >

Variability Sensitive Markov Decision Processes

Considered are time-average Markov Decision Processes MDPs with finite state and action spaces. Two definitions of variability are introduced, namely, the expected time-average variability and time-average expected variability. The two criteria are in general different, although they can both be employed to penalize for variance in the stream of rewards. For communicating MDPs, we construct a randomized stationary policy that is e-optimal for both criteria; the policy is optimal and pure for a specific variability function. For general multichain MDPs, a state space decomposition leads to a similar result for the expected time-average variability. We also consider the problem of the decision maker choosing the initial state along with the policy.

A Game Theoretic Analysis of Secret and Reliable Communication With Active and Passive Adversarial Modes

Secret and reliable communication presents a challenge involving a double dilemma for a user and an adversary. One challenge for the adversary is to decide between jamming and eavesdropping. While jamming can be quite effective in preventing reliable communication of the user, it can also be quite harmful for the adversary since he/she can be detected. On the other hand, eavesdropping is quite safe for the adversary; however, it sometimes may not be so efficient compared to jamming, if the adversary cannot respond to the information gleaned from eavesdropping in a timely manner. The user can either transmit, thus becoming vulnerable to malicious activity, or be in a silent mode in turn delaying his/her transmission. However, by combining these modes properly the user can assist an intruder detection system in detecting the adversary, since transmission can provoke the adversary into a jamming attack, and a strategically allocated silent mode while the jammer continues jamming can increase the probability of detecting the adversary. In this paper, to get insight into this problem, two simple stochastic games are proposed. Explicit solutions are found that lead to the characterization of some interesting properties. In particular, it is shown that under certain conditions, incorporating in the transmission protocol a time slot dealing just with the detection of malicious threats can improve the secrecy and reliability of the communication without extra transmission delay.

Infrastructure security games

Infrastructure security against possible attacks involves making decisions under uncertainty. This paper presents game theoretic models of the interaction between an adversary and a first responder in order to study the problem of security within a transportation infrastructure. The risk measure used is based on the consequence of an attack in terms of the number of people affected or the occupancy level of a critical infrastructure, e.g. stations, trains, subway cars, escalators, bridges, etc. The objective of the adversary is to inflict the maximum damage to a transportation network by selecting a set of nodes to attack, while the first responder (emergency management center) allocates resources (emergency personnel or personnel-hours) to the sites of interest in an attempt to find the hidden adversary. This paper considers both static and dynamic, in which the first responder is mobile, games. The unique equilibrium strategy pair is given in closed form for the simple static game. For the dynamic game, the equilibrium for the first responder becomes the best patrol policy within the infrastructure. This model uses partially observable Markov decision processes (POMDPs) in which the payoff functions depend on an exogenous people flow, and thus, are time varying. A numerical example illustrating the algorithm is presented to evaluate an equilibrium strategy pair.

A price-setting newsvendor problem under mean-variance criteria

The single-product, single-period newsvendor problem with two decision variables, namely price and stock quantity, is considered. The performance measure, in addition to the expected revenue, includes the variance of the income scaled with a risk parameter. We present conditions for the concavity of this risk-sensitive performance measure and the uniqueness of the optimal solution for both risk-averse and risk-seeking cases under the additive demand model, and compare the results to others previously published. These conditions are introduced in terms of the lost sales rate elasticity. Furthermore, we provide numerical examples that aim to endorse the theoretical results herein explained.

Security Games With Unknown Adversarial Strategies

The security community has witnessed a significant increase in the number of different types of security threats. This situation calls for the design of new techniques that can be incorporated into security protocols to meet these challenges successfully. An important tool for developing new security protocols as well as estimating their effectiveness is game theory. This game theory framework usually involves two players or agents: 1) a protector and 2) an adversary, and two patterns of agent behavior are considered: 1) selfish behavior, where each of the agents wants to maximize his payoff; and 2) leader and follower behavior, where one agent (the leader) expects that the other agent (the follower) will respond to the leaders strategy. Such an approach assumes that the agents agree on which strategy to apply in advance. In this paper, this strong assumption is relaxed. Namely, the following question is considered: what happens if it is unknown a priori what pattern of behavior the adversary is going to use, or in other words, it is not known, what game he intends to play? Using a simple game-theoretic model, it is shown that the protector can lose if he does not take into account the possibility that the adversary can play a game other than the one the protector has in mind. Further considered is a repeated game in which the protector can learn about the presence of an adversary, and the behavior of belief probabilities is analyzed in this setting.

Evaluation of incident management strategies and technologies using an integrated traffic/incident management simulation

This paper describes Rutgers Incident Management System (RIMS) software that is developed to evaluate the benefits of various incident management strategies and technologies. This tool can generate incidents and test various response strategies and technologies. South Jersey highway network is used as a test network due to the available historical incident data. The evaluated incident management strategies include the deployment of Variable Message Signs (VMS) to divert traffic during incidents and the use of Freeway Service Patrols (FSPs) for detecting and verifying incidents efficiently. The simulation-based evaluations also include the effect of cellular phone users in the network on the incident detection and verification times. The results show that the studied incident management strategies have positive impacts on reducing incident durations while being cost effective. More specifically, the deployment of VMS for diverting traffic in case of an incident results in a benefit cost ratio of 9.2:1; an additional service unit in freeway patrol results in reduced incident detection and verification time with a corresponding benefit-cost ratio of 3.9:1.

Semi-markov decision processes: Nonstandard criteria

Considered are semi-Markov decision processes (SMDPs) with finite state and action spaces. We study two criteria: the expected average reward per unit time subject to a sample path constraint on the average cost per unit time and the expected time-average variability. Under a certain condition, for communicating SMDPs, we construct (randomized) stationary policies that are e-optimal for each criterion; the policy is optimal for the first criterion under the unichain assumption and the policy is optimal and pure for a specific variability function in the second criterion. For general multichain SMDPs, by using a state space decomposition approach, similar results are obtained.