Muthukrishnan Senthil Kumar

Mean-Field Dynamics of Inter-Switching Memes Competing Over Multiplex Social Networks

This letter characterizes the intertwined behavior of a susceptible-infected-susceptible epidemic model involving multiple mutually exclusive memes, each competing over distinct contact planes of an undirected multi-layer social network, with the possibility of inter-switching. Based on the mean-field theory, we contrast and derive closed-form analytical expressions for the steady-state thresholds that govern the transitions between extinction, co-existence, and absolute dominance of the inter-switchable memes. Moreover, a non-linear optimization formulation is presented to determine the optimal budget allocation for controlling the switching rates to a particular co-existing meme. Validated by simulations, the impact of switching on the tipping thresholds and their implications in reality are demonstrated using data extracted from online social networks.

Stability and Immunization Analysis of a Malware Spread Model Over Scale-Free Networks

The spreading dynamics and control of infectious agents primarily depend on the connectivity properties of underlying networks. Here, we investigate the stability of a susceptible- infected-susceptible epidemic model incorporated with multiple infection stages and propagation vectors to mimic malware behavior over scale-free communication networks. In particular, we derive the basic reproductive ratio (R0) and provide results for stability analysis at infection-free and infection-chronic equilibrium points. Based on R0, the effectiveness of four prevailing immunization strategies as countermeasures is studied and compared. The outperformance of proportional and targeted immunization is justified via numerical results.

System Dynamics of a Refined Epidemic Model for Infection Propagation Over Complex Networks

The ability to predict future epidemic threats, both in real and digital worlds, and to develop effective containment strategies heavily leans on the availability of reliable infection spreading models. The stochastic behavior of such processes makes them even more demanding to scrutinize over structured networks. This paper concerns the dynamics of a new susceptible-infected-susceptible (SIS) epidemic model incorporated with multistage infection (infection delay) and an infective medium (propagation vector) over complex networks. In particular, we investigate the critical epidemic thresholds and the infection spreading pattern using mean-field approximation (MFA) and results obtained through extensive numerical simulations. We further generalize the model for any arbitrary number of infective media to mimic existing scenarios in biological and social networks. Our analysis and simulation results reveal that the inclusion of multiple infective medium and multiple stages of infection significantly alleviates the epidemic threshold and, thus, accelerates the process of infection spreading in the population.

Performance analysis of an unreliable M/G/1 retrial queue with two-way communication

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an M/G/1 retrial queue is investigated where the single server, subject to active failures, primarily attends incoming calls and directs outgoing calls only when idle. The incoming calls arriving at the server follow a Poisson arrival process, while outgoing calls are made in an exponentially distributed time. On finding the server unavailable (either busy or temporarily broken down), incoming calls intrinsically join the virtual orbit from which they re-attempt for service at exponentially distributed time intervals. The system stability condition along with probability generating functions for the joint queue length distribution of the number of calls in the orbit and the state of the server are derived and evaluated numerically in the context of mean system size, server availability, failure frequency and orbit waiting time.

Delay Analysis of Orderly Reattempts in Retrial Queueing System with Phase Type Retrial Time

Retrial queueing systems play a major role in many communication systems. The delay analysis of such systems poses an interesting problem in communication engineering. This has motivated us to analyze the waiting time distribution of a multi-server retrial queueing system with phase type retrial time, impatience and Bernoulli abandonments. The impact of retrial time on waiting time and other system characteristics is analyzed by determining the waiting time distribution. Numerical examples are presented to reveal the impact of the parameters.

Overlay secondary spectrum sharing with independent re-attempts in cognitive radios

Opportunistic spectrum access (OSA) is a promising reform paradigm envisioned to address the issue of spectrum scarcity in cognitive radio networks (CRNs). While current models consider various aspects of the OSA scheme, the impact of retrial phenomenon in multi-channel CRNs has not yet been analyzed. In this work, we present a continuous-time Markov chain (CTMC) model in which the blocked/preempted secondary users (SUs) enter a finite retrial group (or orbit) and re-attempt independently for service in an exponentially distributed random manner. Taking into account the inherent retrial tendency of SUs, we numerically assess the performance of the proposed scheme in terms of dropping probability and throughput of SUs.

Transient analysis of a resource-limited recovery policy for epidemics: A retrial queueing approach

Knowledge on the dynamics of standard epidemic models and their variants over complex networks has been well-established primarily in the stationary regime, with relatively little light shed on their transient behavior. In this paper, we analyze the transient characteristics of the classical susceptible-infected (SI) process with a recovery policy modeled as a state-dependent retrial queueing system in which arriving infected nodes, upon finding all the limited number of recovery units busy, join a virtual buffer and try persistently for service in order to regain susceptibility. In particular, we formulate the stochastic SI epidemic model with added retrial phenomenon as a finite continuous-time Markov chain (CTMC) and derive the Laplace transforms of the underlying transient state probability distributions and corresponding moments for a closed population of size N driven by homogeneous and heterogeneous contacts. Our numerical results reveal the strong influence of infection heterogeneity and retrial frequency on the transient behavior of the model for various performance measures.

Fuzzy VEISV Epidemic Propagation Modeling for Network Worm Attack

An epidemic vulnerable—exposed—infectious—secured—vulnerable (VEISV) model for the fuzzy propagation of worms in computer network is formulated. In this paper, the comparison between classical basic reproduction number and fuzzy basic reproduction number is analyzed. Epidemic control strategies of worms in the computer network—low, medium, and high—are analyzed. Numerical illustration is provided to simulate and solve the set of equations.