Stochastic models, probability theory, Galton Watson Processes, Queueing theory, Statistical Inference
My current research activity is centred on Stochastic Processes, Combinatorial Analysis, Information Theory and Epidemiology. With respect to Stochastic processes, my Ph.D. thesis focused on the behavior of heterogenous packets in a network of switches under varying traffic systems. The work itself combined theories such as direct sum, direct product, combinatorial analysis and packet switching into a queueing system whose arrival is that of a batch Markov arrival process and with multiple service. The whole process engendered a linear system of equation whose origin is from the Transition Probability Matrix (TPM). The construction of this TPM came from the principle of the birth and death process and was consequently solved using the Gauss-Jordan approach to find the steady state probability vector, and upon these, the Mean Recurrence Time, Mean First Passage Times, and then with a mathematical program (MATLAB) find the Minimum Mean First Passage Times, Euclidean distance between vectors, measure of dominance and other such measures for sensitivity analysis.
Recently, I commenced a research in the direction of game theory which emanated from the super imposition of two orthogonal Latin squares in the area of experimental design to form a Graeco-Latin square which was observed to have patterns of the moves of game pieces on the chess board. A comparison of these two powerful and influential officers is necessary for identifying the expected payoff of the two different moves. These officers are the bishop and the knight at specific positions and circumstances on the chess board with to making a possible move. The solution to the problem would involve the Nash equilibrium, saddle point, dominance, arithmetic, calculus, algebraic and a graphical method. All of these methods are such that one attempts to answer what implication those values may mean to a player who wants to decide.
- STAT 250
- STAT 350
- MATH 203
- CDS 102