Research Interests

My current research interests are in Applied Probability and Queuing Theory.

  • Queueing Theory & Random Walks in the Quarter Plane

    1. Application of Boundary Value Problem (BVP) in Queueing Models. The goal is to apply BVP techniques to determine the stationary probabilities for multi-dimensional random walks and their applications in Queueing Systems.
    2. Application of M(t)/M/c/c queue in Health Science.
    3. The spectrum of tridiagonal matrices and Applications in Queueing Systems.
    4. The GI/M/c queue with state dependent arrival and service rates.
    5. Transient solutions of the M/E2/1 and E2/M/1 queues by using eigenvalues.
    6. Waiting time distribution for the GI/G/1 Queue by using eigenvalues.

  • Topology and Data
    Topology is exactly that branch of mathematics which deals with quantitative geometry information. This includes the study of connected components of a space.
  • Optimization Problem on Simultaneous Group Equations & Applications in Sciences.

Pure Mathematics

  • Topology and Small Maps.
  • Topology on a Poset and its Application on Natural Numbers Object in a Topos.
  • An Equivalency between Category of Sheaves and Category of Fuzzy Sets.