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### Javad Tavakoli

#### Associate Professor

###### Mathematics

**Other Titles:**Gradaute Program Advisor, Mathematics

**Office:**SCI 114

**Phone:**250.807.9535

**Email:**javad.tavakoli@ubc.ca

Graduate student supervisor

## Research Summary

Queueing systems; systems dynamics; and categorical algebra; applicable to computer communications and staffing facilities.

## Courses & Teaching

Abstract algebra; linear algebra; topology; probability theory; queueing theory; modelling.

## Degrees

PhD Dalhousie University

## Research Interests & Projects

**Queueing Theory & Random Walks in the Quarter Plane**

- 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.
- Application of M(t)/M/c/c queue in Health Science.
- The spectrum of tridiagonal matrices and Applications in Queueing Systems.
- The GI/M/c queue with state dependent arrival and service rates.
- Transient solutions of the M/E2/1 and E2/M/1 queues by using eigenvalues.
- 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.

**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.

## Selected Publications & Presentations

2015 | Grassmann, Winfried K.; Tavakoli, Javad Efficient Methods to find the Equilibrium Distribution of the number of Customers in GI/M/c Queues. INFOR 52, No. 4, (2015) |

2015 | Grassmann, Winfried K.; Tavakoli, Javad; Tirdad, Ali Optimal policies of M(t)/M/c/c queues with two different levels of servers (accepted, EJOR) |

2013 | Li, Hui; Tavakoli, Javad; Zhao, Yiqiang Q. Analysis of exact tail asymptotics for singular random walks in the quarter plane. Queueing Syst. 74 (2013), no. 2-3, 151-179. |

2010 | Grassmann, Winfried K.; Tavakoli, Javad Comparing some algorithms for solving QBD processes exhibiting special structures. INFOR Inf. Syst. Oper. Res. 48 (2010), no. 3, 133-141. |

2009 | Grassmann, Winfried K.; Tavakoli, Javad Spectrum of certain tridiagonal matrices when their dimension goes to infinity. Linear Algebra Appl. 431 (2009), no. 8, 1208-1217. |

2009 | Grassmann, Winfried K.; Tavakoli, Javad Transient solutions for multi-server queues with finite buffers. Queueing Syst. 62 (2009), no. 1-2, 35-49. |

2008 | Grassmann, Winfried K.; Tavakoli, Javad Stochastic and substochastic solutions for infinite-state Markov chains with applications to matrix-analytic methods. Adv. in Appl. Probab. 40 (2008), no. 4, 1157-1173. |

2008 | Grassmann, Winfried K.; Tavakoli, Javad The continuous spectrum for the M/M/c queue. Linear Multilinear Algebra 56 (2008), no. 3, 319-331. |

2007 | Grassmann, Winfried K.; Tavakoli, Javad A Bayesian approach to find random-time probabilities from embedded Markov chain probabilities. Probab. Engrg. Inform. Sci. 21 (2007), no. 4, 551-556. |

2005 | Grassmann, Winfried K.; Tavakoli, Javad Two-station queueing networks with moving servers, blocking, and customer loss. Electron. J. Linear Algebra 13 (2005), 72-89. |

2002 | Grassmann, Winfried K.; Tavakoli, Javad A tandem queue with a movable server: an eigenvalue approach. SIAM J. Matrix Anal. Appl. 24 (2002), no. 2, 465-474. |

2002 | Khoshkam, M. and Tavakoli, J. “Categorical Constructions in C*-Algebras Theory”. Journal of the Australian Mathematical Society. 73.1: 97 113, 2002. |

2001 | Madanshekaf, A. and Tavakoli, J. “Tiny Objects in the Category of M-sets”. Italian Journal of Pure and Applied Mathematics. 10: 153 162, 2001. |

2000 | Madanshekaf, A. and Tavakoli, J. “On the Category of M-sets”. Far East Journal of Mathematical Sciences. 2.2: 251 260, 2000. |

1996 | Tavakoli, Javad Locally free vector spaces in a topos. Comm. Algebra 24 (1996), no. 4, 1199-1205. |