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PROJECTS and PUBLICATIONS 

Here I've presented some of the current or previous projects and list their presented or published results.

Safe Blues: A Method for Estimation and Control in the Fight Against COVID-19

Collaboration work with â€‹

The spread of viruses is a complicated function of several factors, including biological properties, preventative measures such as sanitation and masks, the environment, and the level of physical proximity. Governments can control this last factor through social-distancing directives. However, with a pandemic like COVID-19, data is always lagging and biased because it can take a week or more for a patient to be infected with SARS-CoV-2 and be recorded as positive. As a result, there is an urgent need for real-time information on the level of physical proximity while maintaining personal privacy. We run an experiment at the University of Auckland City Campus that helps to advance scientific understanding of how physical mobility and epidemic spread interact, as well as how to improve evolving technologies for assessing epidemic spread. The volunteers installed the Safe Blues app on their phones and the experiment entails sending virtual and safe "virus-like" tokens via Bluetooth between their phones, simulating the properties of real virus transmission. The resulting data predicts actual virus prevalence in the population. These predictions would be far more accurate than those obtained using current indicators such as positive test results and hospitalisations. See more details on Safe Blues website.

The Markov Chains tool – an evaluation

Collaboration work with Stephanie Budgett and Heti Afimeimounga

 

Probability education research has repeatedly documented intractable misconceptions prevalent in people’s reasoning processes. In response, the teaching of probability is experiencing a transformation. Rather than using a traditional mathematical approach, educators are now promoting an emphasis on modelling using technology. As part of a previous externally funded project, a prototype dynamic visual tool (the Markov tool) was developed and trialled, in conjunction with accompanying tasks, with six introductory probability students. Findings were promising, indicating that the Markov tool had the potential to deepen students’ understanding related to Markov chains. The aim of this project is to understand if and how the tool contributes to student understanding within the classroom setting, and to understand if and how students in more advanced probability courses retain and utilize aspects of the Markov tool as they progress in their studies.

 

The Role of Information in System Stability with Partially Observable Servers

Collaboration work with Yoni Nazarathy

 

We consider a simple discrete-time controlled queueing system, where the controller has a choice of which server to use at each time slot and server performance varies according to a Markov modulated random environment. We explore the role of information in the system stability region. In the extreme cases of information availability, that is when there is either full information or no information, stability regions and maximally stabilizing policies are trivial. But in the more realistic cases where only the environment state of the selected server is observed, only the service successes are observed or only queue length is observed, finding throughput maximizing control laws is a challenge. To handle these situations, we devise a Partially Observable Markov Decision Process (POMDP) formulation of the problem and illustrate the properties of its solution. We further model the system under given decision rules, using Quasi-Birth-and-Death (QBD) structure to find a matrix analytic expression for the stability bound. We use this formulation to illustrate how the stability region grows as the number of controller belief states increases.

 

Application of Semi-Markov Models to Predict the Expected Trajectory of Patients in Intensive Care Units 

Collaboration work with Benoit Liquet  and  Yoni Nazarathy

 

This project discusses applying semi-Markov models on intensive care units (ICU) in the hospitals. The main result of this project is to compare and differentiate two approaches for defining and estimating semi-Markov models that are applied in ICUs. The comparison of these approaches yields to a contribution of building a prediction model that predicts the risks and chances of the expected trajectories of patients through intensive care units. Moreover, we extend the model to the case of having a multi-absorption phase-type distribution as the sojourn time distribution or intensity distribution of the semi-Markov model.

 

The Challenge of Stabilizing Control for Queueing Systems with Unobservable Server States

Collaboration work with Yoni Nazarathy, Thomas Taimre, Julia Kuhn, Brendan Patch and Aapeli Vuorinen

 

In this project, we address the problem of stabilizing control for complex queueing systems where servers follow unobservable Markovian environments. The controller needs to assign servers to queues without full information about the servers' states. A control challenge is to devise a policy that matches servers to queues in a way that takes state estimates into account and updates these estimates in the best way possible. Maximally attainable stability regions are non-trivial. We present the model, the control problem, and some preliminary methods for analysis and control. We illustrate basic phenomena and then focus on the simplest possible model having a single queue, a fixed state server, and a two state server. For this case, we begin analysis of a partially observable Markov decision process (POMDP) hinting at some structural properties. We also show how to use a quasi-birth-death (QBD) process for analysis and control. The result of this project is sent to AUCC2015. Future work on this project includes considering more complex models and analysing the stability region based on the number of states of the unobserved Markov process.

Parameter Estimation for the Markovian Transition Counting Process as an Alternative to MMPP
Collaboration work with Yoni Nazarathy and Sophie Hautphenne
 

In modelling a variety of phenomena such as queueing processes, traffic intensity in telecommunication networks, requests for Web pages, the frequency of bank transactions, rainfall, and optical communications a special Markovian arrival process known as the Markov modulated Poisson process (MMPP) can be applied. The aim of this project is performing inference for a more computationally convenient alternative MAP which we call the Markovian Transition Counting Process (MTCP). This is a counting point process model (generalizing the Poisson Process) which counts the number of transitions in a finite state space irreducible continuous time Markov chain. To date, we have been able to find some parallels between our MTCP and the MMPP (Markov Modulated Poisson Process). We believe that our MTCP is better suited for parameter estimation since for this model, each observed event corresponds to exactly one transition in the unobserved Markov chain. 

Classification of complete Finsler manifolds and some applications of Finsler geometry
​Collaboration work with Behroz Bidabad
 

During my first PhD, I conducted research on a famous conjecture in Finsler geometry, namely the classification of complete Finsler manifolds and presented some important theories which lead to a classification for complete Finsler manifolds. Moreover, the following open problems had been noticed and some reasonable answers for them discovered:

1. Introducing a definition for the unit Finslerian sphere.

2. The strong rigidity of Finsler spaces of positive constant curvature.

3. A classification of Finsler spaces of constant curvature.

As a side result, using Finsler geometry, a geometrical dynamic model for traffic equilibrium problem had been constructed. This result may be used in the different equilibrium problems. During this period of time, I attended some workshops and seminars and presented or published some papers.

 

Journal Papers

​

  • Asamjarani A. (2023) A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium, Accepted for publication in Journal of Optimization Theory and Applications.
  • Asanjarani A. and Nazarathy, Y. (2022), Stationary Markovian Arrival Processes, Results and Open Problems, accepted for publication in the ANZIAM Journal.
  • Asanjarani A.,  Shausan A., Chew K., Graham T., Henderson S.G.,  Jansen H.M., Short K.R., Taylor P.G., Vuorinen A., Yadav Y., Ziedins I., and Nazarathy Y. (2022), PLOS Digital Health. https://doi.org/10.1371/journal.pdig.0000142
  • Asanjarani A. and Dehkordi H.R. (2022), Some Rigidity Results on Complete Finsler Manifolds, Journal of Finsler geometry and its applications, 3(2), 100-117.
  • Asanjarani, A., Liquet, B., and Nazarathy, Y. (2021), Estimation of Semi-Markov Multi-state Models: A Comparison of the Sojourn Times and Transition Intensities Approaches. The International Journal of Biostatistics 18.1: 243-262.
  • Asanjarani A., Nazarathy Y., and Taylor P. (2021), A Survey of Parameter and State Estimation in Queues. Queueing systems, 97(1), 39-80.
  • Asanjarani, A. and Nazarathy, Y. (2020), The role of information in system stability with partially observable servers. Methodology and Computing in Applied Probability, 1-20.
  • Asanjarani, A. and Bidabad, B. (2008), Classification of complete Finsler manifolds through a second order differential equation. Differential Geometry and its Applications, 26(4), 434-444.
  • Asanjarani A. and Bidabad B. (2008), Application of Finsler Geometry in the Nonlinear Complementarity Problem of Traffic Equilibrium (in Persian), Amirkabir Journal of science and technology, No. 67, 37-44.

 

Annotated Bibliography

 

  • Asanjarani A., Nazarathy Y. and Pollett P.K., Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography, 2017.​
 
Conference Papers
​
  • Asanjarani A. and Budgett S. (2022) An evaluation of the effectiveness of a visualisation tool in the teaching of Markov chains. Proceeding of the International Conference in Mathematics and Applications (ICMA-MU 2022), Bangkok, Thailand.
  • Budgett S., Asanjarani A., and Afimeimounga H. (2022) VISUALISING MARKOV PROCESSES, Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics. International Association for Statistical Education

  • Asanjarani, A. (2016), QBD modelling of a finite state controller for queueing systems with unobservable Markovian environments. QTNA '16 Proceedings of the 11th International Conference on Queueing Theory and Network Applications Wellington, 
    New Zealand.  

  • Asanjarani, A., & Nazarathy, Y. (2016), A queueing approximation of MMPP/PH/1. In T. Van Do, Y. Takahashi, W. Yue, V. H. Nguyen (Eds.) Queueing theory and network applications, 383, 41-51. New York: Springer

  • Nazarathy Y., Taimre T., Asanjarani A., Kuhn J., Patch B., and Vuorinen A. (2015), The Challenge of Stabilizing Control for Queueing Systems with Unobservable Server States, 5th Australian Conference in Control (AUCC), pp. 342-347, IEEE.

  • Asanjarani A. and Bidabad B. (2006), An example of complete Finsler manifolds of positive constant flag curvature, 4th Seminar on Topology and Geometry (In Persian), Urmia University, September 13-14, Urmia, Iran.

  • Asanjarani A. (2000), An application of Finsler geometry in Biological theorem of growth (in Persian), The First Symposium on the Role and Position of Mathematics in Humanities and Medical Sciences, Shahed University, Tehran, Iran.

​

Poster
 

This Poster is presented in 

  • 11th International Conference on Queueing Theory and its Application, Victoria University of Wellington, Wellington, New Zealand, 13-15 Dec. 2016.

  • ACEMS Retreat, UTS, Sydney, Australia, 31 October-4 Nov. 2016.

 
 

Selected Presentations

 

  • Markovian Transition Counting Process as an Alternative to the Markov Modulated Poisson Process, 7-10 April, Barossa, Australia, 2015.

  • Relations between Markovian Transition Counting Process and Markov Modulated Poisson Process, ANZIAM, 1-5 February, Gold Coast, Australia, 2015.

  • Relations between Markovian Transition Counting Process and Markov Modulated Poisson Process, ACEMS, Melbourne University, November 2014.

  • PhD. Confirmation Presentation, The University of Queensland, 29 August 2014.

  • Level process estimation and model selection, ACEMS working seminar, The University of Queensland, May 2014.

  • Level process estimation and model selection, Matrix- Analytic Methods (MAM) workshop, 27-31 January, Melbourne University, Australia, 2014.

  • A conformal equivalence of complete Finsler manifolds, Workshop on Finsler geometry, CIRM, November 11-14,  Marseille, France, 2005.

To discuss possible research collaborations >>
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