Double "almost done" seminar

Speaker: Darryen Sands (MCSC MSc)
Title: Clustering in Non-Reversible Markov Chains and the Influence of Complex Eigenvalues
Abstract: Clustering in directed networks is a difficult task due to the inherent structure of the network. We set out to create an algorithm that can detect clusters within directed networks using the eigenvectors of the transition matrix. We are also working on quantifying the strength of the clustering based on bounds on quantities such as the mean-first passage times and spectral radii of the sub-partitions of the transition matrix.

 
Speaker: Abraham Amini (MCSC MSc)
Title: Staffing Service Queueing Systems with Cyclic Demand and Unreliable Servers
Abstract: Queueing theory, a significant aspect of Operations Research, provides mathematical frameworks for modelling and analyzing systems where customers await and receive service. Our focus is on the SIPP method, often used for staffing systems like call centers and emergency departments, which face cyclical customer arrival rates, fluctuating through lengths such as a day.

We explore the effectiveness of the Stationary Independent Period by Period (SIPP) method in staffing service-based queueing systems, particularly under conditions of server absenteeism, which reflects real-life scenarios in which staff members may not be available for their scheduled shifts.
Using the M(t)/M/c(t) queueing system model, we simulate scenarios where server absenteeism is stochastic. Our model considers non-stationary customer arrival rates and multiple parallel, unreliable, servers. By integrating server absenteeism into the SIPP method, this research provides insights into the method’s robustness and adaptability in real-world scenarios.
To address server absenteeism, we propose adjustments to the SIPP method to better accommodate potential server absence, thus enhancing SIPP’s adaptability to real-world unpredictability. We also systematically evaluate under what conditions each proposed adjustment is most effective, offering an understanding of managing server absenteeism within time-varying arrival systems.